Superconducting materials and their applications : an interdisciplinary approach 9780750322560, 9780750322546, 9780750322577, 9780750322553, 0750322551, 075032256X

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Superconducting Materials and Their Applications An interdisciplinary approach

Superconducting Materials and Their Applications An interdisciplinary approach Jatinder Vir Yakhmi Formerly at Bhabha Atomic Research Centre (BARC), Trombay, Mumbai – 400085, India and Former Sr. Prof., Homi Bhabha National Institute (Deemed to be University of DAE), Anushaktinagar, Mumbai – 400094, India

IOP Publishing, Bristol, UK

ª IOP Publishing Ltd 2021 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the publisher, or as expressly permitted by law or under terms agreed with the appropriate rights organization. Multiple copying is permitted in accordance with the terms of licences issued by the Copyright Licensing Agency, the Copyright Clearance Centre and other reproduction rights organizations. Permission to make use of IOP Publishing content other than as set out above may be sought at [email protected]. Jatinder Vir Yakhmi has asserted his right to be identified as the author of this work in accordance with sections 77 and 78 of the Copyright, Designs and Patents Act 1988. ISBN ISBN ISBN ISBN

978-0-7503-2256-0 978-0-7503-2254-6 978-0-7503-2257-7 978-0-7503-2255-3

(ebook) (print) (myPrint) (mobi)

DOI 10.1088/978-0-7503-2256-0 Version: 20210201 IOP ebooks British Library Cataloguing-in-Publication Data: A catalogue record for this book is available from the British Library. Published by IOP Publishing, wholly owned by The Institute of Physics, London IOP Publishing, Temple Circus, Temple Way, Bristol, BS1 6HG, UK US Office: IOP Publishing, Inc., 190 North Independence Mall West, Suite 601, Philadelphia, PA 19106, USA Cover image: False-colour scanning electron micrograph of a section through a superconducting cable. The six triangular areas seen here contain bundles of fine superconducting wire (in this case a niobium/titanium alloy). The bundles are surrounded by an electrically-insulating layer, the whole being held within a spoke-like pattern of copper. Cables such as this are used to make extremely powerful electromagnets. Superconductors offer no electrical resistance, so adding power to the magnet simply magnifies its strength. However, the cable must be kept at about 10 Kelvin (−263 Celsius) for this to occur. Magnification ×33 at 6 × 7 cm size. Credit: KAGE MIKROFOTOGRAFIE GBR / SCIENCE PHOTO LIBRARY.

Dedicated to my mother, Mrs Shimla Vati (1925–1997), fondly called Biji The odds were heavily loaded against Biji for most of her wedded life. She lost all my four siblings to infant mortality. Became a widow at age 36 after my father succumbed to TB in 1961. She worked hard for the safety of my health, imposing strict social distancing at our home during the last year of my father’s life. She braved deprivation but rarely succumbed to hopelessness, while making sure that I completed my school education. She completed the unfinished part of her own school education only after sending me to college. Biji spent the rest of her life as a rural social worker employed by the state government. As a social crusader, she saved dozens of lives by: exhorting rural womenfolk to install government subsidized environment-friendly smokeless hearths in their kitchens; ensuring vaccinations of newborns in the villages under her charge; and encouraging farmers to install steel silos to store their grain, so they could avoid gunny bags which were prone to pilferage by rats. I dedicate this book to Biji’s grit and determination.

Contents Preface

xii

Author biography

xv

1

Introduction to superconductivity, superconducting materials and their usefulness

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9

Brief introduction to the phenomenon of superconductivity Does the resistance in the superconducting state really become zero? Flow of charge carriers in a metal, an insulator and a superconductor Meissner effect Superconducting elements, alloys, intermetallics and compounds Critical field, Hc Type I and type II superconductors Abrikosov vortices, flux line lattice and the mixed state BCS mechanism: flux quantization and energy gap 1.9.1 The isotope effect 1.9.2 The band gap and heat capacity 1.10 Wires and cables from low Tc superconductors NbTi and Nb3Sn 1.10.1 A3B superconductors 1.10.2 The triumvirate: Tc, Bc2 and Jc 1.10.3 The irreversibility line 1.11 Techniques employed to evaluate the basic physical characteristics of superconducting materials References

1-1 1-1 1-5 1-7 1-7 1-9 1-10 1-11 1-12 1-15 1-17 1-18 1-19 1-19 1-20 1-21 1-22 1-23

2

High-Tc superconducting cuprates and magnesium boride

2.1 2.2 2.3 2.4 2.5 2.6

Introduction 2-1 Oxide superconductors, before cuprates 2-3 Cuprate superconductors: La–Sr–Cu–O and Y–Ba–Cu–O 2-4 Bi-, Tl- and Hg-based cuprate superconductors 2-6 Spin-fluctuation as the pairing mechanism for high-Tc superconductors 2-8 2-9 MgB2 2-9 2.6.1 Superconductivity and crystal structure of MgB2 2-9 2.6.2 Two-gap nature of superconductivity of MgB2 References 2-10

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3

Materials contributing to physics of superconductivity, or holding potential for applications

3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11

Chevrel phase superconductors Rare earth rhodium boride superconductors, MRh4B4 Rare earth nickel borocarbides Heavy fermion superconductors Fe–pnictide superconductors Fe–selenide superconductors Hydride superconductors Organic superconductors Fulleride superconductors Superconducting materials—the continuing search Types of superconductivity References

4

Applications of bulk superconducting materials, and in high-field magnets

4-1

4.1 4.2

Introduction Superconductor wires and cables for winding of magnets 4.2.1 Protection of superconducting magnets from flux jumping and quenching 4.2.2 Factors which distort the magnetic field 4.2.3 The Lorentz force 4.2.4 Advantage of superfluidity of liquid helium for efficient cooling of the superconducting magnets High field superconducting magnets for particle accelerators and colliders Superconducting magnets for nuclear fusion Superconducting RF cavities 4.5.1 Quenching of a cavity and its thermal breakdown Superconducting magnets for MRI 4.6.1 What is MRI, and how does it work? 4.6.2 MRI aiding medical diagnosis and therapy 4.6.3 7 T MRI for brain scans and for stroke patients 4.6.4 Relevance of MRI information, and a caution 4.6.5 Dispelling nuclear fears from MRI Superconducting magnets for maglev trains

4-1 4-2 4-4

4.3 4.4 4.5 4.6

4.7

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3-1 3-1 3-3 3-3 3-5 3-5 3-6 3-8 3-8 3-11 3-12 3-13 3-14

4-5 4-6 4-6 4-7 4-10 4-14 4-16 4-17 4-17 4-17 4-18 4-20 4-21 4-21

Superconducting Materials and Their Applications

4.8 4.9

4.10

4.11 4.12 4.13

4.14

4.15 4.16 4.17 4.18

Superconductors in the power sector 4.8.1 Transmission cables Use of HTSCs for power applications 4.9.1 HTSCs for transmission of electrical power 4.9.2 Superconducting magnetic energy storage (SMES) 4.9.3 HTS generators and motors for ship propulsion HTS power cable projects 4.10.1 Development of HTS power equipment at ISTEC (Japan) 4.10.2 HTS Cable Project at Columbus, OH (USA) 4.10.3 Other efforts for cables and HTS devices Superconducting switches and power transformers State-of-the-art superconducting fault current limiters Miscellaneous applications 4.13.1 Miniature antennas 4.13.2 Interconnects 4.13.3 Bolometers 4.13.4 Magnetic shielding 4.13.5 Passive microwave devices for signal processing and transmission 4.13.6 SC motors and bearings High-field magnets using HTSCs 4.14.1 HTSC magnets for MRI 4.14.2 Possibility of HTSC magnets for separation in industry 4.14.3 Superconducting rotating machines and wind turbines Use of HTS in superconducting cavities for accelerators 4.15.1 RF cavities from MgB2 Applications of MgB2 wires Other applications of superconductors Cryogenics 4.18.1 Handling of cryogens. Safety risks—the danger of suffocation 4.18.2 Cryogenics for frontline research References

4-23 4-23 4-24 4-25 4-28 4-28 4-29 4-29 4-30 4-30 4-30 4-31 4-33 4-33 4-33 4-33 4-33 4-33 4-34 4-34 4-34 4-35 4-35 4-37 4-37 4-38 4-39 4-39 4-39 4-40 4-41

5

Applications in Josephson junctions, SQUIDs, and MEG. Other low field applications

5-1

5.1

From quantum concepts to superconducting technology: Josephson junctions and SQUIDs

5-1

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5.2 5.3 5.4 5.5 5.6

5.7

6

5-2 5-3 5-4 5-6 5-7

Josephson junction electronics, computers and detectors Measurement of ultra-low magnetic fields by SQUIDs Types of SQUIDs Applications of SQUID magnetometers and gradiometers SQUID sensors for magnetoencephalography and biomagnetic applications 5.6.1 General 5.6.2 Magnetocardiography (MCG) 5.6.3 Specific biomagnetic applications of SQUID sensors in human health 5.6.4 Study of brain processes non-invasively by imaging of brain functions 5.6.5 MEG in comparison to EEG, fMRI, and fNIRS 5.6.6 Origin of electromagnetic signals and role of MEG for neurophysiology 5.6.7 Brief details about MEG instrumentation and operation High-Tc SQUIDs References

5-15 5-16 5-17

Applications in the areas of diagnostics and neuroscience

6-1

6.1

Brain imaging and cognitive neuroscience 6.1.1 rt-fMRI-NF 6.1.2 Blood oxygenation level dependent (BOLD) MRI 6.2 Neuro-diseases 6.2.1 Tourette syndrome 6.2.2 rt-fMRI-NF for ADHD 6.3 The salience network (SN) 6.4 SN and the mesolimbic dopamine system 6.5 Magnetic resonance perfusion 6.6 BIO-interface 6.6.1 Studies on dog brains and function 6.6.2 Plant biomechanics 6.7 Signal-space projection/separation for MEG data 6.8 Evoked and induced responses 6.9 Consequences of deprivation of sleep 6.10 Non-destructive imaging of soft tissue using synchrotron radiation 6.11 Carbon-ion radiotherapy References

x

5-7 5-9 5-11 5-11 5-11 5-13

6-2 6-2 6-3 6-4 6-4 6-4 6-5 6-5 6-6 6-6 6-6 6-6 6-7 6-7 6-8 6-8 6-8 6-9

Superconducting Materials and Their Applications

7

Concluding remarks. Slow progress in the commercialization of potential HTS devices. New hopes. Emerging new applications

7-1

7.1 7.2

Why is superconductivity so exciting? Factors hampering the commercial applications of high-Tc superconductors Limitations of hydride and organic superconductors to be overcome before their applications New emerging applications, including those of HTSCs References

7-1 7-2

7.3 7.4

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7-4 7-5 7-7

Preface This book aims at bringing the basic knowledge related to the applications of superconducting materials to students and researchers belonging to the subject areas of chemistry, biology, materials science, bio-medical technology, and even medicine. There exist many books, indeed, on different aspects of superconductivity, such as the phenomenon of superconductivity and its theoretical understanding, its historical development, the different categories of superconductors, or on devices such as superconducting magnets, SQUIDs (superconducting quantum interference devices), and their applications. However, nearly all of them are written with a physics reader in mind; expecting a good knowledge of physics as a pre-requisite. To cite an example, the emerging field of biomagnetism encompasses the detection of extremely weak magnetic fields generated by biological systems, e.g. by ion currents in nerve cells and heart tissue. Applications of biomagnetism are relevant for non-invasive medical diagnostics, including the study of heart and brain function. SQUIDs, the most sensitive detectors of magnetic fields which can detect signals as low as 5 aT (5 × 10−18 Tesla), can be used for non-invasive detection of the magnetic signals arising from the human heart (i.e. magnetocardiography), or the human brain (magnetoencephalography), providing new avenues to exploit these nerve signals for diagnostics. However, in most countries there is often a disconnect between the medical doctors and the knowledge-base on applications of superconductivity, purely because the cryogenics, the superconductivity, Josephson junctions, the SQUID magnetometry/gradiometry, or even the underlying principles of MRI (magnetic resonance imaging) are thought to be in the realm of specialized physics, leading to an aversion of the medical profession to them. Biologists or clinicians have no love for derivations, theory or complexities. Non-physicists need a simple readable narrative on the multidisciplinary approach to the applications of superconducting materials, which is what I have planned to provide in this book. But I knew the task at my hands is not simple. Therefore, before submitting a proposal to IOP Publishing, I circulated the plan of my book and the topics to be covered in each of its chapters to a large number of senior Professors/scientists, across the world to seek their opinion and suggestions on the project of this book. Thankfully, 31 of them responded with useful comments/ suggestions, most of them encouraging me to go ahead with my book. Among them, Professor M Brian Maple (Chair, Department of Physics, and Berndt T Matthias Endowed Chair, University of California, San Diego, USA), a well-known expert on superconductivity, wrote to me: ‘In looking over the outline of the book on superconductivity you are considering to write, it seems to me that you have chosen a rather interesting set of topics that differ from those I have seen in other books on this subject. Thus, I think your book will appeal to a more general audience and stand out from other books on superconductivity. I think you should go ahead with this interesting project, which should appeal to a fairly wide audience’. During my long career spanning 45 years at BARC, I have always tried to champion the cause of multidisciplinary interface among researchers. Hence, I was

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glad that after a review of my proposal of the book in October 2018, IOP approved the title of this book to be Superconducting Materials and Their Applications: An Interdisciplinary Approach, and gave me the go-ahead signal to write a book not exceeding about 130 pages. IOP asked me to focus on the interdisciplinary and practical nature of the book to make it more useful for the ‘non-physicist’ readership including materials scientists, engineers, chemists, and biotechnologists, etc, who typically look for practical information, written in a simple manner. The book has in all seven chapters. Chapter 1 provides a general introduction and historical perspective on the phenomenon of superconductivity, and to the so-called low-Tc materials. Chapter 2 explains briefly the high-Tc cuprates, and MgB2, and the status of applications using them at relatively higher temperatures. Chapter 3 attempts to describe all other categories of superconductors, especially the hydrides and organic superconductors which have potential for exhibiting superconductivity at room temperature. Chapter 4 deals with the existing and emerging applications based on RF cavities and high-field magnets, etc; and chapter 5 is on low-field applications such as those based on highly sensitive SQUID detectors and MEG/ MCG, etc. Chapter 6 deals exclusively with the applications of superconductors in bio-magnetism, particularly some recent ones towards diagnostics and neuroscience. The successful use of high- Tc superconductors is also highlighted, wherever it has been accomplished. Finally, chapter 7 discusses two seemingly opposing things: tardy record of commercialization of potential high temperature superconductor devices, versus the continued excitement in the field of superconductivity and recent new emerging applications, which sustain a continued interest in the theme of this book. It is a pleasure for me to acknowledge help received by me from a number of senior colleagues, experts in the field of superconductivity in their own right, during the preparation of this book. Dr S K Gupta, my senior colleague at BARC, has read the drafts of all chapters in detail, and offered his valuable suggestions. Dr V P S Awana (NPL, New Delhi) also read the drafts of all chapters and made useful comments. Professor G Baskaran, the renowned theoretician from Institute of Mathematical Sciences, Chennai, read through the finalized versions of the drafts of all the chapters and offered helpful remarks. A large number of figures were drawn, after discussions with me, by a senior scientist from BARC, Dr V K Aswal. Some figures were made by Dr S K Gupta and Dr V P S Awana, too. My special thanks to all of them for doing so. I am thankful to my life-time institution, Bhabha Atomic Research Centre at Mumbai to have provided me opportunities galore to learn and practise the science of superconductivity. Ms Caroline Mitchell, the Commissioning Editor of ebooks at IOP Publishing, and her team of ebooks Editorial Assistants, first Mr Daniel Heatley, and later Mr Robert Trevelyan, have been providing me all guidance and help during the preparation of this book. My gratitude to them. Finally, I undertook to write this book from home, after I had retired from all official positions. That means I ate into a lot of time, which rightfully belonged to my wife, Mrs Amar Upasana Yakhmi, and the family of my son, Ashish Yakhmi,

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Superconducting Materials and Their Applications

with whom we live. But that also meant my young grandchildren Om and Jia providing me the much-needed relaxation off and on. My daughter’s 14 years daughter, Sanaa Singh, nudged me often, asking me when would I finish the book, and why I am taking so long. Jatinder Vir Yakhmi

xiv

Author biography Jatinder Vir Yakhmi Professor (Dr) Jatinder Vir Yakhmi (b. 1946), has spent a research career of 45 years at Bhabha Atomic Research Centre, at Mumbai. Before his retirement in 2010, he was Associate Director of Physics Group, BARC, and Head of Technical Physics & Prototype Engineering Division. During 2012–2016, he served as DAE Raja Ramanna Fellow at the Homi Bhabha National Institute— a Deemed University of DAE at Mumbai. Simultaneously, during 2012–2015, he worked as Chairman, Atomic Energy Education Society, Mumbai, which runs 31 Schools and Junior Colleges across India. A 1975 PhD in condensed matter physics from Mumbai University, his focus of research has been on the topics related to magnetism, superconductivity and soft matter. He is credited with the establishment of a program on the use of molecular materials for fabrication of molecular magnets, sensors, bio-sensors, and organic electronic devices at BARC. Dr Yakhmi has a U.S. and European patent on artificial heart, and has contributed over 450 publications in international journals, including 65 review articles in journals/books. Out of these, 140 have been on different aspects of superconductors. He has edited/written eight books, including Thallium-Based High Temperature Superconductors co-edited by A M Hermann and J V Yakhmi, published by Marcel Dekker, Inc., N.Y. (USA), in 1994. He has a Google Scholar h-Index of 50, and his name appears in the world’s top two per cent most-cited scientists, as per a list compiled in 2020 by Stanford University. Dr Yakhmi has delivered 150 invited seminars in reputed international labs, and about 50 at international conferences. He is a Fellow of National Academy of Sciences (India), and an elected Member of Asia Pacific Academy of Materials. He is a winner of the triennial MRS-ICSC Superconductivity and Materials Science Award (Senior) by MRSI, Distinguished Alumni Award by Kurukshetra University, and the IIS Gold Medal by University of Tokyo.

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Superconducting Materials and Their Applications An interdisciplinary approach Jatinder Vir Yakhmi

Chapter 1 Introduction to superconductivity, superconducting materials and their usefulness

1.1 Brief introduction to the phenomenon of superconductivity Ohm’s law governs the flow of electrical current, I, through a conductor in units of amperes. It states that the current I, passing through a conductor between any two points in it is directly proportional to the voltage applied across these two points, V in units of volts, i.e.

I∝V the constant of proportionality in this relation is 1/R, where R is the electrical resistance of the conductor between the above two points, in units of Ohms, which when used gives the Ohm’s law,

I = V /R The Ohm’s law used in materials science and electromagnetics is given as

J = σE where J denotes the current density at a point in a conductor, E the electric field at that point and σ (called sigma) denotes the conductivity, a parameter which is characteristic of a given conducting material, and is related to σ = neμe where n is the density of electrons (charge carriers), e is the fundamental unit of electric charge, and μe is the mobility of the charge carriers, the electrons in this case. Electrical resistivity, ρ, is the inverse of electrical conductivity, and is defined as electrical resistance of a conductor of unit cross-sectional area and unit length. Electrical resistivity is a characteristic property of each material. SI units of electrical conductivity, σ, are Siemens per meter, and of ρ are Ohm meter.

doi:10.1088/978-0-7503-2256-0ch1

1-1

ª IOP Publishing Ltd 2021

Superconducting Materials and Their Applications

Generally, atoms enter a crystal lattice as ions, with one or more electrons removed, resulting in positive ions forming a rigid lattice with the electrons stripped from ions generally free to move around, which determine the electrical conductivity of the material. Depending on how freely the electrons move, i.e. the mobility of charge carriers in that material, the conductivity of materials varies from high for metals, to medium for semiconductors and low for insulators. At absolute zero temperature (0 K), one presumes that ions in a crystal lattice are static, though there is still what is known as a zero point motion, as per quantum mechanics. At finite temperatures (say, at room temperature of ~300 K), the thermal energy makes them (i.e. the ions or atoms) vibrate around their equilibrium positions. Since these ions are part of a typical crystal structure, their vibrations are collective, with a large number of them being involved in any typical mode of vibration, which is characteristic of a given material. The vibration energy of any mode is quantized in multiples of hω (where ω is vibration frequency and h is Planck’s constant), the quantum of this energy, which is called a phonon. Phonons can be thought of as quanta of sound waves, just as photons are quanta of light waves. At finite temperatures (>0 K), thermal vibrations of the ionic lattice, i.e. the phonons, disturb the periodicity of a given lattice and cause resistance in the path of free conduction electrons which would have, otherwise, travelled without getting scattered at all in a perfectly periodic structure, of a metal, for instance. Further, even at temperature T = 0 K, when thermal vibration of the ionic lattice dies down, conduction electrons can still be scattered by defects, because all real crystals can have a variety of defects, some of which are, in fact, introduced deliberately in order to alter the useful properties of a given material in a controlled manner, towards different applications. The defects can be point defects, which can be a missing atom (vacancy) in a crystal lattice, or an additional atoms placed irregularly (called interstitial), or even impurity atoms inserted deliberately in the crystal. Among other defects which can exist in a crystal lattice are: (a) dislocations, which are linear in nature, arising from irregular placement of a group of atoms; and, (b) grain boundaries, which arise at an interface of two regions of a lattice when both of the regions are ordered individually as crystals but placed irregularly w.r.t. to each other, at the interface. The above discussion points to the production of electrical resistance due to scattering of conduction electrons on two counts, by the lattice phonons, and by the defects in the lattice. The scattering by phonons gives rise to a component of the electrical resistivity of a metal which is proportional to its temperature, ρ ∝ T, at ambient and higher temperatures. This should imply that the electrical resistivity should, in principle, fall to zero at a temperature of absolute zero (T = 0 K), but that does not happen due to the scattering of conduction electrons by the defects in the lattice, as mentioned above, giving rise to what is called the residual resistivity, a component of resistivity which remains largely unchanged with rise in temperature. This component, while resisting the flow of electrical current causes dissipation of some energy as heat.

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Superconducting Materials and Their Applications

The effective resistivity of a pure conducting crystalline material, say a metal, is described by Matthiessen’s rule as: ρ = ρT + ρR where ρT describes the contribution from phonon scattering, essentially due to thermal effects, and, ρR arising from scattering by defects in the lattice. ρR arises from two components, ρI, a contribution arising from scattering of conduction electrons by the impurities present in it, even if on a very minor scale, and, ρD arising from scattering by defects in the lattice, ρR (=ρI + ρD). Therefore, one can write the total resistivity to be arising from three components, viz. ρ = ρT + ρI + ρD Above about 100 K, the electrical resistivity of a pure metal, such as copper, which invariably has some defects, shows a linear relationship with temperature, ρ ∝ T, which continues almost up to its melting temperature, 1358 K, and is similar to the behavior of an ideal defect-free pure metal (figure 1.1). Before the availability of liquid helium to cool a metal sample to temperatures below 10 K, it was understood from the electrical resistivity measurements that at temperatures below about 100 K the resistivity of a pure metal falls steeply on cooling and varies as ρ ∝ T 5 [1]. In fact, on a log–log scale (not shown in figure 1.1), the ρ versus T plot for a pure metal like copper, can be fitted to two separate behaviors, viz. ρ ∝ T above ~ 100 K, and ρ ∝ T 5 for the low-temperature region 0 and B > H. Examples of such paramagnetic materials are aluminum, platinum and sodium etc, having typical susceptibility values of ~10−6 CGS units. Then there are ferromagnetic materials (such as iron, cobalt and nickel) which get strongly magnetized in the direction of the applied field, with B » H and have typical values of χ > 104 CGS units. Superconductors are unique in their magnetic behavior in that the susceptibility is χ = −1/4π and Β = 0.

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Superconducting Materials and Their Applications

Figure 1.5. A permanent magnet disc levitating over a high-Tc superconductor at 77 K. Figure courtesy of Dr V K Aswal.

Li

Be 0.026 Na Mg K

Ca

Rb

Sr

Cs

Ba

B

Sc

Ti 0.39 Y Zr 0.54 La Hf 6.0 0.12

V Cr Mn Fe Co 5.38 Nb Mo Tc Ru Rh 9.5 0.92 7.7 0.51 0.03 Ta W Re Os Ir 4.48 0.01 1.40 0.65 0.14

Ni Pd Pt

C

N

O

F

Ne

Al Si P 1.14 Cu Zn Ga Ge As 0.87 1.09 Ag Cd In Sn Sb 0.56 3.40 3.72 Au Hg Tl Pb Bi 4.15 2.39 7.19

S

Cl

Ar

Se

Br

Kr

Te

I

Xe

Po

At

Rn

Figure 1.6. Elements of periodic table which can superconduct, shaded in yellow color. Values of Tc, the transition temperatures for each such element are provided in degrees kelvin. Figure courtesy of Dr S K Gupta.

1.5 Superconducting elements, alloys, intermetallics and compounds As superconductivity was discovered in many metallic elements of the periodic table (figure 1.6), some thumb-rules emerged to rationalize their behavior, viz. 1. Metals with the highest conductivities (Cu, Pd, Ag, Pt and Au) are not superconductors. 2. The magnetic 3d elements, Cr, Mn, Fe and Co are not superconducting. 3. Transition temperatures (Tc) and critical fields of metallic elements are generally low. Subsequently, however it was discovered that several other elements of the periodic table can become superconducting under application of pressure. Among them were (with the value of Tc, transition temperature, given in brackets): iron (2 K under 20 GPa), Ca (15 K), Sr (4 K), Ba (5.1 K), Y (2.7 K), B (11 K), P (18 K), S (17 K), Ge (5.4 K), Si (8.5 K), Se (5.6 K), As (2.7 K), Sb (5.6 K), Te (7.4 K), Bi (8.7 K). Most lanthanides, except La, are magnetic/non-superconducting. A few other elements become superconducting at much lower temperatures ( ξ, leading to vortex–vortex repulsion. An attractive vortex–vortex interaction results in the formation of macroscopic normal domains in the intermediate state [18], while vortex–vortex repulsion leads to the appearance of the Abrikosov lattice [19]. Density of vortex lines in a plane is given by their number/unit area, is: n = B/ϕo. Magnetic flux enters a type II superconducting sample in its mixed state as an Abrikosov lattice of vortex lines (figure 1.12(a)), cores of which are separated by superconducting regions. More specifically, Meissner effect in the mixed state of type II superconductors is not complete, and magnetic flux lines enter them as vortices (figure 1.12(b)), with each flux line carrying a flux quantum of: ϕo = h/2e = 2.07 ×10−7 gauss cm2. The penetration of the magnetic field in the intermediate range Hc1 < H < Hc2 has been clearly evidenced and studied; and the dynamics of the vortices has been clarified. The vortices have been found to move very easily for temperatures not so far below Tc and they control the transport properties. Only below a so-called irreversibility temperature Tirr < Tc can the vortices be considered fixed (in a way depending from impurities and/or defects) and thus no dissipation occurs. First quantitative description of the properties of the superconducting state was formulated by the London brothers in 1935 [20]. Seven years before the publication of the microscopic BCS theory, a phenomenological theory developed by Ginzburg and Landau [21], which was based on Landau’s concept of an order parameter used to describe a thermodynamic phase transition, succeeded in explaining many of the observed properties of superconductors, in spite of the prevailing uncertainties on the pairing mechanism. Even the two characteristic length scales, λ and ξ, came out as solutions of the G–L equations.

1.9 BCS mechanism: flux quantization and energy gap The BCS theory applies well to the conventional low-Tc superconducting materials and explains the phenomenon of superconductivity in them. This microscopic theory was proposed in 1957 by Bardeen, Cooper, and Schrieffer, the BCS theory [11], almost 50 years after the experimental discovery of superconductivity. According to the BCS theory, the key microscopic factor behind this phenomenon is the attraction between electrons mediated by the exchange of phonons, such that below Tc within the electronic system there forms a macroscopic manifold of bound electron pairs (known as the Cooper pairs). Thus the attraction has its origin in the ionic system— the lattice, and the pairing of electrons leads to macroscopic coherence and perfect diamagnetism. According to this theory, superconductivity arises because of the formation of bound pairs of electrons. For this to occur, a pre-requisite is a strong attractive interaction between pairs of electrons, strong enough to overcome the normal Coulomb repulsion between these pairs. A second condition to be fulfilled is that the superconducting state must exhibit a unique electrodynamic behavior under which all the bound pairs of electrons must exist in one and the same quantum mechanical state.

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The BCS attractive mechanism of superconductivity owes itself to the conduction electrons deforming the crystal lattice, slightly. A simple model to describe the BCS mechanism of stabilizing the superconducting state by the electron–phonon interactions is as follows. The ionic lattice of a metal is a periodic crystalline array of positive ions immersed in the sea of conduction electrons. Consider a negatively charged conduction electron traveling through this array of positive ions. As it moves it pulls the much heavier positive ions towards it, though only slightly since the movement of the ion is restrained by neighboring ions of the ionic lattice, elastically. The maximum displacement of the ions occurs a bit after the fast moving electron has passed. That leaves a region of excess positive charge, behind the electron that passed. This positively charged region attracts (pulls in) a second passing electron towards it. This way, these two electrons get coupled via the ‘virtual quanta’ of phonons of the ionic lattice. It is pertinent to take note that superconductivity exists even at T = 0, where there are no thermal phonons, which are ‘real quanta’, which in fact degrade superconductivity! Effectively, this leads to the formation of mutually attracted pair of electrons, a stable bound Cooper pair, arising from the dynamic distortion of the lattice, called phonons, and hence the attractive interaction under the BCS theory is known as the phonon-induced electron–electron attraction. Since at any reasonably high temperature, the lattice of ions undergoes lattice vibrations due to thermal effects, the pair of electrons, the Cooper pair, owes its coupling (attraction) to phonons. The electrons are fermions, but the Cooper pairs are bosons, and the superconducting state is characterized by the Bose condensation of Cooper pairs. A Cooper pair is formed by two electrons (spin singlets) having equal and opposite momentum and spin. Thus the angular momentum of a Cooper pair is 0 (it is in s-state), and the pair has a coherence length (~100 nm which is » atomic spacings). e–ph coupling occurs between two electrons with opposing spin directions and opposite momenta, viz. an electron with momentum k and spin direction ↑, coupled via a phonon with another electron with momentum −k and spin direction ↓. A theoretician would describe this attraction as due to exchange of ‘virtual phonons’. The superconducting state involves the pairing of a sizeable part of about 1022 electrons per cubic centimeter. The pairs at S = 0 obey the Bose–Einstein statistics and all can set in a single quantum state, while single electrons are continuously scattered in different single-electron states. The BCS theory describes a variety of properties of the superconducting state resulting from the transition driven by pair condensation. The energy price of breaking a Cooper pair is 2Δ0 where Δ0 is the band-gap, known as superconducting gap. But to pick up a single Cooper pair to do so is not simple since this is a part of a Bose condensate which is a sea of such pairs at the Fermi level. The energy relation for the band-gap for a BCS superconductor is given as: 2Δ0 = 3.52 kBTc and the value of Δ0 drops gradually to zero as the temperature of this material rises to its Tc value. The second condition for superconductivity, namely, that all the pairs should be in the same state, allows one to satisfy the conditions of coordinated motion. It is 1-16

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thus energetically favorable for many pairs to be in the same state so that at low enough temperatures a condensate of paired electrons can result. As we raise the temperature we eventually come to the point where some of the pairs are thermally disrupted. The effect of these disrupted pairs is two-fold. Firstly, they reduce directly the number of bound pairs, and secondly, due to the now uncoordinated motion of the individual electrons, they interfere with and weaken the attractive interaction of the remaining pairs making it easier for the remaining pairs to be broken. As the temperature is raised further this break up becomes catastrophic, and above a welldefined transition temperature Tc, no bound pairs can exist. This transition reflects the transition from the superconducting to the normal state. The factor 2 in the relation for a flux quantum (ϕo = h/2e = 2.07 ×10−7 gauss cm2) is itself a proof of the charge carriers acting as Cooper pairs in the superconducting state. Flux quantization has been demonstrated in the superconducting state experimentally [22, 23]. Flux quantization has been observed in YBa2Cu3O7−x, too, which shows that electrons are paired in the case of this high-Tc material, just like the low-Tc superconductors which obey the BCS mechanism, although what holds a pair of electrons together in YBa2Cu3O7–δ is debatable, because it is thought that the typical e–ph–e attraction is not valid in the case of cuprate superconductors. As discussed above, there are two fundamental length scales of the superconducting state: (a) the penetration depth (λ)—the length over which magnetic flux can penetrate a superconductor; and (2) the Pippard coherence length (ξ)—the length over which the super-electron density ns rises from zero at the boundary between normal and superconducting regions, to a maximum value over a distance ξ (order of which is 10−4 cm). Phonons (lattice waves) can propagate in any metal and usually cause some attraction between electrons near the Fermi surface. According to the BCS theory, electrons with opposite momenta pair up, and for the phonon mechanism of superconductivity Tc ⩽ 20–40 K. The penetration depth λ and the coherence length ξ emerge as natural consequence of the BCS theory. The London equation is obtained for magnetic fields that vary slowly in space. Thus, the central phenomenon in superconductivity, the Meissner effect, is obtained in a natural way. Magnetic flux through a superconducting ring is quantized and the effective unit of charge is 2e rather than e. And that gives evidence of pairing of electrons. 1.9.1 The isotope effect The first hint of the underlying electron–phonon interaction being responsible for superconductivity came from the discovery of the isotope effect. It was observed that the critical temperature, Tc, of a superconductor varies with the isotope of that element, as per the relation: MαTc = constant, where α ~ 0.5 [24–26], where M is the isotopic mass. For instance, for the superconductors Hg, Sn, Pb, Cd and Tl, the term α was found to be in the range of ~0.50. This is called the isotope effect. The dependence of Tc on the isotopic mass M, points to the involvement of the lattice vibrations (phonons). The e–e interaction via the phonons (ph), the e–ph–e interaction, orders the participating e’s in the k-space w.r.t. the Fermi gas of

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electrons, a cornerstone of the origin of superconductivity in the BCS theory. In solid phase, the lattice vibrations are quantized and can be described by quasiparticles, called phonons. Under the quantum mechanical approach, it is assumed that the phonons represent a normal mode vibration such that all parts of the lattice vibrate with the same frequency. Thus the isotope effect can also be elaborated as: Tc ∝ θDebye ∝ M−α, where α = 1/2, and θ, the Debye temperature, can be taken to be proportional to the frequency of the vibration of the lattice ν, implying: θ ∝ ν ∝ M−1/2. 1.9.2 The band gap and heat capacity A model was developed by Peter Debye in 1912 for estimating the phonon contribution to the specific heat (heat capacity) of a solid. As against the Einstein model which treats a solid as many individual, non-interacting quantum harmonic oscillators, the Debye model treats the phonons (i.e. the atomic lattice vibrations or the thermal vibrations) as particles in a box, and predicts the low temperature dependence of the heat capacity to T 3—the Debye T 3 law. The Debye model is to solid-state, what Planck’s law is to black body radiation, where one treats electromagnetic radiation as a photon gas3. At temperatures much below the Debye temperature and the Fermi temperature (TF), the heat capacity of metals is a sum of electron- and phonon contributions: C = γT + AT3, where γ is called the Sommerfeld parameter. The electronic term dominates at low temperatures. A heat capacity jump, a second-order phase transition occurs for a superconductor at Tc. Below Tc, the total heat capacity (electronic + lattice contributions together) shows an exponential temperature dependence. The electronic part of the heat capacity contains an experimental factor, Eg/2, that may be used to determine the value of Eg, the energy gap. In a normal metal, at T = 0 K, all states below the Fermi energy are filled, and all states above it are empty. Superconductors exhibit energy gap between the ground state and the lowest excited state. BCS theory predicts that at T = 0, Eg = 3.52 kBTc. Unlike the energy gap of insulators, which arises from electron–lattice interaction, the energy gap of superconductors is due to e–e interaction, which orders the electrons in k-space with respect to the Fermi gas of, electrons. Electrons in the excited state above the energy gap behave as normal electrons causing resistance. Representative values of the energy gap Eg are (in meV): Nb (3.05), Pb (2.73), La (1.9), Hg (1.65), and In (1.05). Therefore, the energy gap (energy needed to break apart a Cooper pair) in a superconductor is very small, of the order of kBTc (10−3 eV) at 0 K, as compared with the band gap in semiconductors (~1 eV).

3 The beauty of the Debye model was that it could arrive at, just as the Einstein model did, the classical Dulong–Petit law (c. 1819) in thermodynamics, which states that for a solid at normal (room) temperatures, or higher, the heat capacity per mole is nearly constant and is equal, as was later established to, C = 3kBN where N is total number of atoms in the sample. The Debye T 3 model is followed well only at temperatures T ≫ θD where lattice heat capacity prevails, θD, the Debye temperature being the approximate temperature limit below which quantum effects dominate.

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The electronic part of heat capacity Ce in the superconducting state is given as:

Ces / γTc ∝ a exp ( −bTc / T ) proportional to −1/T, suggestive of excitation of electrons across an energy gap. In a superconductor, the energy gap Eg arises due to the electron–electron interaction via phonons, and the energy gap term, −Eg/2kBT, is related to the exponential factor in the electron heat capacity of a superconductor, i.e.

Ces = γ Tc exp ( −1.76 T / Tc ) The weak e–ph coupling superconductors have a typical value: Eg(0)/kBTc = 3.52, whereas the strong e–ph coupling superconductors have Eg(0)/kBTc > 3.52.

1.10 Wires and cables from low Tc superconductors NbTi and Nb3Sn The workhorse for high field magnets used in superconducting accelerators is NbTi wires/cables. Stability criteria requires making of superconductors as fine filaments embedded in a matrix of copper. Magnetic fields induce persistent screening currents in a superconductor. Flux jumping occurs when screening currents go unstable and quench the magnet. To avoid this one uses fine filaments. Screening currents produce magnetization and the use of fine filaments leads to their getting coupled in changing fields. Increased magnetization can be tackled by twisting. Accelerator magnets need high currents, and coupling can be controlled by using oxide layers on wires or by using resistive core foils. Performance of superconductors is described by the critical surface in B–J–T space. It is important to take note that the performance of superconducting magnets gets often degraded and shows ‘training’. 1.10.1 A3B superconductors Perhaps the most widely used class of type-II superconducting compounds are the A3B family having the A-15 structure (beta-tungsten), where A are TM-atoms, such as V or Nb, and B denote non-transition metal atoms such as Sn, Al, Ga, Si, Ge (figure 1.13). Six A15 compounds have transition temperatures over 17 K, and high values of upper critical fields Hc2 at 4.2 K [27]. Specifically, the values of Tc and Hc2 (at 4.2 K) for different A-15 compounds, respectively, are: V3Ga (15.4 K, 23 T), V3Si (17.1 K, 23 T), Nb3Sn (18.3 K, 24 T), Nb3Al (18.9 K, 33 T), Nb3Ga (20.3 K, 34 T), and Nb3Ge (23.0 K, 38 T). Nb3Ge thin films held the record for the highest known Tc of 23 K for a number of years up to 1986. This was thought to be close to the limit imposed by BCS theory, within phonon exchange mechanism! Nb3Sn, is the most widely used material while constructing very high field superconducting magnets for particle accelerators. Fabrication of Nb3Sn cables is not an easy task because the phase diagram of Nb–Sn is complex, such that one can get Nb3Sn (A-15 structure) only after an annealing process above 930 °C. One method that is deployed is to take Sn strands surrounded by Nb strands and embed the Nb–Sn strands into a Cu-matrix, swage 1-19

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Figure 1.13. The unit cell of A15 Nb3Sn, showing the Sn atoms in blue and the Nb atoms in red. This structure holds for other A3B compounds, too, where A stands for Nb or V, and B is a non-transition metal atom like Sn, Al, Ga, Si or Ge. Reproduced from [28]. Copyright IOP Publishing. Reproduced with permission. All rights reserved

them first before annealing at high temperatures to get multifilamentary Nb3Sn cables embedded in a Cu-matrix. Another choice to fabricate Nb3Sn films is to adopt liquid Sn diffusion method, under which one dips a Nb-substrate in a liquid Sn bath for about 15 min. Subsequent annealing above 1025 °C yields Nb3Sn films with characteristic Tc value of 17.7 K. One may recall that pure Nb superconducts below 9.3 K and pure Sn below 3.6 K. Current applications of high-field magnets fabricated from type-II superconductor wires are for magnetic resonance imaging (MRI), magnetically levitated trains, high-energy particle accelerators, and toroidal fusion reactors. Superconducting cables also find applications in magnetic energy power storage rings. 1.10.2 The triumvirate: Tc, Bc2 and Jc Both Nb3Sn and NbTi can provide upper critical magnetic fields Hc2 ~ 10 T. There are other superconducting materials giving much higher Hc2 such as 41 T by Nb3Al0.7Ge0.3 and >100 T by some high-Tc cuprates (all values at 4.2 K), but to make wires/cables of these materials for commercial use is still difficult. It is the successful pinning of flux lines which makes a superconducting material useful for high-field applications. It has to stay hard to remain useful against increase in the magnetic induction B. As shown by the triumvirate (figure 1.14) the superconducting state can be destroyed by raising either of the three parameters beyond their critical values, viz. the Critical temperature (Tc), critical current density (Jc) and critical induction (Bc2). In addition to the two parameters, Tc and Bc2, which are intrinsic characteristics of a superconductor, the superconducting state is also destroyed if the material carries a current density higher than a critical value, Jc, called the critical current 1-20

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Figure 1.14. The triumvirate—Tc, Bc2 and Jc. Figure courtesy of Dr V K Aswal.

density. Temperature, magnetic field and current density thus determine together whether a material would remain superconducting or not. The superconducting state thrives below and vanishes above a three-dimensional critical surface unique to each superconductor. In contrast to Tc and Bc2, the Jc of a superconductor can be controlled by metallurgical processing and by introducing defects in it. A superconductor may have high Tc and Bc2 values, but their Jc is very much dependent on the processing and fabrication conditions. Thus, the quality of a candidate superconductor material is assessed on the basis of: (i) how high the Tc is, the higher the better; (ii) how much current it can carry in the superconducting state; and (iii) how large a magnetic field (internal as well as externally applied) it can withstand without losing its superconductivity. 1.10.3 The irreversibility line The potentially useful state of a type II superconductor is below the irreversibility line (shown in figure 1.15) below which the material is in a state where the flux lines are trapped (pinned) in the vortex lattice. Above the irreversibility line there is almost no pinning, fluxoids are not trapped, and magnetization is reversible, rendering the Jc to plunge to negligible levels. The increase of the superconducting temperature, the critical fields and critical currents in the alloys is related to the reduction of the coherence length accompanying the decrease of the mean free path of the electrons. The alloying process transforms the metallic superconductors from type I to type II. Pinning has technological importance in order to lock the vortices and avoid dissipation. For a current flowing perpendicular to the field H, the Lorentz force pushes the vortices along the j × H direction. In the early 1900s, we had elemental sp metals like Hg, Pb, Al, Sn, Ga, etc. In the middle of the 1900s we saw the discovery of transitional metals, alloys, and compounds with somewhat higher Tc values, like Nb, NbN (16 K), Nb3Al (17.5 K), Nb3Sn (18.5 K), Nb3Ge (23 K), K3C60 (19.2 K), V3Ga (16.5 K), V3Si (17.1 K) La3In (16 K), etc. In the late 1900s, we saw the emergence of high-Tc perovskite oxides YBa2Cu3O7−x (90.0 K), Rb2CsC60 (31.3 K). Whereas, the A-15 compounds A3B had Tc = 15–23 K, the highest Tc observed in the case of an oxide superconductor, under ambient pressures is 138 K for (Hg0.8Tl0.2)Ba2Ca2Cu3O8.33. 1-21

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Figure 1.15. The irreversibility line, Hirr(T ), of a type II superconductor, shown in blue color, separates two distinct regions of the H–T plane. Below Hirr(T ), we have a useful state, where the flux lines are trapped (pinned) in the vortex lattice, and above it, there is almost no pinning, and magnetization is reversible, rendering the Jc to plunge to negligible levels, making the latter useless for applications. Figure courtesy of Dr S K Gupta.

1.11 Techniques employed to evaluate the basic physical characteristics of superconducting materials Crystal structure of new materials is established by employing various complementary diffraction techniques which use x-rays, neutrons, or electrons, and high resolution electron microscopy [29, 30]. However, when materials with known crystal structures are prepared, then one just goes for x-ray diffraction to match the fingerprints of diffraction peaks with a standard x-ray pattern from literature. The superconducting transition temperature Tc (and its sharpness), Hc, and current density Jc are evaluated using DC/AC magnetization techniques; electrical resistance of a sample is measured using the four-probe method, which is also used commonly to check the value of Tc and the transport current density. Heat capacity, particularly the electronic part is measured by using adiabatic calorimetry; valence state of relevant cations is checked using XPS (x-ray photoelectron spectroscopy); and band-gap details using ARPES (angle-resolved photoemission spectroscopy). Details of these experimental methods are explained in several textbooks, book chapters and review articles. It is, nonetheless, relevant to describe the four-probe method (also called fourpoint probe method) [31] used to measure electrical resistance of a superconducting sample, as we cool it from its normal state through its superconducting transition, when its electrical resistance disappears. Quite often a doubt comes to the mind of beginners in this field as to how the very low value of resistance (say, less than microohms and tending to zero), can be measured, when the resistance of lead-wires and the resistance of the contacts applied are themselves orders of magnitude higher, of the order of a few to hundreds of milliohms. Contact and lead resistances become irrelevant because voltmeters have very high internal resistance (typically 106–1012 ohm) and practically do not draw any current (figure 1.16). Thereby true sample

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Figure 1.16. DC resistivity measurements are performed using a four probe technique to eliminate the influence of the contact and lead resistances. The contacts are made by pasting fine 25 μm gold wires with a small amount of silver or carbon paint. Figure courtesy of Dr V K Aswal.

voltage between the inner two contacts is accurately measured without any drop on lead/contact resistances [32]. Zero resistance in superconducting materials implies absence of a voltage drop along the material when a current is passed through it, and thereby no dissipation of power. But this happens only for a DC current of constant value, but not when we pass an AC current. The JJ decoupling can play a significant role in the AC response obtained below critical temperature in granular YBCO, for instance. The AC loss due to frequent JJ decoupling is directly proportional to the applied AC frequency [33], and therefore, the AC resistance depends directly on the applied AC frequency and increases with an increase in frequencies.

References [1] Kasap S O 2017 Principles of Electronic Materials and Devices 4th edn (Dubuque, IA: McGraw-Hill) [2] Kasap S, Koughia C and Ruda H E 2017 Electrical Conduction in Metals and Semiconductors (Springer Handbook of Electronic and Photonic Materials) ed S Kasap and P Capper (Berlin: Springer) ch 2 [3] Onnes H K 1908 The liquefaction of helium Proc. R. Acad. Amsterdam 11 168 [4] Onnes H K 1911 Further experiments with liquid helium. G. On the electrical resistance of pure metals, etc. VI. On the sudden change in the rate at which the resistance of mercury disappears Communications from the Physical Laboratory of the University of Leiden vol 124C (Dordrecht: Springer) pp 21–6 [5] Onnes H K 1911 Communications from the Physical Laboratory of the University of Leiden vol 120b KAWA (Proc. of the Koninklijke Akademie van Wetenschappen te Amsterdam, 28 Apr 1911) pp 1479–81 [6] The Nobel lecture delivered by Prof. Heike Kamerlingh Onnes, on Dec. 11, 1913: https:// nobelprize.org/uploads/2018/06/onnes-lecture.pdf [7] Matthiessen A and Vogt C 1864 On the influence of temperature on the electric conductingpower of alloys Philos. Trans. R. Soc. 154 167–200 [8] Kelvin L 1902 XXIX. Aepinus atomized Philos. Mag. Ser. 6 3.15 257–83 [9] Dewar J 1904 On electric resistance thermometry at the temperature boiling hydrogen Proc. R. Soc. Lond. 73 488–96

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[10] Onnes H K 1991 Through Measurement to Knowledge—The Selected Papers of Heike Kamerlingh Onnes 1853-1926 1 edn (Dordrecht: Springer) [11] Bardeen J, Cooper L N and Schrieffer J R 1957 Theory of superconductivity Phys. Rev. 108 1175–204 [12] Meissner W and Ochsenfeld R 1933 Ein neuer Effekt bei Eintritt der Sup raleitfähigkeit Naturwissenschaften 21 787–8 [13] https://en.wikipedia.org/wiki/List_of_superconductors [14] Matthias B T 1952 Superconductivity in the cobalt–silicon system Phys. Rev. 87 380 [15] Abrikosov A A 1952 Dokl. Akad. Nauk SSSR 86 489 [16] Shubnikov L V et al 1937 Zh. Eksp. Teor. Fiz. 7 221 [17] Brandt E H 1986 Phys. Rev. B 34 6514 [18] Huebener R P 1990 Magnetic Flux Structures of Superconductors (New York: Springer) [19] Abrikosov A A 1957 Zh. Eksp. Teor. Fiz. 32 1442 Abrikosov A A 1957 On the magnetic properties of superconductors of the second group Sov. Phys. JETP 5 1174–82 [20] London F and London H 1935 The electromagnetic equations of the supraconductor Proc. R. Soc. A: Math. Phys. Eng. Sci. 149 71–88 [21] Ginzburg V L and Landau L D 1950 On the theory of superconductivity Zh. Eksp. Teor. Fiz. 20 1064–82 [22] Doll R and Näbauer M 1961 Experimental proof of magnetic flux quantization in a superconducting ring Phys. Rev. Lett. 7 51–2 [23] Deaver B S Jr and Fairbank W M 1961 Experimental evidence for quantized flux in superconducting cylinders Phys. Rev. Lett. 7 43–6 [24] Lock J M, Pippard A B and Shoenberg D 1951 Superconductivity of tin isotopes Proc. Camb. Phil. Soc. 47 811–9 [25] Maxwell E 1952 Superconductivity of the isotopes of tin Phys. Rev. 86 235–42 [26] Serin B, Reynolds C A and Lohman C 1952 The isotope effect in superconductivity. II. Tin and lead Phys. Rev. 86 162–4 [27] Testardi L R 1975 Structural instability and superconductivity in A-15 compounds Rev. Mod. Phys. 47 637–48 [28] Posen S and Hall D L 2017 Nb3Sn superconducting radiofrequency cavities: fabrication, results, properties, and prospects Supercond. Sci. Technol. 30 033004 [29] Barrett C and Massalski T B 1987 Structure of metals Crystallographic Methods, Principles, and Data (International Series on Materials Science and Technology) vol 35 3rd rev edn (Oxford, New York: Pergamon) [30] Ashcroft N W and Mermin N D 1976 Solid State Physics (New York: Holt, Rinehart, and Winston) [31] Smits F M 1958 Measurement of sheet resistivities with the four-point probe Bell Syst. Tech. J. 34 711–8 [32] Samarappuli S, Schilling A, Chernikov M A, Ott H R and Wolf T 1992 Comparative study of AC susceptibility and resistivity of a superconducting YBa2Cu3O7 single crystal in a magnetic field Physica C 201 159–65 [33] Sarangi S, Chockalingam S P and Bhat S V 2005 Frequent Josephson junction decoupling is the main origin of ac losses in the superconducting state J. Appl. Phys. 98 073906

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Superconducting Materials and Their Applications An interdisciplinary approach Jatinder Vir Yakhmi

Chapter 2 High-Tc superconducting cuprates and magnesium boride

2.1 Introduction The search for superconducting materials with higher and higher critical temperatures has been an ongoing quest. In the first 75 years after the discovery of the phenomenon of superconductivity the progress was rather modest—from Tc = 4.2 K for mercury up to Tc ≈ 23 K in Nb3Ge, as depicted in figure 2.1. Owing to such low values of Tc, the known superconductors until 1986 could be put to use in just a few critical areas, because of the need to use expensive liquid helium as a coolant, in addition to the need to use special thermal insulation so as not to let liquid He evaporate away, quickly. The need to conserve scarce He gas required recycling it, too. A breakthrough came in 1986 when Bednorz and Mueller discovered superconductivity at higher temperatures (~30 K) in a novel cuprate ceramic belonging to the system Ba–La–Cu–O [1], which led to a spurt in the synthesis of candidate materials in the cuprate families and quick successes in discoveries of what are now known as high-Tc superconducting cuprates. Before we discuss the systematics of these oxide materials in some detail in this chapter, it is pertinent to state that the observations made by Bednorz and Muller were received very enthusiastically in the scientific world, leading to the award of the Physics Nobel Prize to them in the very next year. Justifiably so, because their findings led to quick discoveries of new cuprate families by different research groups, internationally, which can be summarized as: (i) a La–Sr–Cu–O compound with perovskite structure with Tc ~ 40 K [2], (ii) Y–Ba–Cu–O ceramics with superconductivity at 90 K in 1987 [3], (iii) Bi(Pb)–Sr–Ca–Cu–O with superconducting Tc at ~ 110 K in 1988 [4, 5], followed by, (iv) the discovery of superconductivity at 125 K in Tl–Ba–Ca–Cu–O [6–8], also in 1988.

doi:10.1088/978-0-7503-2256-0ch2

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Superconducting Materials and Their Applications

Figure 2.1. Increase in superconducting transition temperature, Tc, with time after the discovery of superconductivity in Hg at ~4 K in 1911. The curve showed a slow rise initially, with an increase of merely 18 K for the first 75 years. But with the discovery of high-Tc superconducting cuprates in 1986, the Tc value galloped to 133 K, and under applied pressures to 164 K, in 1994. Figure courtesy of Dr V K Aswal.

A few years later, in 1993, superconductivity was discovered at 133 K for HgBa2Ca2Cu3O8+δ belonging to the Hg–Ba–Ca–Cu–O system [9, 10]. The same compound, HgBa2Ca2Cu3O8+δ, subsequently showed a Tc ≈164 K under pressure of ~30 GPa, in 1994 [11]. These discoveries, which took the Tc values from 23 K to 164 K in a span of just eight years (shown by a steep rise in the Tc versus year plot in figure 2.1), were all made on cuprates, having Cu-oxide layers, as an inherent component. What was remarkable was that these developments removed the dependence on the use of expensive liquid helium, and its complex usage technology, to cool the above-mentioned Y-, Bi-, Tl-, or Hg-based high-Tc cuprates (HTSCs) into their superconducting state since liquid nitrogen at 77 K was adequate to do that job. This also increased the possibilities of exploitation of these high-Tc superconductors into many envisioned applications, due to abundantly available, cheap liquid nitrogen as a coolant. On top of this, it was also discovered that several HTSCs have rather useful superconducting characteristics suitable for numerous applications, inasmuch that they are strongly of type II, with high granularity and anisotropy in their superconducting behavior. The London penetration length, λ, for HTSCs lies within the range of 1500 Å and 5000 Å, while the coherence length, ξ, is typically between 4 Å and 40 Å. At a temperature close to zero degrees Kelvin, the value of the lower critical field, Hc1, for them scales to a few hundreds of Oe, while Hc2, when extrapolated to zero degrees Kelvin is quite high, being generally ~106 Oe.

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Figure 2.2. (a) The perovskite structure ABO3. The large filled circles located at the corners of the cube denote cations A. An example of this structure is the compound Ba1−xKxBiO3, where Ba-cations (large filled circles), partially substituted by K-ions, are at the corners of the cube. Bi-cation (denoted by small filled circles) is hexacoordinated to oxygen anions, (empty circles). (b) shows the hexa-coordinated building block, of the perovskite structure, showing a metal ion, such as Cu/Bi (small filled circle, denoting B in ABO3), surrounded by six oxygen ions. Figure courtesy of Dr V K Aswal.

However, the HTSCs being granular materials prepared by high-temperature sintering of ceramic oxides, it soon dawned on the technologists that their processing into useful shapes such as wires, cables, tapes, or ribbons for applications posed several difficulties vis-à-vis the well-established processing protocols of till-then known metal/alloy low-temperature superconductors (LTSC), such as Nb–Ti or Nb3Sn. In chapter 4, before describing the areas of technology in which HTSCs have found applications thus far, we shall also discuss the issues related to the fabrication of HTSCs into the above-mentioned technologically useful shapes, apart from discussing the influence of their granular nature on the critical superconducting parameters, and problems related to environmental degradation undergone by some of them which must be solved for large scale applications. However, in what follows, we discuss the different categories of oxide superconductors and their significance in the realm of the development of the subject of superconductivity, historically.

2.2 Oxide superconductors, before cuprates Discovery of superconductivity in an oxide was first made by Arthur W Sleight, at Dupont, in 1975, specifically in the system BaPb1−xBixO3 (BPBO), where the Tc depended upon the Bi-content (x) for x ≅ 0.05–0.3 [12]. The maximum Tc was 13 K for x ~ 0.25. In 1988, Cava et al [13] discovered the first oxide superconductor system, Ba1−xKxBiO3, having a Tc value of 30 K (at x = 0.4), which was above that of all the A-15 compounds. For K-content x ⩾ 0.35 in this oxide system, one obtains a regular cubic perovskite structure (figure 2.2). It may be mentioned in passing that the non-cuprate, LiTi2O4, having fcc normalspinel structure displays superconductivity with Tc = 13.7 K [14].

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Superconducting Materials and Their Applications

2.3 Cuprate superconductors: La–Sr–Cu–O and Y–Ba–Cu–O A breakthrough came in the search of superconductors in 1986 when Bednorz and Muller published Possible High-Tc Superconductivity in Ba–La–Cu–O system [1]. They observed the onset of superconductivity at ~30 K for BaxLa5−xCu5O5(3−y), a compound in this oxide (cuprate) system. This Tc value was higher than the Tc of Nb3Ge, known to be the highest then. Hence, they called it a high-Tc system. It was soon discovered that their samples were based on La2CuO4, a perovskite (figure 2.2), which was known to be an antiferromagnet (TN of over 240 K) and an insulator. When doped with M = Ba or Sr, this antiferromagnet became a hole-doped superconductor La2−xMxCuO4. The compound La2−xSrxCuO4 gained quick acceptance as the first high-Tc superconductor with a Tc of 38 K [2]. It is often referred to as the 214 structure because it has two La (Sr), one Cu and four O atoms. It has a tetragonal structure which transforms to orthorhombic upon Sr substitution for La. Upon substitution, La2−xAxCuO4 (A = Ba2+ or Sr2+ in place of La3+), Cu2+ gets partially oxidized to Cu2+/Cu3+, and the compound gets hole-doped, bringing in p-type superconductivity, the Tc for which peaks at x = 0.15 for A = Sr. In this structure, Cu-atoms forming Cu–O6 octahedra have Cu–O (apical) = 2.4 Å, a distance much larger than the planar Cu–O distance (1.9 Å). Conducting CuO2 planes are ~6.6 Å apart, separated by two LaO planes which act as charge reservoirs (figure 2.3(a)). In a parallel, one can also get electron-doped (n-type) superconductivity when one dopes Ce4+ for Nd3+ in the perovskite Nd2CuO4, which implies doping of electrons partially, reducing Cu2+ to Cu2+/Cu1+ in Nd2−xCexCuO4, for which the Tc value peaks at 24 K for x = 0.14–0.18. Though both La2−xAxCuO4 and Nd2−xCexCuO4 are body-centered tetragonal structures, the difference in them is in the position of the oxygen atoms of the charge reservoirs. Cuprate superconductivity is associated with doping Mott insulators, such as La2CuO4, with charge carriers, and the Bose–Einstein condensation of Cooper pairs.

Figure 2.3. Crystal structures of (a) La2−xSr(Ba)xCuO4; and (b) YBa2Cu3O7−δ. Figure courtesy of Dr V K Aswal.

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The first superconductor to have a Tc above the liquid nitrogen temperature was YBa2Cu3O7−δ (known also as YBCO, Tc = 90 K), the orthorhombic structure of which has two CuO2 planes and CuO chains (ribbons) (figure 2.3(b)). The parent compound of the YBCO system is YBa2Cu3O6, an antiferromagnetic (AF) tetragonal (a = b) insulator, with Cu in +2 state. YBa2Cu3O6 has no CuO chains since the O6-composition leads to a loss of oxygen ions from the Cu–O planes incorporating the chains. One can recall that the long-range magnetic order and superconductivity do not coexist, except under very special conditions. To become metallic (and beyond that a superconductor at low temperatures), YBa2Cu3O6 is doped with holes (h-doped), directly by adding additional O-atoms which form the CuO chains. At oxygen = 6.4, the AF-order disappears and the superconducting phase starts to develop. The maximum value of Tc is achieved at an oxygen level of about 6.95. Superconducting behaviour of YBa2Cu3O7−δ is extremely sensitive to O-content. Overdoping, as well as underdoping, can lead to a reduction in Tc. In fact, for best results, the material is carefully annealed in oxygen by observing a set protocol (figure 2.4) of annealing and slow cooling of the samples, to get a composition close to the desired O~7 value. O-content can be changed reversibly from 6.0 to 7.0, and while doing so, the oxygen ions just move in and out of the parallel CuO chains running along the b-axis. In addition to being sensitive to the stoichiometry of oxygen, the properties of YBCO are influenced by the crystallization methods used. Care must be taken to sinter YBCO, appropriately. YBCO is a crystalline material, and the best superconductive properties are obtained when its grain boundaries are aligned by careful control of annealing and cooling temperature rates. YBa2Cu3O7−δ has an orthorhombic structure and is the only high-Tc compound having one-dimensional CuO chains. The CuO chains play only the role of charge

Figure 2.4. Protocol of annealing and slow cooling followed to obtain YBa2Cu3O7−δ with optimised O-content. Figure courtesy of Dr V P S Awana.

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reservoirs, and superconductivity is almost confined within the puckered twodimensional basal CuO2 layers, in which Cu-ion lies at the center of a square configuration of oxygen ions, resulting in a pyramid of five O-ions around each Cuion in the CuO2 planes (figure 2.3(b)). Usually, the optimal doping level is ~0.2 holes per Cu atom, as reported by Mook and Dowan [15]. The role of Y in the superconductivity of YBa2Cu3O7−δ is only minor—just to hold the two CuO2 layers. Interestingly, the trivalent Y can be replaced by most Ln-elements, without affecting the superconducting properties much. Outside the CuO2–Y–CuO2 sandwich, we have BaO planes and CuO chains. Ba is in +2 state. Planar Cu–O distance is 1.9 Å in both chains and planes. The role of doping in high-Tc cuprates needs to be understood. The onset of superconductivity and the optimization of the Tc-values of all high-Tc cuprates is associated with doping, mostly with holes (except the e-doped superconducting cuprates such as Nd2−xCexCuO4). This becomes clear when we look at the formal valences. The case of La2−xAxCuO4: 2La3+ + Cu2+ + 4O21.875La3+ + 0.125Ba2+ + Cu2.125+ + 4O2−

Gives insulating La2CuO4 Gives superconducting La2−xBaxCuO4

The case of YBa2Cu3O7−δ: Y3+ + 2Ba2+ + Cu1+ + 2Cu2+ + 6O2− Y3+ + 2Ba2+ + 3Cu2.3+ + 7O2−

Gives insulating Antiferromagnetic YBa2Cu3O6 Gives superconducting YBa2Cu3O7−δ

The compound YBa2Cu3O6 is obtained by calcinating an appropriate mixture of BaO, CuO and Y2O3 at about 800 °C. Annealing of YBa2Cu3O6 in oxygen/air at 950 °C gives YBa2Cu3O7−δ.

2.4 Bi-, Tl- and Hg-based cuprate superconductors Three different series of high-Tc superconductors based on Bi-, Tl- and Hg-based cuprate systems were discovered soon after the discovery of the compound, YBa2Cu3O7−δ. These, too have layered crystal structures formed by CuO2 planes and charge reservoir layers, and are four-component systems with a general formula: AmB2Can−1CunO2+m+2n, where A = Bi, Tl or Hg; and B = Ba or Sr. The highest Tc value is shown for the member n = 3 in each of these four-component systems, viz. Bi2Sr2Ca2Cu3O10 = Bi-2223 (Tc = 110 K), Tl2Ba2Ca2Cu3O10 = Tl-2223 (Tc = 125 K), HgBa2Ca2Cu3O9 = Hg-1223 (Tc = 135 K). There are structural similarities between these three systems. Bi2Sr2Can−1CunO2n+4 series has three compounds n = 1, 2, and 3, all with ‘micaceous’ weakly bonded BiO layers, viz. 2-6

Superconducting Materials and Their Applications

n = 1, Bi2Sr2Cu1O6+y (Bi-2201, Tc = 10 K), n = 2, Bi2Sr2Ca1Cu2O8+y (Bi-2212, Tc = 85 K), n = 3, Bi2Sr2Ca2Cu3O10+y (Bi-2223, Tc = 110 K). The compounds Bi2Sr2Can−1CunO2n+4 have a pseudo-tetragonal structure (figure 2.5), with the stacking of basic Bi2Sr2CuO6 unit (Bi-2201) with zero, one, or two CaCuO2 slabs inserted in the unit cell, respectively, each such slab being about 3 Å thick. The stacking sequence is Bi–Sr–Cu–Ca–Cu–Sr–Bi for Bi-2212, and Bi–Sr–Cu–Ca–Cu–Ca–Cu–Sr–Bi for Bi-2223. Consequently, the c-parameter of the pseudo-tetragonal lattice increases from c ≈ 24.6 Å for Bi-2201, to c ≈ 30.8 Å for Bi-2212, to c ≈ 37.1 Å for Bi-2223. The lattice constant a ~ b ≈ 5.4 Å, remains nearly unchanged. Bi and Sr have a valence of +3 and +2, respectively. Bi-cuprates (unlike YBCO) are water-resistant and have the advantage of stability in compositional/ oxygen content. The thallium cuprates series Tl2Ba2Can−1CunO2n+4 has four members, viz. Tl2Ba2Cu1O6 (Tl-2201, Tc = 80 K), Tl2Ba2Ca1Cu2O8 (Tl-2212, Tc = 108 K), Tl2Ba2Ca2Cu3O10, (Tl-2223, Tc = 125 K), and Tl2Ba2Ca3Cu4O12 (Tl-2234, Tc = 115 K). Their structures are very similar to those of the members of the series Bi2Sr2Can−1CunO2n+4, with Bi replaced by Tl, and Sr replaced by Ba [8]. There are two Tl-cuprate homologous series of superconductors: (a) Tl2Ba2Can−1CunO2n+4 and (b) TlBa2Can−1CunO2n+3 which can be together written as TlmBa2Can−1CunO2(n+1)+m (m = 1, 2 and n = 1–6). Both have pseudo-tetragonal crystal structures, consisting of alternating single (or double) Tl–O layers and the perovskite-like Ba2Can−1CunO2n+1 layers, except Tl2Ba2CuO6, which exhibits a symmetry closer to orthorhombic/monoclinic.

Figure 2.5. Schematic of the structures of the series Bi2Sr2Can−1CunO2n+4. The tetragonal unit cell contains two semiconducting BiO and two insulating SrO layers, in addition to a single CuO2 layer for Bi-2201, and two and three CuO2 layers intercalated by Ca, for Bi-2212 and Bi-2223, respectively. Figure courtesy of Dr V K Aswal.

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The Tl monolayer series of superconducting oxides, namely TlBa2Can−1Cun O2n+3 (n = 1–5), incorporates Tl-1201 (Tl1Ba2Cu1O5, Tc = 0–50 K), Tl-1212 (Tl1Ba2Ca1Cu2O7, Tc = 80 K), Tl-1223 (Tl1Ba2Ca2Cu3O9, Tc =110 K), Tl-1234 (Tl1Ba2Ca3Cu4O11, Tc = 122 K), Tl-1245 (Tl1Ba2Ca4Cu5O13), and even Tl-1256 (Tl1Ba2Ca5Cu6O13). In a parallel development, a similar series of Hg-based superconducting cuprates were discovered having the general formulae Hg(Ba,Sr)2Can−1CunO2n+2+y (figure 2.6) which are very exciting because the members of this series Hg1Ba2Cu1O5 (Tc = 94 K), Hg1Ba2Ca1Cu2O7 (Tc = 129 K), Hg1Ba2Ca2Cu3O9 (Tc = 134 K), and Hg1Ba2Ca3Cu4O11 (Tc = 126 K), have the highest Tc values (~134 K, at ambient pressures) [9, 10]. Subsequently, a Tc of 164 K was recorded for Hg1Ba2Ca2Cu3O9 at 31 GPa [11]. Also known is a tetragonal superconductor (Tl, Pb)Sr2Ca2Cu3O9 having a Tc value of 122 K [17]. A layered structure reminiscent of the high-Tc cuprates is presented by another oxide, RuSr2GdCu2O8, which shows an interesting coexistence of ferromagnetism and superconductivity, too. It has double CuO4 layers alternating with layers of corner-sharing RuO6 octahedra interspersed with Gd and Ba. It becomes ferromagnetic at 132 K and superconducting at 40 K, without loss of ferromagnetism [18], The coexistence is considered to be an effect of crystal symmetry, ensuring that nodes in the conduction electron density occur exactly at the magnetic centers.

2.5 Spin-fluctuation as the pairing mechanism for high-Tc superconductors While the exact mechanism of high-Tc superconductivity is still highly controversial and elusive, most theoretical calculations, including phenomenological approaches, converge on magnetic fluctuations as the pairing mechanism for these systems. We shall provide a brief perspective on the type of superconductivity in different systems in chapter 3. A qualitative explanation on it is as follows.

Figure 2.6. Crystal structure of HgBa2CuO4+δ, HgBa2CaCu2O6+δ and HgBa2Ca2Cu3O8+δ. Reproduced from [16]. Copyright IOP Publishing. Reproduced with permission. All rights reserved.

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Superconducting Materials and Their Applications

In a high-Tc superconductor, the mechanism of superconductivity is thought to be similar to that for a conventional superconductor, except that in this case, the phonons virtually play no role and their role is replaced by a spin-density wave system, within close vicinity of a magnetic transition to, say an antiferromagnet. When an electron moves in a high-Tc superconductor, its spin creates a spin-density wave around it. This spin-density wave, in turn, causes a nearby electron to fall into the spin depression created by the first electron. Hence, a Cooper pair is formed. Eventually, when the system temperature is lowered, more spin density waves and Cooper pairs are created and superconductivity occurs when an unlimited supply of Cooper pairs, adequate to create a phase transition, happens. There is a strong Coulomb repulsion between electrons, which prevents pairing of the Cooper pairs on the same lattice site. Instead, the pairing of the electrons occurs at near-neighbor lattice sites. This is the so-called d-wave pairing, where the pairing state has a node (zero) at the origin. Quantitative theory of high-Tc superconductivity, in the name of ‘doped Mott insulator’ and ‘strongly correlated systems’, ‘quantum spin liquids (resonating valence bond)’ is an actively pursued front in the field of novel superconductors and related materials.

2.6 MgB2 2.6.1 Superconductivity and crystal structure of MgB2 Until 2001, the highest Tc for metals/alloys/intermetallics was 23 K, first set by Nb3Ge, and then equaled by an Y–Pd–B–C compound in 1994. The superconductor MgB2, discovered in 2001 has a Tc value of 39 K [19, 20], which raised high expectations in the field of fundamental and applied research. Although the critical field for MgB2 is modest (10 T), it is a material that can sustain Jc values of up to 104 A cm−2 and is also amenable to being fabricated into wires for applications where high field magnets made from wires and tapes are required, or where coils and solenoids are useful (see chapter 4). Since its useful temperature range can easily extend up to 25 K, it opens up possibilities of using liquid H2 as a coolant, the boiling point of which is ~20 K. The structure of MgB2 has graphite-type boron layers, separated by hexagonal close-packed layers of magnesium (figure 2.7). It is an intercalated graphite-like quasitwo-dimensional intermetallic, having B-planes, Mg-planes, and s–p electrons [21]. 2.6.2 Two-gap nature of superconductivity of MgB2 Quite similarly to the low-temperature superconductors (LTSC), such as Nb3Sn (Tc = 18 K), superconductivity in MgB2 arises from the phonon-mediated s-wave pairing (BCS mechanism), except that it has a two-gap nature, i.e. it is correlated with two distinct energy bands [22]. Specifically, MgB2 has two different types of electronic bondings, π and σ, giving rise to two superconducting gaps with energies Δπ (0) = 2.2 meV [23], and Δσ (0) = 7.1 meV [24], which arise from 3D π-bands and 2D σ-bands, respectively. Superconductivity in MgB2 mainly occurs in σ bands, though it has contributions also from π bands. 2-9

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Figure 2.7. MgB2 has the AlB2-type structure with a = 3.08 and c = 3.51 Å (space group: P6/mmm). 2D honeycomb layers formed by B-atoms are sandwiched by the triangular Mg-layers. Each Mg-atom is at the center of a hexagonal prism of B-atoms and each B-atom is surrounded by three other B-atoms, forming an equilateral triangle, as shown on the right. Figure courtesy, Dr V K Aswal.

STM data [25] on MgB2 confirms two distinct energy gaps, both of which vanish (close) simultaneously at the bulk Tc-value. Sp. heat measurements [26], too, supported two gaps in the superconducting state of MgB2. Most properties of MgB2 are anisotropic, e.g. the coherence length ξ, the penetration depth λ, the upper critical field Bc2 and the electrical resistivity ρ. Using the BCS expression ξ(0) = ℏvF/π Δ(0), where vF is the Fermi velocity (5.35 × 105 m s−1 for the π band and 4.40 × 105 m s−1 for the σ band) [25], one obtains two coherence lengths: ξπ (0) = 51 nm and ξσ (0) = 13 nm. The calculated value of ξπ (0) is in agreement with ξπ (0) = 49.6 ± 0.9 nm obtained from the fit of the vortex profile measured by scanning tunneling spectroscopy [23]. Josephson tunneling in MgB2-based junctions is discussed theoretically in the framework of a two-band model by Brinkman et al [27], and in the dirty limit by Mazin et al [28]. For single crystal samples of MgB2, having the critical temperature of 38.6 K as determined from the AC-susceptibility response at zero field, the temperature dependence of the lower and upper critical fields Hc1(T ) and Hc2(T ) have been determined from DC-magnetization and AC-susceptibility measurements. From the extrapolated value Hc2(T ) = 5.1 T, the value of ξab (0) = 8.0 nm obtained is close to the value found from the BCS theory for ξσ (0). Considering ξπ (0) = 33.6 nm, for the type-1 component and taking into account ξab (0) = ξσ (0) = 8.0 nm and Hc1(T ) = 0.241 T, one obtains λab = λσ = 38.2 nm.

References [1] Bednorz J G and Miiller K A 1986 Possible high Tc superconductivity in the Ba–La–Cu–O System Z. Phys. 64 189–93 [2] Tarascon J M, Greene L H, McKinnon W R, Hull G W and Geballe T H 1987 Superconductivity at 40 K in the oxygen-defect perovskites La2-xSrxCuO4-y Science 235 1373–6

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[3] Wu M K, Ashburn J R, Torng C J, Hor P H, Meng R L, Gao L, Huang Z J, Wang Y Q and Chu C W 1987 Superconductivity at 93 K in a new mixed-phase Y–Ba–Cu–O compound system at ambient pressure Phys. Rev. Lett. 58 908–10 [4] Cava R J et al 1988 Studies of oxygen-deficient Ba2YCu3O7-δ and superconductivity Bi(Pb)– Sr–Ca–Cu–O Physica C 153–5 560–5 [5] Statt B W, Wang Z, Lee M J G, Yakhmi J V, De Camargo P C, Major J F and Rutter J W 1988 Stabilizing the High-Tc superconductor Bi2Sr2Ca2Cu3010+x by Pb substitution Physica C 156 251–5 [6] Hazen R M et al 1988 100 K superconducting phase in the Tl-Ca-Ba-Cu-0 system Phys. Rev. Lett. 60 1657–60 [7] Gopalakrishnan I K, Sastry P V P S S, Gangadharan K, Phatak G M, Yakhmi J V and Iyer R M 1988 Synthesis and properties of a 125 K superconductor in the TI-Ca-Ba-Cu-O system Appl. Phys. Lett. 53 414–6 [8] Torardi C, Subramanian M A, Calabrese J C, Gopalakrishnan J, Morrissey K J, Askew T R, Flippen R B, Chowdhury U and Sleight A W 1988 Crystal structure of Tl2Ba2Ca2Cu3Ol0, a 125 K superconductor Science 240 631–4 [9] Putilin S N, Antipov E V, Chmaissem O and Marezio M 1993 Superconductivity at 94 K in HgBa2Cu04+δ Nature 362 226–8 [10] Schilling A, Cantoni M, Guo J D and Ott H R 1993 Superconductivity above 130 K in the Hg–Ba–Ca–Cu–O system Nature 363 56–8 [11] Gao L, Xue Y Y, Chen F, Xiong Q, Meng R L, Ramirez D, Chu C W, Eggert J H and Mao H K 1994 Superconductivity up to 164 K in HgBa2Cam-1Cum02m+2+δ (m =1, 2, and 3) under quasi-hydrostatic pressures Phys. Rev. B 50 4260–3 [12] Sleight A W, Gillson J L and Bierstedt P E 1975 High-temperature superconductivity in the BaPb1-xBixO3 systems Solid State Commun. 17 27–8 [13] Cava R J, Batlogg B, Krajewski J J, Farrow R, Rupp L W Jr., White A E, Short K, Peck W F and Kometani T 1988 Superconductivity near 30 K without copper: the Ba0.6K0.4BiO3 perovskite Nature 332 814–6 [14] Johnston D C 1976 Superconducting and normal state properties of Li1+x Ti2−x O4 spinel compounds. I. Preparation, crystallography, superconducting properties, electrical resistivity, dielectric behavior, and magnetic susceptibility J. Low Temp. Phys. 25 145–75 [15] Mook M A and Dogan F 2002 Phase diagram for stripes in YBa2Cu3O6+x supercondutors J. Phys. Chem. Solids 63 2163–6 [16] Antipov E V, Abakumov A M and Putilin S N 2002 Chemistry and structure of Hg-based superconducting Cu mixed oxides Supercond. Sci. Technol. 15 R31–49 [17] Subramanian M A, Torardi C C, Gopalakrishnan J, Gai P L, Calabrese J C, Askew T R, Flippen R B and Sleight A W 1988 Bulk superconductivity up to 122 K in the Tl-Pb-Sr-CaCu-O system Science 242 249–52 [18] Bernhard C, Tallon J L, Niedermayer C, Blasius T, Golnik A, Brücher E, Kremer R K, Noakes D R, Stronach C E and Ansaldo E J 1999 Coexistence of ferromagnetism and superconductivity in the hybrid ruthenate-cuprate compound RuSr2GdCu2O8 studied by muon spin rotation and dc magnetization Phys. Rev. B 59 14099–107 [19] Nagamatsu J, Nakagawa N, Muranaka T, Zenitani Y and Akimitsu J 2001 Superconductivity at 39 K in magnesium diboride Nature 410 63–4 [20] Kang W N, Kim H J, Choi E M, Jung C U and Lee S I 2001 MgB2 superconducting thin films with a transition temperature of 39 kelvin Science 292 1521–3

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[21] Muranaka T and Akimitsu J 2011 Superconductivity in MgB2 Z. Kristallogr. 226 385–94 [22] Souma S et al 2003 The origin of multiple superconducting gaps in MgB2 Nature 423 65–7 [23] Eskildsen M R, Kugler M, Tanaka S, Jun J, Kazakov S M, Karpinski J and Fischer Ø 2002 Vortex imaging in the π band of magnesium diboride Phys. Rev. Lett. 89 187003 [24] Choi H J, Roundy D, Sun H, Cohen M L and Louie S G 2002 The origin of the anomalous superconducting properties of MgB2 Nature 408 758–60 [25] Iavarone M et al 2002 Two-band superconductivity in MgB2 Phys. Rev. Lett. 89 187002 [26] Bouquet F, Fisher R A, Phillips N E, Hinks D G and Jorgensen J D 2001 Specific heat of Mg11B2: evidence for a second energy gap Phys. Rev. Lett. 87 047001 [27] Brinkman A, Golubov A A, Rogalla H, Dolgov O V, Kortus J, Kong Y, Jepsen O and Andersen O K 2002 Multiband model for tunneling in MgB2 junctions Phys. Rev. B 65 180517(R) [28] Mazin I I, Andersen O K, Jepsen O, Dolgov O V, Kortus J, Golubov A A, Kuz’menko A B and van der Marel D 2002 Superconductivity in MgB2: clean or dirty? Phys. Rev. Lett. 89 107002

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Superconducting Materials and Their Applications An interdisciplinary approach Jatinder Vir Yakhmi

Chapter 3 Materials contributing to physics of superconductivity, or holding potential for applications

In the previous two chapters, we have presented a historic perspective of superconductors which fall in the categories of metals, alloys, intermetallics, high-Tc cuprates and MgB2. In this chapter, we discuss various other categories of superconductors, which not only have historic importance, but the discoveries of which have also given meaningful inherent characteristics of superconductors, in general, and guidelines for exploring the potential for the applications of superconductors in particular.

3.1 Chevrel phase superconductors The Chevrel phases were discovered in 1971 [1] They are ternary molybdenum chalcogenides of the type MxMo6X8 where M could be any one of a number of metals or rare earth (4f) elements and X is S, Se or Te, and x is either 1 or 2. The building blocks of the crystal structure are M atoms which form a nearly cubic lattice in which the Mo6X8 molecular cluster units are inserted (figure 3.1). Each Mo6X8 is a slightly deformed cube with X atoms at the corners, and Mo at the face centres. Superconductivity depends on the Mo6X8 group, with the M ion having very little effect (for a review, see reference [2]). Chevrel phases can have Tc values as high as ~15 K, and high critical fields (see table 3.1). Critical current densities as high as 3 × 105 A cm−2 have been observed in a typical Chevrel phase, at 4.2 K. Chevrel phases were the first class of materials in which magnetic order and superconductivity were found to coexist. This made them exciting for physicists to study them as a model system where such an anomalous coexistence was actually occurring, even though the superconducting Tc-values, for a Chevrel phase compound with such a ‘coexistence’ were low, between 1.5 and 2 K, while the Néel temperatures TN) were even lower, between 0.5 and 1 K. But, the interesting conclusion was that the long-range magnetic order could be sustained even while the superconducting state is doi:10.1088/978-0-7503-2256-0ch3

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Superconducting Materials and Their Applications

Figure 3.1. On the left is shown the arrangement of Mo6X8 Building blocks of the Chevrel phase, MxMo6X8. structure. Each tilted box denotes an Mo6X8 (X = S, Se or Te) unit. The dashed lines show (Mo–Mo) intercluster liaisons and (Mo–X1) intercluster liaisons between different Mo6X8 units. On the right is shown the elementary cell of rhombohedral structure of MxMo6X8. Inserted cations M, such as Pb are located in position (0,0,0), the unit block Mo6X8 is turned by an angle of about 27° around the ternary axis. Reproduced from [4]. Copyright IOP Publishing. Reproduced with permission. All rights reserved. Table 3.1. Values of Tc and critical field for selected Chevrel phase superconductors.

Chevrel phase

Tc (K)

B* (Τ)

PbMo6S8 SnMo6S8 LaMo6S8 PbMo6Se8

15 12 7 3.6

60 34 45 3.8

prevalent! This was enigmatic because all previous observations had shown that long range magnetic order and superconductivity, the two ground states of matter, do not like to coexist in any material! Specifically, the long-range magnetically ordered state is associated with the localization of electrons, whereas superconductivity, on the other hand, is a state in which electrons form pairs which can flow without resistance. There are just four Chevrel phase compounds where superconductivity is found to coexist with magnetic order (though only of the antiferromagnetic type), viz. (RE)Mo6X8 with RE = Gd, Tb, Dy and Er, where antiferromagnetism sets in, respectively, at TN = 0.84, 0.9, 0.4 and 0.15 K, coexisting with superconductivity which occurs below Tc = 1.4, 1.65, 2.1 and 1.85 K in them, respectively. However, a re-entrant superconductivity was observed in the case of HoMo6S8, where a superconducting state exists only between two critical temperatures, viz. 2 K and 0.65 K. Between these two temperatures a non-uniform ferromagnetic phase appears in the presence of the superconducting state. Below 0.65 K, of course, a long-range ferromagnetic order develops, destroying superconductivity. Lynn et al [3] found that for HoMo6S8, superconductivity and a spiral ferromagnetic state coexist at temperatures between 0.71 K and 0.61 K.

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Despite high values of the critical field, B*, for some Chevrel Phase superconductors, their potential for utilization in applications such as high-field magnets is limited, since all of them are extremely brittle, making it difficult to draw wires from them.

3.2 Rare earth rhodium boride superconductors, MRh4B4 As early as in 1977, superconductivity at fairly high temperatures (up to 12 K) was demonstrated in rare earth rhodium borides having a general formula MRh4B4, where M is a transition element, or a rare-earth element such as Y, Nd, Sm, Er, Tm, Lu, Gd, Tb, Dy, Ho or Th, by Bernd Matthias and co-workers [5]. Their superconducting transition temperatures range from ~2.5 K for SmRh4B4 to about 12 K for LuRh4B4. Interestingly, some of them showed ferromagnetic behaviour, too, but mostly at temperatures below their superconducting region of temperature, and not as a coexistent state. Neutron scattering studies showed that the destruction of superconductivity observed for the re-entrant superconductor ErRh4B4 at Tc2 = 1.0 K is accompanied by the development of long-range ferromagnetic ordering of the Er-sublattice [6]. Further studies showed evidence of oscillatory magnetic fluctuations in ErRh4B4 caused by the electromagnetic coupling of ferromagnetic and superconducting order parameters [7]. For different rare-earth rhodium borides, RERh4B4, the values of superconducting transition temperature, Tc (av.), are (in brackets): YRh4B4 (11.30 K), NdRh4B4 (5.30 K), SmRh4B4 (2.48 K), ErRh4B4 (8.53 K), TmRh4B4 (9.80 K), LuRh4B4 (11.65 K), Lu0.75Th0.25Rh4B4 (11.93 K), Sc0.65Th0.35Rh4B4 (8.74 K), and ThRh4B4 (4.32 K). As mentioned above, a few of the RERh4B4 compounds are ferromagnetic with Curie temperatures Tc (av.) being GdRh4B4 (5.62 K), TbRh4B4 (7.08 K), DyRh4B4 (12.03 K), and HoRh4B4 (6.56 K). Noticeably, there is a sudden switch to magnetism when Er is replaced with Ho in these ternary borides, which have tetragonal symmetry. This is in contrast with the rhombohedral RE–molybdenum sulphides, i.e. the Chevrel phase superconductors [1, 8].

3.3 Rare earth nickel borocarbides Also called quaternary borocarbides (QBCs), a new class of layered transition metal rare-earth borocarbide superconductors RNi2B2C (nonmagnetic R = Y, Lu, Sc; magnetic R = lanthanide elements in a R3+ state) was discovered in 1994 [9–11]. An excellent review of this unique class is provided by L C Gupta [12]. QBCs have provided the first instance of a homogeneous coexistence of superconductivity and ferromagnetism at all temperatures below Tc. This becomes possible because the two antagonistic long-range orders are carried by different species of electrons that interact only weakly. The crystal structure of RNi2B2C (R = Y, RE) compounds is tetragonal of the ThCr2Si2 type, (space group, I4/mmm) with carbon atoms, C, located in the plane of R (RE) atoms [13, 14], as depicted in figure 3.2, showing RC rock salt type planes (R = RE, and C = carbon), separated by Ni2B2 layers stacked along the c-axis [15]. More general structures with more than one RC layer are also possible [16].

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Superconducting Materials and Their Applications

Figure 3.2. Tetragonal crystal structure of RNi2B2C, where R stands for a rare earth atom. Representative cell parameters are a = 0.352 nm, c = 1.053 nm for R = Ho. Figure courtesy of Dr V K Aswal. Table 3.2. Superconducting and antiferromagnetic transition temperatures of RNi2B2C (R: rare earth).

RE

Tc (K)

TN (K)

Tm Er Ho Y Yb Lu Dy Tb Gd

10.8 10.5 8.5 15 0 16 6.2 0 0

1.5 6.5 6 0 0 0 10 15 19.5

Note: Ni can be substituted in certain cases, with Pd. YPd2B2C superconducts below 23 K.

Some QBCs also order magnetically at temperatures comparable to the superconducting transition temperature, Tc, and are therefore model systems to probe the interplay between superconductivity and magnetism. Magnetic superconductors among RNi2B2C (R = Dy, Ho, Er, Tm) depict superconductivity coexisting with antiferromagnetic order, with approximate values of Tc and TN as listed in table 3.2 [14]. Cava et al reported superconductivity below 15.5 K, 16.5 K, 11 K, 11 K, and 8 K, respectively, in single phase materials, RNi2B2C for R = Y, Lu, Tm, Er, and Ho [9]. In fact, superconductivity at 23 K was observed for the multi-phase YPd5B3C0.3, matching the highest known then for intermetallic Nb3Ge. Interestingly, it is the nonmagnetic compounds, YNi2B2C and LuNi2B2C, having comparatively high Tc values of 16.5 K and 15.5 K [table 3.2], which serve as reference systems to study the 3-4

Superconducting Materials and Their Applications

effects of competition of magnetic order and superconductivity in the more difficult systems RNi2B2C with both magnetic and superconducting phases.

3.4 Heavy fermion superconductors Certain materials called heavy fermion (HF) systems, exhibit a variety of interesting phenomena, including quantum phase transitions between magnetically ordered state and superconductivity. First reported by Steglich and co-workers in 1979 [17], these are compounds in which the conduction electrons move very sluggishly, as if they carry a very large effective mass, m* ≈ 100–1000 me, which is the reason these are known as heavy fermion superconductors. They often contain RE (4f) elements such as Ce or Yb, or actinides (5f) elements like U. They generally have an antiferromagnetic ground state, with large effective masses of electrons (m* up to 1000 × me) at low temperatures. The transition temperatures for them are low, such as Tc = 0.5 K for CeCu2Si2, 0.48 K for UPt3, 6 K for CeRu2, and 2 K for UPd2Al3. There are other known compounds of this class, such as UBe13 and URu2Si2 which offer novel physics at low temperatures. The HF superconductors are of special interest to researchers who want to investigate and establish the mechanism of superconductivity in materials where the electrons move sluggishly. For instance, the HF superconductors CePd2Si2, CeMIn5 exemplify tunable superconductors obtained through competition between the ground states of magnetism and superconductivity, where the e–ph BCS mechanism is breaking down. Many heavyfermion materials possess a novel form of superconductivity thought to originate from pairing by magnetic fluctuations, or with a quantum critical point (QCP). CeCoIn5 has the highest transition temperature Tc = 2.3 K amongst heavy-fermion superconductors with quantum criticality, and is an excellent candidate to study the relationship between QCP and unconventional superconductivity [18].

3.5 Fe–pnictide superconductors Iron, being magnetic, has long been seen as a non-candidate while looking for new superconductors, simply because magnetism and superconductivity are traditionally considered incompatible. Nevertheless, Professor Hideo Hosono from Tokyo Institute of Technology, succeeded in producing a new type of Fe-based superconductors (the Fe-oxypnictides), in 2008, reporting a critical temperature of 26 K for LaFeAsO pnictides with composition La[O1−xFx]FeAs (x = 0.05–0.12) [19]. This became possible because the five unbound electrons in iron facilitated superconductivity by sustaining the pairing mechanism, possibly, through magnetic excitations. Quickly thereafter, a Tc as high as 55 K was reported for another Fe–pnictide, a layered quaternary compound Sm[O1−xFx]FeAs [20], which was 15 K above that of MgB2, lower only than that of the cuprate superconductors. When superconductivity in the Fe-based superconductors was discovered, the question immediately arose: how similar are they to cuprates? Indeed, they are, to the extent that Fe–pnictides, too, are layered compounds like cuprate superconductors, with FeAs layers in them; and d-electrons (from Fe, as from Cu in cuprates) play a key role in the origin of their superconductivity.

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Superconducting Materials and Their Applications

Interestingly, a layered structure, which plays the role of a superconducting layer, such as the CuO2 plane among high-Tc cuprates or the Fe2An2 (An = P, As, S, Se, Te) layer in Fe-based superconductors, has opened new vistas in the fields of physics and chemistry of low-dimensional superconductors, because many structural analogs could be designed by varying the structure or the alignment of the spacer layers and/ or superconducting layers. Doping in cuprates is accomplished by replacing one of the spacer ions with another one with different valence or adding extra out-of-plane oxygen, e.g. La2−xSrxCuO2, Nd2−xCexCuO2, and YBa2Cu3O6+δ. Quite similarly, doping in Fe-based superconductors is achieved by replacing the spacer ion, as has been done in the case of LaFeAsO1−xFx and Sr1−xKxFe2As2, or by in-plane substitution of Fe with Co or Ni, as in Ba(Fe1−xCox)2As2 and Ba(Fe1−xNix)2As2, or by replacing Ba with K, Ba1−xKxFe2As2. A typical feature common to the crystal structure of Fe-pnictide superconductors is the occurrence of an Fe square lattice among them, such as in LaFeAsO, BaFe2As2, and FeSe [21]. The phase diagrams of cuprates and many Fe-based superconductors are also similar. In both cases, the undoped compounds exhibit antiferromagnetism, which vanishes with doping; and superconductivity appears at some non-zero doping content, and then disappears with further doping, such that the plot of Tc versus doping content exhibits a ‘dome’-like curve. However, that is where the similarity ends. The first striking difference is that the undoped cuprates are Mott insulators, but Fe-based superconductors are metals. Besides, the long-range ordered Néel phase in cuprates vanishes before superconductivity appears, whereas in Fe-based superconductors, the competition between these orders can take several forms. One theoretical idea links the emergence of superconductivity in Fe-based superconductors to an uncorrelated metallic state in Fe-based superconductors where ‘nesting’ features of the Fermi surface geometry generate antiferromagnetic spin fluctuations, which then mediate Cooper pairing leading to superconductivity [22].

3.6 Fe–selenide superconductors α-FeSe has a layered crystal structure with space group, P4/nmm. In the absence of any applied pressure, Fe1.01Se undergoes a tetragonal to orthorhombic structural distortion at 90 K. This compound shows superconductivity at 8.5 K which rises to 36.7 K under applied pressure of 8.9 GPa [23]. An off-stoichiometric compound FeSe0.88 exhibits superconductivity with Tc = 8 K at ambient pressure, which rises to about 20 K under 4 GPa. Superconductivity above 100 K has been reported in single-layer FeSe films grown on doped SrTiO3 [24]. FeTe, has a structure analogous to that of FeSe, but it is antiferromagnetic. FeTe1−xSex shows superconductivity at temperatures up to 14 K under ambient pressure for x = 0.4, when the AF order in FeTe is suppressed by raising the value of Se-content x [21]. It appears that the correlated superconductivity in FeSe arises from orbital selective Cooper pairing of electrons, predominantly from the dyz orbitals of Fe atoms [25]. Partial substitution of Te by S also suppresses antiferromagnetism in FeTe, leading to superconductivity at Tc value of 7 K for FeTe1−xSx (for 0.06 > x > 0.12 approximately), as shown by Deguchi et al [26]. 3-6

Superconducting Materials and Their Applications

Five Fe-based systems that show superconducting behaviour, namely FeSe, LiFeAs, SrFe2As2, LaFeAsO/SrFeAsF, and Sr3Sc2O5Fe2As2, all have tetragonal structure. Each one of these pnictide superconductors has an active planar Fe layer [27]. For BaFe2As2, superconductivity exists for applied pressures in the range of P = 2.2 GPa to 6 GPa. At 5.5 GPa the value of Tc is 30.5 K. Application of pressure and chemical substitution have similar influence. For Ba1−xKxFe2As2, the application of pressure leads to a phase transition suppressing the tetragonal to orthorhombic phase, and reduction in the As–Fe–As bond angle and Fe–Fe bond distance, which converts the material from a semimetal into a superconductor, with Tc peaking at about 38 K at x = 0.4 at ambient pressure. According to an analysis made by Okabe et al [28], anion height is a key factor determining the Tc of Fe-based superconductors containing various anions. Tc, as a function of anion height (hanion) for various iron-based superconductors shows a clear correlation between Tc and hanion, indicating the importance of anion positions in these ironbased superconductors (figure 3.3). As the value of anion height increases, Tc of the iron-based superconductors starts to increase dramatically, going up to ~55 K at anion height hanion of 1.38 Å, which corresponds to the optimum value of the LnFeAsO system. Interestingly, the magnetic state associated with a spin-density wave (SDW) coexists with the superconducting state for a limited range of K-content (x = 0.2) for Ba1−xKxFe2As2. SDW and superconductivity (Tc = 25 K) coexist also for Sr0.82K0.18Fe2As2. The parent compound SrFe2As2 has a high value of SDW transition temperature (TN = 205 K) among iron pnictides.

Figure 3.3. Tc versus anion height (hanion) for various iron- and Ni-based superconductors. Triangle: FeSe, circle: other pnictides. Lanthanides (Ln) indicate LnFeAsO (1111) system. 111, 122, and 42226 represent LiFeAs, Ba0.6K0.4Fe2As2, and Sr4Sc2Fe2P2O6, respectively. The yellow line is a fit. The inset shows a schematic view of hanion. Reproduced with permission from [28], copyright (2010) by the American Physical Society.

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Superconducting Materials and Their Applications

3.7 Hydride superconductors As early as in 1968, Ashcroft had proposed that metallic hydrogen would become a high temperature superconductor [29], but to date this goal has not been realized. Nonetheless, that has given rise to an impetus to search for high temperature superconductivity in different categories of hydrogen-rich metallic materials under the experimentally available high pressures up to 200–300 GPa [30]. Superconductivity was indeed reported, in 2015, at 203 K, confirming both zero electrical resistance and the Meissner effect by compressing of H2S at 150 GPa by Drozdov et al [31]. Superconducting phase has been established in this case to be the bcc cubic H3S [32]. Superconductivity in sulfur hydrides is considered to owe its origin to the phonon mechanism. However, the picture differs from the conventional one in important ways. The phonon spectrum in sulfur hydride is broad, and it has a complex structure. In a narrow region near P ≈ 150 GPa the critical temperature rises sharply from Tc ≈ 120 to ≈ 200 K. The sharp structural transition, which produces the highTc phase, is a first-order phase transition caused by interaction between the order parameter and lattice deformations. Other hydrides, e.g. CaH6 and MgH6, are expected to display even higher values of Tc, perhaps up to room temperature. However, the fundamental challenge lies in the creation of a structure which is capable of displaying a high Tc at ambient pressure [33]. More recent research to look for superconductivity at higher temperatures has focused on hydrogen-rich superhydride materials, LaHn with n > 6, under very high pressures. Electrical transport studies conducted under pressures of 180–200 GPa have shown signatures of superconductivity for lanthanum superhydride samples, LaH10±x, at 260 K. The transition temperature is close to that predicted by the BCS-type calculations for LaH10 at such pressures, as demonstrated by Somayazulu et al [34].

3.8 Organic superconductors The diamagnetic ring currents of aromatic molecules are nondissipative currents similar in many respects to the persistent currents of superconducting rings. Therefore, London [35] had suggested that aromatic compounds (viz. anthracene, naphthalene, etc) might exhibit a permanent current running along their aromatic ring systems even under magnetic fields. Metal-like conduction was first observed for a, not-so-stable, molecular salt of perylene oxidized with bromine, which showed metal-like conduction between open shell molecular species [36]. π-electron molecules are able to accept or donate their electron depending on their electro-affinity or their ionization potential. Historically, tetracyanoquinodimethane (TCNQ, formula (NC)2CC6H4C(CN)2) became the first example an electrically conducting acceptor molecule, credit for the discovery of which was earned by DuPont in 1960 [37]. TCNQ can be used to prepare charge transfer salts, such as by reducing it to form an open shell anion radical, and placing it in contact with π-electron donors, such as tetrathiafulvalene (TTF) (figure 3.4). A fillip to the search for superconductivity among organic materials was given in 1964 when W A Little [38, 39], proposed a model for a macromolecular high 3-8

Superconducting Materials and Their Applications

Figure 3.4. (a) Schematic of structures of donor molecule TTF (tetrathiafulvalene), having formula (H2C2S2C)2, and (b) acceptor molecule TCNQ (tetracyanoquinodimethane) having formula (NC)2CC6H4C (CN)2. Figure courtesy of Dr V K Aswal.

temperature superconductor in which he suggested that a hypothetical molecule might turn into a superconducting solid, if the structure of this molecule has two attributes: (a) a ‘conjugated’ spine of carbon atoms connected by alternating single and double bonds, which not only serves as an electronic conductor, but also forms the backbone of the polymeric system, along which electrons could travel freely; and (b) attached to the above spine are the side chains, or side groups which are highly polarizable molecules. Little suggested that these side groups could be made of a dye such as diethylcyanine iodide, a hypothetical dye. These side groups should be joined periodically to the spine (like ribs), as shown in a schematic in figure 3.5. The electronic polarization of the side molecules should lead to some attraction between electrons in the main thread, which exchange excitons propagating along the side molecules. Little hypothesized that electrons (charge carriers) moving along the spine would create a +ve charge at the dye molecule, at its end closer to the spine, since their electric field polarizes the side group. As the electron moves up the spine, it would leave a trail of induced positive charges, thereby allowing a second electron (sort of pulling it in) to be attracted towards this region and hence to the first electron, and the two electrons then form a pair. Little predicted that this model can provide organic superconductors with very high Tc values, even in excess of 1000 K. The suggestion made by Little for very high Tc values was based in the excitonic mechanism [40], which in turn was based on the isotope effect, as per the BCS theory in the phononic mechanism [41], viz. Tc ∝ M−1/2. Since, it is the much lighter electrons which get polarized instead of the heavy polarizable dye molecules (ions) attached to a conjugated spine in Little’s model of the organic lattice, the small

3-9

Superconducting Materials and Their Applications

Figure 3.5. Schematic of Little’s suggestion. Charge carriers moving along a conducting spine are bound via polarizable side groups. Polarizable sidechains are intended to provide a means for screening the repulsive interaction for delocalized carriers moving along the spine. Charge carriers e1 and e2 form a Cooper pair in the conducting spine. Figure courtesy of Dr V K Aswal.

electronic mass me predicts very high Tc values of the order of (M/me)1/2 compared to that seen for a conventional superconductor! Superconductivity was first discovered in 1980 in organic charge-transfer (donor– acceptor) compounds, which have come to be known as the Bechgaard salts, though Tc values were quite low, and that too mostly under applied pressures [42]. These compounds have a triclinic structure and a general formula (TMTSF)2X, where X is an anion, and are nearly one-dimension chain conductors, with very low carrier densities. The donor cation molecule TMTSF stands for tetramethyl tetraselenafulvalene (figure 3.6(a)). The Tc values for X = ClO4, PF6 and ReO4 were 1.2 K (at ambient pressure), 1.2 K (under 9 kbar) and 9.5 K (under 9.5 kbar), respectively. The electronic properties of Bechgaard salts are extremely anisotropic, as expected from chain compounds, and the samples are often available as single crystals. The sulfur-donor TMTTF (tetramethyl tetrathiafulvalene, with Se replaced with S in TMTSF) based structures TMTTF2X have also been found to be superconducting. The search for superconductivity in donor–acceptor compounds further led to the development of the largely two-dimensional organic superconducting charge-transfer salts, β-(BEDT-TTF)2X, where BEDT (figure 3.6(b)) stands for the donor molecule bis(ethylenedithio)-tetrathiafulvalene, and X is an anion (acceptor) such as I3, IBr2 or AuI2 [43–47]. κ-type molecular arrangement consists of two types of BEDT-TTF dimers with different orientations. Values of superconducting transition temperatures, Tc, for κ-(BEDT-TTF)2X are 1.2 K, 8.1 K, 2.5 K and 10 K, respectively, for X = I3 (βL phase), I3 (βH phase), IBr2 and Cu(NCS)2. Subsequently, superconductivity at

3-10

Superconducting Materials and Their Applications

Figure 3.6. (a) Structure of tetramethyl tetraselenafulvalene (TMTSF) molecule, formula C10H12Se4. Colors of atoms shown are selenium (orange), carbon (green) and hydrogen (grey). (b) Structure of bis(ethylenedithio)tetrathiafulvalene (BEDT-TTF) molecule, formula C10H8S8. Colors of atoms shown are as sulfur (yellow), carbon (green) and hydrogen (grey). Figures courtesy of Dr V K Aswal.

Tc = 11.2 K has been observed for the compound (BEDT-TTF)2Cu[N(CN)2]Br in 2011 [48]. There are several other examples of organic superconductor molecules, such as, λ-BETS2FeCl4 in which the very planar BETS (bisethylendithiotetraselenafulvalene) molecules form conduction layers parallel to the ac-plane, shows a field-induced superconducting transition. [(CH3)4N][Ni(dmit)2]2 is an example of the a molecular superconductor without TTF-type π-donor molecules. In 2012, Xue et al [49] reported superconductivity at 33 K in K-doped 1,2:8,9dibenzopentacene (C30H18), the highest Tc value thus far for an organic superconductor under ambient pressure, raising the possibility of exploring the polycyclic-aromatichydrocarbons (PAHs) as candidates for high-Tc superconductivity.

3.9 Fulleride superconductors Buckminsterfullerene molecule C60 with a diameter of 7.1 Å, contains 60 C-atoms. C60 itself is not a superconductor, but it can be doped with alkali metals to form A3C60, the fullerides, which form an fcc lattice with a lattice parameter of 10 Å (figure 3.7), where A = the alkali atoms K or Cs which occupy interstitial sites between the large C60 molecules. Several fullerides have been shown to become superconductors at fairly high temperatures. Starting with K3C60 which showed superconductivity at Tc = 18 K in 1991 [50, 51], several other examples are Cs3C60 (Tc = 40 K), Rb3C60 (29 K) [52], Cs2RbC60 (Tc = 33 K) [53], K2RbC60 (22 K), Rb2KC60 (25 K), and Cs3C60 (>40 K, under high applied pressure) [51, 54]. Although the isotope effect observed in fullerides is BCS-like, there is some evidence that superconductivity might not be ‘conventional’. Intramolecular C60 phonons seem to contribute the most important part of the pairing interactions [55].

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Superconducting Materials and Their Applications

Figure 3.7. Schematic of the structure of A3C60, where A = an alkali atom K, Cs, or Rb. Large grey spheres represent fulleride molecules C60, in an fcc lattice and A = an alkali atom K,Cs, or Rb. Among A-ions, those in octahedral sites are shown in orange color and those in tetrahedral sites in green. Figure courtesy of Dr V K Aswal.

3.10 Superconducting materials—the continuing search The journey from oxides to cuprates took the values of superconducting transition temperatures, Tc, through quantum jumps several times during a period of just about 25 years. Starting with the discovery of superconductivity in semiconducting SrTiO3, in its reduced form SrTiO3−δ. at a Tc of ~0.3 K in 1964 [56], the oxide system BaPb1−xBixO3 was shown to superconduct at 9 K for x = 0.05, rising to a maximum Tc of 13 K for x = 0.3 by Sleight et al in 1975 [57]. Quickly thereafter, the spinel oxide Li1+xTi2−xO4 was shown to become superconducting with Tc = 13 K in 1976 [58]. The search among oxides (the non-cuprates) culminated in the demonstration of superconductivity at 30 K in Ba1−xKxBiO by Cava et al in 1988 [59]. But this was two years after the historic discovery of superconductivity at about 30 K in La1−xBaxCuO4 by Bednorz and Muller in 1986 [60], which led to a glorious phase of the emergence of high-Tc cuprates, first in 1987 when the liquid nitrogen temperature ceiling was pierced by the demonstration of superconductivity at 90 K in YBa2Cu3O7−δ, and then with quick discoveries of Bibased, Tl-based and Hg-based cuprate superconductors culminating in a value of Tc = 165 K (though under pressure) in HgBa2Ca2Cu3O8+x, in 1988. We tried earlier to show the progress of high-Tc superconductivity in cuprate superconductors in this book in figure 2.1. We now show a complete picture of the journey of increasing Tc of superconductors with time, in almost every category of materials, since the discovery of the phenomenon of superconductivity in 2011, in figure 3.8. We have also shown in this figure 3.8 the combined data on hydrides, viz. Tc of 203 K obtained on H3S samples at 150 GPa by Einaga et al in 2016 [32], and a Tc of 260 K for LaH10 obtained at 180 GPa by Somayazulu et al in 2019 [34], updating it with the most recent 2020 results of superconductivity seen at 288 K for C–S–H ternary system at applied pressures of 267 GPa by Snider et al [61], and a Tc of 294 K reported by Grockowiak et al [62] by applying a pressure of 180 GPa on samples of a La-based superhydride which, most excitingly, shows signatures of superconductivity at 550 K under the same 180 GPa pressure, but after several thermal excursions. 3-12

Superconducting Materials and Their Applications

Figure 3.8. The journey of increasing Tc of superconductors with time since the discovery of superconductivity phenomenon in 2011. Please note a change in the scales of time once, and of Tc (K) twice for a clearer perspective. Figure courtesy of Dr V K Aswal.

The progress made by materials scientists in discovering the large variety of superconducting materials is indeed noteworthy. A few points need to be made before we move on: (i) Over 55 elements in the periodic table have been shown to exhibit superconducting behavior (many of them were listed in figure 1.6), though most of them do so at very low temperature, assisted often by application of high pressures. Among them, a notable example is Li, which has a Tc of 20 K under applied pressure; (ii) boron-doped diamond shows superconductivity below 11 K; (iii) superconductivity is shown by some graphite intercalation compounds, viz. C6Yb at 6.5 K and C6Ca, at 11.5 K; and (iv) it stands out that the Chevrel phase compound PbMo6S8 (Tc = 14 K) has a high value of Hc2, 65 T at 4.2 K, but it is not convenient to shape it into wires/cables for exploitation in high-field magnets. Similarly, the Tc and Hc2 (at 4.2 K) values for Nb3Ge and Nb3(Al,Ge) are 23.2 K and 37 T, and 20.5 K and 41 T, respectively, the workhorses for making high-field magnets, nonetheless still continue to be NbTi (10.2 K and 12 T) and Nb3Sn (18.3 K and 26 T). Further discussion on the potential of high-Tc cuprates and MgB2 towards their application for high-field magnets appears elsewhere in this book.

3.11 Types of superconductivity Superconducting wave-function has spin (S) part and orbital (L, spatial) part. Antisymmetric spin singlet Cooper pairs have even-parity orbital angular wavefunction (S = 0, L = 0, s-wave; S = 0, L = 2, d-wave) and symmetric spin triplet Cooper pairs have odd-parity orbital wave function (S = 1, L = 1, p-wave; S = 1, 3-13

Superconducting Materials and Their Applications

L = 3, f-wave). For p-, d-, and f-wave superconductors the phase and/or momentumdependence of superconducting wave function matters. Compared with the low-Tc compounds like Nb3Ge which were typical s-wave paired BCS superconductors, the compound Sr2RuO4 [63], and some organic superconductors exhibit what is known as p-wave pairing, whereas the class of cuprate superconductors are thought to obey d-wave superconductivity. We can have either singlet pairing, with a complex scalar order parameter, Or triplet pairing with a complex vector order parameter. Singlet pairing, s-, has full square symmetry, may have nodes, while the d states have nodes required by symmetry. s-wave superconductors are protected against non-magnetic impurity scattering (Anderson’s theorem), but unconventional superconductors are not. Famous examples of superconductors in these categories are as follows. For s-wave: Nb, NbTi, Nb3Ge, and perhaps pnictides; for p-wave triplet superconductivity: Sr2RuO4; for d-wave: cuprates (as stated above), and probably CeCoIn5; and for f-wave: most probably UPt3. Superfluid 3He has triplet pairing, whereas high-Tc cuprates obey dx2–y2 pairing. To determine the nature of superconductivity experimentally, whether it is s-wave or d-wave, one makes use of the power laws in low temperature properties, such as the penetration depth, or even makes direct observations of gap structure with ARPES. For instance, experimental data on both MgB2 and K3C60 seem to indicate a full s-wave like gap, whereas the borocarbides, and 2D organics have shown evidence for gap nodes indicating possibly d-wave (though it is still controversial). On the other hand, the iron-based pnictide materials appear to conform to s-wave paired BCS superconductivity. A special technique employed to check symmetry-breaking among superconductors is MuSR (muon spin rotation). Muons are produced preferentially in a single spin orientation (because of parity violation in the weak force). Injected into a solid they precess in any local magnetic field before decaying. In an MuSR (muon spin rotation) experiment, the gamma detected from the decay is also dependent on the spin orientation, making it possible to determine the field B inside the material. The sudden change of internal field B at Tc indicates a magnetic transition, but at exactly the same temperature as superconductivity. Hence the superconductivity is intrinsically magnetic and T breaking. The bct crystal of Sr2RuO4 shows only two possible time reversal pairing states: d-wave singlet or p-wave triplet. The muon spin rotation experiments show spontaneous time reversal symmetry breaking below Tc for the case of LaNiGa2 [64].

References [1] Chevrel R, Sergent M and Prigent J 1971 Sur de nouvelles phases sulfurées ternaires du molybdène J. Solid State Chem. 3 515–9 [2] Peña O 2015 Chevrel phases: past, present and future Physica C 514 95–112 [3] Lynn J W, Shirane G, Thomlinson W, Shelton R N and Moncton D E 1981 Magnetic properties of the reentrant ferromagnetic superconductor HoMo6S8 Phys. Rev. B 24 3817–29

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[4] Roche C, Pecheur P, Toussaint G, Jenny A, Scherrer H and Scherrer S 1998 Study of Chevrel phases for thermoelectric applications: band structure calculations on MxMo6Se8 compounds (M = metal) J. Phys.: Condens. Matter 10 L333–9 [5] Matthias B T, Corenzwit E, Vandenberg J M and Barz H E 1977 High superconducting transition temperatures of new rare earth ternary borides Proc. Natl. Acad. Sci. USA 74 1334–5 [6] Moncton D E, McWhan D B, Eckert J, Shirane G and Thomlinson W 1977 Neutron scattering study of magnetic ordering in the reentrant superconductor ErRh4B4 Phys. Rev. Lett. 39 1164–6 [7] Moncton D E, McWhan D B, Schmidt P H, Shirane G, Thomlinson W, Maple M B, MacKay H B, Woolf L D, Fisk Z and Johnston D C 1980 Oscillatory magnetic fluctuations near the superconductor-to-ferromagnet transition in ErRh4B4 Phys. Rev. Lett. 45 2060–3 [8] Fischer O, Treyvaud A, Chevrel R and Sergent M 1975 Superconductivity in the RExMo6S8 Solid State Commun. 17 721–4 [9] Cava R J et al 1994 Superconductivity in the quaternary intermetallic compounds LnNi2B2C Nature 367 252–3 [10] Nagarajan R, Mazumdar C, Hossain Z, Dhar S K, Gopalakrishnan K V, Gupta L C, Godart C, Padalia B D and Vijayaraghavan R 1994 Bulk superconductivity at an elevated temperature (Tc ~12 K) in a nickel containing alloy system Y-Ni-B-C Phys. Rev. Lett. 72 274–7 [11] Müller K-H and Narozhnyi V N 2001 Interaction of superconductivity and magnetism in borocarbide superconductors Rep. Prog. Phys. 64 943–1008 [12] Gupta L C 2006 Superconductivity and magnetism and their interplay in quaternary borocarbides RNi2B2C Adv. Phys. 55 691–798 [13] Siegrist T, Zandbergen H W, Cava R J, Krajewski J J and Peck W F Jr 1994 The crystal structure of superconducting LuNi2B2C and the related phase LuNiBC Nature 367 254–6 [14] Mazumdar C and Nagarajan R 2015 Quaternary borocarbides: relatively high Tc intermetallic superconductors and magnetic superconductors Physica C 514 173–83 [15] Hott R, Kleiner R, Wolf T and Zwicknagl G 2004 Superconducting materials—a topical review Frontiers in Superconducting Materials ed A V Narlikar (Berlin: Springer) pp 1–69 [16] Hilscher G and Michor H 1999 Superconductivity and magnetism in quaternary borocarbides and boronitrides Studies in High Temperature Superconductors vol 28 (New York: Nova Science) pp 241–86 [17] Steglich F, Aarts J, Bredl C D, Lieke W, Meschede D, Franz W and Schäfer H 1979 Superconductivity in the presence of strong Pauli paramagnetism: CeCu2Si2 Phys. Rev. Lett. 43 1892–6 [18] Tanatar M A et al 2005 Unpaired electrons in the heavy-fermion superconductor CeCoIn5 Phys. Rev. Lett. 95 067002 [19] Kamihara Y, Watanabe T, Hirano M and Hosono H 2008 Iron-based layered superconductor La[O1-xFx]FeAs (x = 0.05−0.12) with Tc = 26 K J. Am. Chem. Soc. 130 3296–7 [20] Zhi-An R et al 2008 Superconductivity at 55 K in iron-based F-doped layered quaternary compound Sm[O1-xFx]FeAs Chin. Phys. Lett. 25 2215–6 [21] Mizuguchi Y and Takano Y 2011 Superconductivity in PbO-type Fe chalcogenides Z. Kristallogr. 226 417–34 [22] Hirschfeld P J, Korshunov M M and Mazin I I 2011 Gap symmetry and structure of Fe-based superconductors Rep. Prog. Phys. 74 124508

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[23] Medvedev S et al 2009 Superconductivity at 36 K in beta-Fe1.01Se with the compression of the interlayer separation under pressure Nat. Mater. 8 630–3 [24] Ge J-F, Liu Z-L, Liu C, Gao C-L, Qian D, Xue Q-K, Liu Y and Jia J-F 2015 Superconductivity above 100 K in single-layer FeSe films on doped SrTiO3 Nat. Mater. 14 285–9 [25] Sprau P O, Kostin A, Kreisel A, Böhmer A E, Taufour V, Canfield P C, Mukherjee S, Hirschfeld P J, Andersen B M and Davis J C S 2017 Discovery of orbital-selective Cooper pairing in FeSe Science 357 75–80 [26] Deguchi K, Mizuguchi Y, Kawasaki Y, Ozaki T, Tsuda S, Yamaguchi T and Takano Y 2011 Alcoholic beverages induce superconductivity in FeTe1−xSx Supercond. Sci. Technol. 24 055008 [27] Paglione J and Greene R L 2010 High-temperature superconductivity in iron-based materials Nat. Phys. 6 645–58 [28] Okabe H, Takeshita N, Muranaka T and Akimitsu J 2010 Pressure-induced high-Tc superconducting phase in FeSe: Correlation between anion height and Tc Phys. Rev. B 81 205119 [29] Ashcroft N W 1968 Metallic hydrogen: a high-temperature superconductor? Phys. Rev. Lett. 21 1748–9 [30] Ashcroft N W 2004 Hydrogen dominant metallic alloys: high temperature superconductors? Phys. Rev. Lett. 92 187002 [31] Drozdov A P, Eremets M I, Troyan I A, Ksenofontov V and Shylin S I 2015 Conventional superconductivity at 203 Kelvin at high pressures in the sulfur hydride system Nature 525 73–6 [32] Einaga M, Sakata M, Ishikawa T, Shimizu K, Eremets M I, Drozdov A P, Troyan I A, Hirao N and Ohishi Y 2016 Crystal structure of the superconducting phase of sulfur hydride Nat. Phys. 12 835–8 [33] Gor’kov L P and Kresin V Z 2018 Colloquium: High pressure and road to room temperature superconductivity Rev. Mod. Phys. 90 011001 [34] Somayazulu M, Ahart M, Mishra A K, Geballe Z M, Baldini M, Meng Y, Struzhkin V V and Hemley R J 2019 Evidence for superconductivity above 260 K in lanthanum superhydride at megabar pressures Phys. Rev. Lett. 122 027001 [35] London F 1937 Supraconductivity in aromatic compounds J. Chem. Phys. 5 837–8 [36] Akamatu H, Inokuchi H and Matsunaga Y 1954 Electrical conductivity of the perylene– bromine complex Nature 173 168–9 [37] Acker D S, Harder R J, Hertler W R, Mahler W, Melby L R, Benson R E and Mochel M E 1960 7,7,8,8-Tetracyanoquinodimethane and its electrically conducting anion-radical derivatives J. Am. Chem. Soc. 82 6408–9 [38] Little W A 1964 Possibility of synthesizing an organic superconductor Phys. Rev. A 134 1416–24 [39] Little W A 1965 Superconductivity at room temperature Sci. Am. 212 21–7 [40] Little W A 1970 The exciton mechanism in superconductivity J. Polym. Sci.: Part C 17–26 [41] Bardeen J, Cooper L N and Schrieffer J R 1957 Theory of superconductivity Phys. Rev. 108 1175–204 [42] Jérome D, Mazaud A, Ribault M and Bechgaard K 1980 Superconductivity in a synthetic organic conductor (TMTSF)2PF6 J. Phys. Lett. 41 L95–8 [43] Williams J M, Wang H H, Beno M A, Emge T J, Sowa L M, Copps P T, Behroozi F, Hall L N, Carlson K D and Crabtree G W 1984 Ambient-pressure superconductivity at 2.7 K and

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[44]

[45]

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higher temperatures in derivatives of (BEDT-TTF)2IBr2: synthesis, structure, and detection of superconductivity Inorg. Chem. 23 3839–41 Murata K, Tokumoto M, Anzai H, Bando H, Saito G, Kajimura K and Ishiguro T 1985 Superconductivity with the onset at 8 K in the organic conductor β- (BEDT-TTF)2I3 under pressure J. Phys. Soc. Jpn. 54 1236–9 Tokumoto M, Murata K, Bando H, Anzai H, Saito G, Kajimura K and Ishiguro T 1985 Ambient-pressure superconductivity at 8 K in the organic conductor β-(BEDT-TTF)2I3 Solid State Commun. 54 1031–4 Carlson K D, Crabtree G W, Nunez L, Wang H H, Beno M A, Geiser U, Firestone M A, Webb K S and Williams J M 1986 Ambient pressure superconductivity at 4-5 K in b-(BEDTTTF)2Aul2 Solid State Commun. 57 89–92 Urayama H, Yamochi H, Saito G, Nozawa K, Sugano T, Kinoshita M, Sato S, Oshima K, Kawamoto A and Tanaka J 1988 A new ambient pressure organic superconductor based on BEDT-TTF with Tc higher than 10 K (Tc = 10.4 K) Chem. Lett. 17 55–8 Kobayashi H, Kobayashi A and Tajima H 2011 Studies on molecular conductors: from organic semiconductors to molecular metals and superconductors Chem. Asian J. 6 1688–704 Xue M, Cao T, Wang D, Wu Y, Yang H, Dong X, He J, Li F and Chen G F 2012 Superconductivity above 30 K in alkali-metal-doped hydrocarbon Sci. Rep. 2 389 Hebard A F, Rosseinsky M J, Haddon R C, Murphy D W, Glarum S H, Palstra T T M, Ramirez A P and Kortan A R 1991 Superconductivity at 18 K in potassium doped C-60 Nature 350 600–1 Hebard A F 1992 Superconductivity in doped fullerenes Phys. Today 45 26–32 Fleming R M, Ramirez A P, Rosseinsky M J, Murphy D W, Haddon R C, Zahurak S M and Makhija A V 1991 Relation of structure and superconducting transition temperatures in A3C60 Nature 352 787–8 Tanigaki K, Ebbesen T W, Saito S, Mizuki J, Tsai J S, Kubo Y and Kuroshima S 1991 Superconductivity at 33-K in CsxRbyC60 Nature 352 222–3 Pennington C H and Stenger V A 1996 Nuclear magnetic resonance of C60 and fulleride superconductors Rev. Mod. Phys. 68 855–910 Gunnarsson O 1997 Superconductivity in fullerides Rev. Mod. Phys. 69 575–606 Schooley J F, Hosler W R and Cohen M L 1964 Superconductivity in semiconducting SrTiO3 Phys. Rev. Lett. 12 474–5 Sleight A W, Gillson J L and Bierstedt P E 1975 High-temperature superconductivity in the BaPb1-xBixO3 systems Solid State Commun. 17 27–8 Johnston D C 1976 Superconducting and normal state properties of Li1+xTi2-xO4 spinel compounds. I. Preparation, crystallography, superconducting properties, electrical resistivity, dielectric behavior, and magnetic susceptibility J. Low Temp. Phys. 25 145–75 Cava R J, Batlogg B, Krajewski J J, Farrow R, Rupp L W Jr., White A E, Short K, Peck W F and Kometani T 1988 Superconductivity near 30 K without copper: the Ba0.6K0.4BiO3 perovskite Nature 332 814–6 Bednorz J G and Muller K A 1986 Possible high Tc superconductivity in the Ba−La−Cu−O system Z. Phys. B, Condens. Matter 64 189–93 Snider E, Dasenbrock-Gammon N, McBride R, Debessai M, Vindana H, Vencatasamy K, Lawler K V, Salamat A and Dias R P 2020 Room-temperature superconductivity in a carbonaceous sulfur hydride Nature 586 373–7

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[62] Grockowiak A D et al 2020 Hot hydride superconductivity above 550 K (arXiv: 2006.03004 [cond-mat.supr-con]) [63] Mackenzie A P and Maeno Y 2003 The superconductivity of Sr2RuO4 and the physics of spin-triplet pairing Rev. Mod. Phys. 75 657–712 [64] Hillier A D, Quintanilla J, Mazidian B, Annett J F and Cywinski R 2012 Nonunitary triplet pairing in the centrosymmetric superconductor LaNiGa2 Phys. Rev. Lett. 109 097001

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Superconducting Materials and Their Applications An interdisciplinary approach Jatinder Vir Yakhmi

Chapter 4 Applications of bulk superconducting materials, and in high-field magnets

4.1 Introduction Since superconducting materials offer zero electrical resistance and are, therefore, capable of carrying extremely high currents, which can, in turn, produce very high magnetic fields with minimal energy loss required, say, for fusion confinement. Most applications of superconductors for high-field magnets are still based on the use of the traditional superconducting materials known as low-temperature superconductors (LTSCs), which have relatively low values of the critical temperature Tc. They can, therefore, operate only at a few degrees Kelvin above absolute zero. Apart from the constraint imposed by a low Tc, the use of any superconductors is also limited by two more factors: they can carry currents only up to a critical value known as the critical current, Jc and can produce high magnetic fields only up to a limit known as the upper critical field, Bc2. The actual applications, in fact, require that the superconducting materials stay reasonably well below the critical values of all three parameters—the triumvirate (figure 4.1). The same figure is also shown as figure 1.14 in chapter 1. Hence, it is desirable to improve the current-carrying capabilities and field tolerance. A successful way to do so is to introduce grain boundaries into the LTSC materials by reducing the grain size down to nanometer scales to produce nanocrystalline superconductors. Materials processed in this way can offer both upper critical fields, and higher critical currents, higher in values by a factor of 40, compared to large-grained materials [1]. With some exceptions, metal alloys/intermetallics (LTSCs) are used at 4.2 K, and ceramic superconductors (HTSCs) are used at 77 K. The applications of LTSCs can be categorized broadly into three areas: (i) electronics and thin-film devices operated under low field conditions; (ii) devices requiring high field superconducting magnets; and (iii) devices necessarily requiring

doi:10.1088/978-0-7503-2256-0ch4

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Superconducting Materials and Their Applications

Figure 4.1. The triumvirate: Tc, Bc2, and Jc. Figure courtesy of Dr V K Aswal.

high current densities at high magnetic fields such as in power engineering. Talking of HTSCs, virtually all the applications currently envisaged for them are extrapolations of devices already operated using LTSCs at liquid He temperatures. Conventional iron-core electromagnets with Cu windings are bulky and can provide a maximum field of only 2 T since their iron-core gets saturated, and the enormous joule-heating caused by the passage of large currents through the windings requires effective heat removal, such as by water-cooling. One can do away with the iron core in superconducting magnets since the superconducting wire can carry current many more times. The absence of joule-heating ensures a compact size and no power losses, while the possibility of persistent currents allows the SC magnets to function at low temperatures, even after the current supply is disconnected. Magnets with LTSC windings, such as NbTi or Nb3Sn, which are the conventional (BCS) type II superconductors, can carry currents >5 × 105 A cm−2 at 4.2 K as against less than 1000 A cm−2 in water-cooled Cu-windings in conventional magnets. Superconducting wires of both NbTi and Nb3Sn are drawn in Cu-matrix, which is highly conducting, and are strongly twisted (5–50 mm pitch length) for stability in the varying field. For applications of superconductors in interconnects, electronics, and SQUIDs, the magnetic field requirements are 0 K, though it is quite small in a superconducting state, as compared to the normal state. The Cooper pairs do move without friction, but they have inertial mass, and for AC currents to flow, one needs to apply force to bring about alternative directions of flow. An AC electric field will be present on the surface, which will also accelerate the normal electrons and gives rise to dissipation. Copper becomes uneconomical for applications requiring continuous wave (CW, or long-pulse high voltage) when the demand for high CW voltage grows with particle energy. This is because Ohmic losses increase as the square of the accelerating voltage.

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An RF cavity is essentially a metallic box in which a resonant RF wave generates electromagnetic (EM) field modes to accelerate charged particles. An RF cavity has a specific resonant frequency. The capacitance C and the inductance L of the cavity are important parameters that influence the efficiency of the transfer of power between the RF amplifying system and the cavity. The most efficient transfer of power occurs when the impedance appears to the RF amplifying system as a simple resistor. The accelerating voltage is defined as

V (t ) = d · E (t ) where d is the effective cavity length; and

the resonant frequency is w0 ∼ 1/ √ (LC ). Q, the quality factor of an RF cavity measures its ability to store energy. One wishes to drive a cavity at its specific resonant frequency. The high resistance of the cavity walls, Rskin, is the largest source of power loss. For RF fields, the RF current resides at the surface, and the surface resistance of a superconductor is 5 orders of magnitude less than that of copper. Electrical power losses in a Cu-cavity can be huge (say, 70 times) as compared to the electric power needed to cool an RF source. The power loss can be significantly reduced by using a superconducting RF cavity, where Rskin is 106 times smaller than that in a typical copper cavity. The use of superconducting materials in radiofrequency (rf) accelerating cavities has thus become a critical requirement because it can curb severe energy loss in accelerators. For RF cavities, the leading figures of merit are the quality factor Q0 and its average accelerating field Eacc. Due to the reduced microwave surface resistance offered by them, Q0 values as high as 1010–1011 have been achieved at 2 K for superconducting RF cavities used currently in particle accelerators. To build superconducting RF cavities, we need high-purity Nb, obtained by thermal treatment to deplete H2, and round or elliptic shaped cavities. Presently, SC improves the acceleration voltage of a charged particle, Vacc, by a factor 10, and Q by 6 orders of magnitude in comparison with Cu-cavities for which Q ≈ 104. Input power is also about a factor 103 lower when using superconducting cavities instead of normal conducting cavities, leading to drastic savings in operating costs. Superconducting RF cavities (figure 4.11) have an enormous potential for application in linear accelerators, which utilize a linear array of RF cavities and become increasingly protracted, with lengths up to the tens of kilometer range, to achieve particle energies in the GeV to TeV energy range for high energy physics experiments [12]. Power requirements are enormous—such as from 100 to 250 MW for a 500 GeV LINAC. The main goal of R&D in superconducting RF cavities today is to increase the accelerating voltage gradient, E. The units of E are MV m−1. The goal chosen by ILC is E ∼ 35 MV m−1.

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Figure 4.11. (a) Single cell 500 MHz SRF cavity. Such cavities are used in high current ring colliders, and storage ring light sources; (b) A 9-cell SRF accelerating cavity. Reprinted with permission from [12]. Copyright IOP Publishing. All rights reserved.

Quite similar to the use of superconducting magnets in particle accelerators, the main reasons to introduce superconducting RF cavities in particle accelerators, too, are power savings and superior performance. Nb3Sn thin films are future candidates for SRF cavities due to their low surface resistivity, high critical temperature, and critical field, as compared to bulk Nb, which is the current state of the art. Schäfer et al [13] have described a low temperature (435 °C) magnetron co-sputtering process to deposit Nb3Sn thin films which show a Tc of 16.3 K, a high Jc of 1.60 × 105 A cm−2, and a strong shielding effect. 4.5.1 Quenching of a cavity and its thermal breakdown When the temperature of the wall of the cavity is above the superconducting transition temperature, i.e. Twall > Tc, the SC RF cavity becomes normal conducting and starts dissipating all its stored energy, very rapidly. Even a small defect in the RF surface dissipates power more rapidly than the surrounding walls can conduct away. The quench field of the SC RF cavity depends upon the thermal conductivity of the bulk Nb used, heat transfer from Nb to liquid He bath, and size and resistance of the defect encountered. The best option to arrest the dissipation of the stored energy is to improve the thermal conductivity of Nb metal used by improving its purity. The parameter used for checking the purity of Nb is its residual resistivity ratio (RRR), which is the ratio of the resistivity at 300 K to that at 4.2 K.

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4.6 Superconducting magnets for MRI 4.6.1 What is MRI, and how does it work? Magnetic resonance imaging (MRI) technique is based upon nuclear magnetic resonance, i.e. resonance phenomenon of nuclear spins (magnetic moments of atomic nuclei) in a strong external magnetic field. Nuclei with odd atomic mass number A (#n + #p) or odd atomic number Z (#p), possess non-zero spin. In a human body, the most crucial nucleus is hydrogen, which has a single proton having a nuclear spin (magnetic moment). The spins act like ‘little magnets’. Placing a patient in a strong magnetic field affects the protons: spin dipoles turn and point along the field direction, just as tiny bar magnets would do to line up in parallel with the magnetic field, i.e., their spins align in parallel with the applied field. These protons are transferred from their equilibrium state into an excited state using radiofrequency pulses, and when they return to the ground state, they emit radiation whose intensity varies in relation to the radio frequency pulses. This manifests as a voltage induced in a receiver coil that can be characterized by its change in magnitude over time. These time-dependent changes in voltage are a function of the local environment of the protons, and therefore, can give much information about the tissue being examined. Due to its sensitivity to soft tissue, MRI produces much more detailed images than CT scans. 4.6.2 MRI aiding medical diagnosis and therapy The large-scale application of superconductivity in medical diagnosis has come about largely from the use of SC magnets in MRI machines. As stated above, MRI is based upon the behavior of atoms (specifically their nuclei or protons) in a magnetic field. MRI machines are superior to x-ray technology in producing a diagnosis. Paul Leuterbur and Sir Peter Mansfield were awarded the 2003 Nobel prize in physiology/medicine, ‘for their discoveries concerning magnetic resonance imaging,’ and by implication, the application of superconductors to medicine. Powerful SC magnets, using a liquid helium refrigeration system, produce large and uniform magnetic fields inside the patient’s body, and the MRI machines can then picture the small regions of the organs in the body, and their health in detail, as the machine eventually produces an image, called MRI scan. MRI has become an indispensable imaging technique due to its superior soft-tissue contrast and the absence of any ionizing radiation during the recording of an MRI scan. It is estimated that more than half a million MRI scans are performed in the world every day. Almost all of the MRI magnets with a field strength greater than 0.35 T are made of superconducting wires that generate a strong static magnetic field that is spatially uniform over the imaging volume. Most magnets use niobium–titanium (NbTi) lowtemperature superconductors (LTS) cooled to temperatures at or below 4.2 K using liquid helium (LHe) and are operated in persistent current mode. Full-body magnets for 1.5 T and 3.0 T MRI systems (figure 4.12) require 2000–3000 l of liquid helium to cool down the magnet and to fill the reservoir. The helium required for MRI 4-17

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Figure 4.12. A 3 T MRI unit at SCTIMST, Trivandrum (India). A non-invasive technique, MRI provides high-quality images of the inside of the human body. Persistent current SC magnets surround the human body with a strong and stable magnetic field. Reproduced with permission from SCTIMST.

machines amounts to about 20% of total helium usage worldwide every year. Helium is a gas obtained from scarce natural resources. Its heavy usage is pushing its price up. This brings an impetus to try and shift the design from liquid He cooled MRI magnet systems to conduction-cooled ones which can operate at a temperature higher than 4.2 K, and therefore will not use costly liquid He, and will also eliminate the need for magnet cryostats to be constructed as pressure vessels, as per ASME codes. It will also obviate the need to use features such as rupture discs and facility vents, for safety in the event of an emergency boil-off of liquid He. 4.6.3 7 T MRI for brain scans and for stroke patients The U.S. Food and Drug Administration approved the first 7 T whole-body human MRI scanner for clinical imaging in 2017, and large medical centers are increasingly using them to diagnose and study illnesses. Perhaps the most detailed look ever at a whole human brain has been captured by taking a 100 h MRI scan, which has given very precise 3D images of a postmortem sample, with a resolution of better than 0.1 mm. The MRI recording was done at Massachusetts General Hospital in Boston

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Figure 4.13. A 3D view of the entire human brain, taken with a powerful 7 T MRI, shown here from two angles. Selected sections display the sagittal (left) and axial (right) planes. Reproduced from figure 3 in Edlow et al [14], under the Creative Commons CC BY license. Resolution of the MRI is 100 μm.

on a healthy brain from a 58 year-old woman who had died of viral pneumonia and had no history of neurological or psychiatric disease and had donated her brain, which had been preserved [14]. Since it was a still brain without cardiorespiratory or head motion, the scans presented an unprecedented view of the three-dimensional neuroanatomy of the human brain that has been obtained in vivo (figure 4.13). This study will be valuable for investigational, educational, and clinical applications that will advance understanding of human brain anatomy in health and disease. Wholebrain imaging allows observing neuroanatomic relationships across distant brain regions. Imaging has become an indispensable tool in the work-up, treatment planning, and follow-up of ischemic and hemorrhagic stroke, as well as in the identification of cerebrovascular anomalies predisposing to stroke. Compared to CT and other imaging modalities, brain magnetic resonance imaging (MRI) is by far the best technique to assess the total extent of cerebrovascular diseases in individual patients. Although the routine clinical practice is currently still limited to standard (1.5 T) and high-field (3 T) MRI, cerebrovascular disease evaluation at ultra-high-field (7 T) MRI may benefit from a high signal-to-noise ratio (SNR) which would get translated into high spatial resolution, as well as high contrast-to-noise ratio (CNR). The advent of 7 T MRI during the past decade has resulted in new developments in cerebrovascular imaging, which are finding their way into clinical practice. The emerging applications of 7 T MRI in the clinical evaluation of cerebrovascular disorders is very valuable. 7 T MRI has been proven superior to lower field-strength MRI for the evaluation of the intracranial vessel lumen and vessel walls and allows a study of the brain parenchyma for microvascular pathology on a submillimeter scale [15]. Using high magnetic fields (∼7 T) in human MR imaging provides improved time resolution, reduces the duration of examination, which in turn facilitates MR visualization of moving organs, such as the heart, liver, and bowels. It has enabled physicians to examine the liver and other parenchymal organs within a single breath hold with high spatial resolution and improved soft tissue contrast, which is of

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special importance for diagnosing cancer. in vivo MRS (magnetic resonance spectroscopy) conducted with the nuclei: 31P, 13C, 17O, 23Na, and 19F is of clinical relevance. For instance, recording the 23Na MRS is useful during clinical and preclinical MRI, including for stroke diagnostics, characterization of tumor masses, the early diagnosis of osteoarthritis, the assessment of articular cartilage conditions, and the evaluation of muscular and renal functions [16]. An ambitious whole-body 11.7 T MRI Iseult machine with a large 900 mm bore system has been built by the CEA/Irfu in France (figure 4.14), using an Nb–Ti magnet, operating in a non-persistent mode at 1.8 K in a helium bath that is permanently connected to a helium reliquifier. With Nb–Ti magnets one can go only to field below 12 T. Any system operating above 12 T needs to use Nb3Sn magnets. 4.6.4 Relevance of MRI information, and a caution MRI and computed tomography (CT) emerged in the 1970s, and at present many physicians use scans routinely to make a diagnosis. Though x-rays are inexpensive, they zap a patient with radiation, which may raise one’s risk of getting cancer. CT scans also use radiation and are more expensive. MRI does not use radiation, but it is expensive and can provide excessive information, to the extent that much of it may be irrelevant to the problem, such as that of low back pain which brings patients for an MRI. Quite often, the disc herniations, protrusions, or disc degenerations, as shown by an MRI scan may not be the cause of low back pain. MRIs of the lower

Figure 4.14. Iseult 11.7 T, whole-body system built by CEA/Irfu. Reproduced with permission from [17]. Copyright IOP Publishing. All rights reserved.

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spine can also detect abnormalities on nearby organs, such as adrenal glands. For instance, adrenal glands may show cysts, which may be harmless. Nevertheless, once a radiologist spots even a small mass on the adrenal gland, it has to be reported to the primary care doctor because it could be cancer. However, that will likely lead to more tests and sometimes spine surgery for uncomplicated low back pain, which may put the patient at additional risks, such as those associated with high rates of hospital-acquired complications, infections. Therefore, MRI scans need to be conducted judiciously, at the instance of acknowledged experts. 4.6.5 Dispelling nuclear fears from MRI Nuclear magnetic resonance is a versatile technique employed in chemistry, physics, and materials research to describe resonant excitation of atomic nuclei spins residing in a magnetic field using electromagnetic waves. The same magnetic resonance technique also provides the basis for MRI—the key noninvasive tool in diagnostic medicine and medical research, discussed above. The general public often have their concerns about MRI procedures they need to undergo in a hospital. They associate it with radiation, due to the first word ‘nuclear’ in NMR, which forms the basis of MRI. In order to dispel their concerns, a handson, table-top experiment has been designed by Cookson et al [18], which provides a visual explanation for the underlying physics. In this experiment, a compass is placed in the middle of a wire coil, which is fed with a small alternating voltage. A refrigerator magnet in the vicinity of the compass aligns its needle. When the fridge magnet is brought closer to the compass, the needle starts to oscillate at a ‘sweet spot.’ When the magnet is moved away from the sweet spot, the oscillation stops. This oscillation corresponds to the magnetic resonance of the compass needle in the magnetic field of the fridge magnet.

4.7 Superconducting magnets for maglev trains The maglev (magnetic levitation) is a train that travels on the principle of magnetic levitation, exploiting the diamagnetic property of a superconductor, in such a way that this train floats 10–20 mm above a track, under the influence of a magnetic field. Powerful superconducting magnets levitate the train and also guide it along so that it can cruise at high speeds (500 km h−1) in a frictionless mode. Maglev trains can operate on principles of either magnetic attraction or repulsion (figure 4.15) and are light in weight and easy to maintain and cause no pollution. It is expected that maglev trains would eventually compete favorably with short air journeys (1000 MW) are to be transported.

4.9 Use of HTSCs for power applications HTSCs can offer high magnetic fields with high current densities without a loss (DC), or with reduced losses (AC). In power applications, in contrast with using normal conductors, the use of HTSCs allows a reduced ratio of weight/volume when used in motors, higher power densities when used as HTS cables, and better efficiencies for energy savings. HTSCs, when used in transformers, can offer better safety features and life-extensions. When used in flywheels, bulk HTSCs can offer the advantages of energy savings, higher energy density, and enhanced safety. When used in SMES, HTSCs can save resources. The use of HTSCs in FLCs (fault current limiters) in power grids can lead to savings of resources, and better power quality. Power cables made from HTS offer high current densities and more efficient use of the right of way. Applications of HTS in generators, transformers, magnets, current leads, and magnetic separators offer energy savings [21–23]. Useful high-field magnets can be made for a field rating of up to ∼2/3 of the Hc2 value. To help sustain high Hc2 values, one goes for flux pinning in superconductors. Pinning of all types helps, be they point-like zero-dimensional disorder, linearlycorrelated 1D disorder, stacking faults (2D), or suitable micro-cracks. All of these defects can help to pin the lines of magnetic flux, retaining the superconducting regions between the vortices.

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One way to introduce pins in bulk YBCO is to go for melt textured growth. In granular ceramics like YBCO, the grain boundaries act as weak links, which results in lowering the critical current values sharply. The technique of melt texture growth (MTG) can prevent this for both bulk ceramics as well as thin films. Applications of melt-texture grown ceramic bulk superconductors are in the area of low-loss highfield magnets, low-loss transformers, fault current limiters, motors/actuators, levitation bearings, flywheels, and current leads. Fabrication techniques such as melt-texture growth (MTG) and quench and melt growth (QMG) or liquid-phase processing have led to high transport Jc values, of 75 000 A cm−2 under zero-field and 37 000 A cm−2 under 0.6 T, under pulsed-current conditions. Claims of 106 A cm−2 under 5T have also been made for samples synthesized using the QMG process. There is no doubt that with sustained research efforts, HTSCs will make a deep impact on modern technology. Defects in thin-films, anything that locally disturbs the crystalline perfection over a scale of 0.1–1 nm, can act as flux pinning sites in YBCO. As stated above, they can be point defects, planar defects such as stacking faults, misfit dislocations, twin boundaries, precipitates, anti-phase domain boundaries, surface roughness, or voids. The challenges in engineering defect structures for the best performance are to determine which defects are beneficial and to tailor their density to produce the desired effect without obstructing the flow of current. Strain fields associated with defects may also pin vortices [24]. Among the methods employed to do a large-area deposition of YBCO highquality films with reproducibility are laser MBE, PLD, MOD, and MOCVD. Hundreds of meters of lengths of multifilamentary BiSrCaCu-oxide (2223) tapes have been prepared in Ag/AgMg-sheath using a powder-in-tube method. The powder-in-tube method for making BSCCO wire/tape consists of several steps, namely, sintering the powder and packing it in a tube, which is cold-drawn and rolled (crimped) and made into a coil, which is heated, and re-rolled and re-heated. Ag used is expensive but soft and useful in the fabrication of Bi-cuprate HTS tapes, which sustain higher critical fields. 4.9.1 HTSCs for transmission of electrical power Modern technology has made it possible to produce electric power by a dam, reactor, or a furnace located hundreds of kilometers away from significant users and bring it by transmission cables and distribution networks to run factories, home ACs or even our computers at faraway locations. Currently, electrical power is directed from a generator to the consumers by overhead lines and underground cables. The North American blackout of 2003, which lasted about four days, affected over 50 million persons, and caused about $6 billion in economic loss. That underlines the importance of the electric power grid as an essential service. Superconductor technology provides loss-less transmission through superconducting wires and cables, which also improves the reliability and efficiency of the power grid. HTS cables can conduct large currents at low voltages through small cross-sections, vis-à-vis the conventional cables, with little dissipation of electrical

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energy within the conductor (figure 4.17). Commercial use of HTS cables promises transmission of over three times higher power density through the same crosssectional area as used by conventional cables. A superconducting cable power transmission system occupies less real estate and is buried underground, unlike the present-day grids. It is desirable to replace the existing power grid with a superconducting power grid. An HTS cable can offer large transmission capacity, low losses and it requires less space, all of which make them good candidates for tackling the problem of large power transmission. Wei et al [25] have discussed the design of a three-phase belted HTS cable which keeps the three cores together in a shared cryogen (LN2) space, thus saving space and materials, as compared to the case of the single-phase independent HTS cables (figure 4.18). But a fault in one of the phases may trigger the quench of other two phases, leading possibly to an overall failure of the three-phase belted cable. Therefore, it

Figure 4.17. Schematic of under-ground HTS transmission line, with a warm dielectric scheme. Reproduced with permission from [23]. Copyright IOP Publishing. All rights reserved.

Figure 4.18. A cut-out of three-phase belted HTS cable showing its parts. Reproduced with permission from [25]. Copyright IOP Publishing. All rights reserved.

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was considered necessary to incorporate an online monitoring system to monitor this three-phase HTS cable system, viz. the cable body, the cooling system and the terminations of the cable [25]. Several HTS cable projects are being carried out across the world to fulfill the goal of taking a big jump in the electric power that could be delivered. This is worth attempting because a large part of the cost of conventional alternatives comes from the cost of right-of-way, tunnels, and ducts and the cost of new infrastructure (underground or underwater) to house the cable, rather than the cable itself. The use of HTS cables can ensure reduced cost of substations because, with HTS, these can be made smaller even as they deliver more power, reliably, at lower voltages. A good compatibility exists between DC transmission and distribution and high temperature superconductor (HTS) technology since negligible losses occur during DC operation. What is possibly not highlighted enough is that the use of HTS cables allows much better control of the flow of electrical current and power in other parts of the grid by using what is called a phase changing transformer, i.e. using a phase angle regulator in series with a low impedance HTS cable. YBCO HTS conductors have shown the best potential to meet the requirements of high power density generators. Siemens has reported operational experiences on a 3600 RPM 4 MV A HTS generator. The weight and volume of the HTS generator are greatly reduced when compared to a similar capacity conventional generator [26]. The technology of second-generation superconducting wires is based on depositing a thin (5000 MW) are projected to be 99.5% efficient as against 98.5% efficiency of conventional generators. In the event of a short circuit, an SC generator would isolate the short circuit quicker. The use of HTSCs would mean large savings in energy and cost of equipment required for the job. Conventional propeller drive is subject to inherent limitations in the speed it can move a ship. MHD thrusters using SC magnets can do away with propellers and aid in attaining higher speeds. The concept of an HTS ship propulsion motor (figure 4.20) has been reported by Haran et al [26].

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Figure 4.20. A conceptual design of HTS propulsion motor. Reproduced with permission from [26]. Copyright IOP Publishing. All rights reserved.

4.10 HTS power cable projects American Superconductor Co. makes multifilamentary Bi-2223/Ag tapes in long lengths (up to a km) for which polyimide/polyester is used for insulation. It can sustain critical transport currents of 200 A at 77 K. ASC also makes long lengths (kms) of coated wires of YBCO/alloy. HTS cables have, of course, to be cooled with liquid nitrogen and need good thermal insulation for sustaining high currents and low transmission losses. Unlike the loss-free flow of DC in a superconducting cable, the AC power cables can have AC loss due to magnetic-flux flow, a coupling loss, and an eddy current loss induced in a metal matrix of HTS wire. HTSC cables, if developed with the required Jc-rating and low AC-loss, would be much cheaper. In order to keep the AC losses low, the required Jc would be in the region of 2 MA cm−2 for a typical operating current density of 2 × 105 A cm−2. A low AC loss of 1 W m−1 has been achieved in a 3 kA HTS cable, recently [28]. An about 200 m long Bi-2223 cable was commissioned at Albany, in 2006, and was upgraded with a YBCO section for testing purpose in 2008. The world’s first ingrid transmission HTS power cable (length ∼ 600 m, 138 kV, 574 MV A rating) was installed at Long Island, NY, in 2006, under a project (2003–8) carried out by American Superconductor Co., (the supplier of the HTS wire, and project lead), Nexans (cable manufacturing) and Air Liquide (cryogenics). This superconducting power transmission line, made operative in 2008, has cables with a core of Y-123 conductor and copper for backup, a channel for liquid nitrogen, and thermal insulation. It can handle energy equivalent to the consumption of 300 000 homes. 4.10.1 Development of HTS power equipment at ISTEC (Japan) This project was set up during 2008–12 to develop new prototype power systems such as: (a) basic technology of 2 GJ energy SMES for the stabilization of power systems; (b) superconducting power cables for high-voltage (275 kV) and high 4-29

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current (66 kV) transmission systems, and (c) superconducting power transformers. Under the Actual Application Project in Japan, an HTS Cable program was taken up during 2007–11, under NEDO (New Energy and Industrial Technology Development Organization), incorporating SEI (Sumitomo Electric Industries), TEPCO (Tokyo Electric Power Co) and Maekawa Manufacturing (for cooling). This program had three separate groups, working on power network, cable, and cooling system, respectively. It was aimed at developing a 300 m long, 200 MV A, 3 core, 150 mm diameter 1 case HTS (Bi-2223) cable, to work under the actual 66 kV substation operation for AC loss of 1 W m−1 phase at 3 kA and 31.5 kA, for 2 s under field test. Among the benefits of using HTS cables are: (a) increased grid reliability, security, efficient power interconnections with high capacity; (b) minimal environmental impact because HTS cables are OK even in densely populated areas; (c) low impedance design for AC power flow, to alleviate grid congestion; and (d) reduced right-of-way (smaller footprint), because HTS can be laid underground. 4.10.2 HTS Cable Project at Columbus, OH (USA) A 200 m long, three-phase (in 1 cable) HTS power cable (13.2 kV, 69 MV A) was developed, tested, and put in place in 2006, and has a rating equivalent to power consumption of 36 000 homes. It was operated without incident or interruption for 195 days (>4680 h) in 2007. A backup cryogenics system performed as designed. Cable was maintained within operating temperature and pressure, along with a working UPS. 4.10.3 Other efforts for cables and HTS devices About 10 km length of HTS wire, in 43 m lengths capable of Ic > 70 A, manufactured by SuperPower, USA, was delivered to Sumitomo and tested. A three-phase, 50 Hz, 630 kVA HTS (Bi-2223) transformer was built in China. For primary parameters of 10.5 kV and 35 A, a 25× multiplier was obtained at secondary, viz. at 0.4 kV, a current of 909 A, for a short circuit of 0.2 s. The impulse voltage was 75 kV. Losses for this transformer were 1 kW at core and 2 kW at coils, compared to a total loss of 8 kW for a conventional transformer for the same ratings. A high-rating (36 MW, 120 rpm) HTS motor was built by American Superconductor Co., USA, which passed acceptance tests in 2007.

4.11 Superconducting switches and power transformers Bulk superconducting materials, including HTSC, can be used as high-current (5000 A cm−2) switches in power transmission. It is estimated that about 15% of power losses occur in electric power transmission due to inefficiencies in the transformers. If SC windings were used in a transformer, losses could be reduced drastically, if not eliminated. An HTS transformer has twice the overload capacity without insulation damage and is also environmentally

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friendly due to the lack of oil used in its operation. HTS transformers have been tried for a rating of 5/10 MV A.

4.12 State-of-the-art superconducting fault current limiters Fault current limiters (FLCs) are increasingly employed in smart grids for improved security, distributed generation, and better grid quality. Superconducting fault current limiters (SFCLs) are installed in the electric power system, and expected to limit fault current and improve system stability. SFLCs are fail-safe and provide fast and effective current limitations (cut-off) in case of a short-circuit. The SFCLs offer negligible impedance at normal operating conditions but generate large impedance in fault condition, thereby not influencing the power systems in steady state condition. Instead, SFCL limits currents only in fault condition, mainly with reactance component. Any temperature rise occurring by joule heating is small and the SCFLs have fast and automatic recovery, as they return quickly to their superconducting state, ready for the next fault-incidence. They can also handle high voltages. All of this can lead to substantial economic gains. Three kinds of superconducting FLCs have been demonstrated: 1. Resistive type (115 kV, 1200 A) made largely from YBCO tapes (by Siemens); 2. DC biased iron core (220 kV, 280 MV A) made from Bi 2223 tapes (Innopower); 3. Hybrid type (22.9 kV, 3.0 kA) using YBCO tapes (by KEPRI). In addition, 12 kV FLCs have also been fabricated from bulk B-2212, with current ratings of 100 A, 400 A, and 800 A, respectively. As an application of superconductors in power systems, a superconducting fault current limiter (SFCL) has no classical equivalent. An SFCL makes use of two key properties of superconducting materials—an ideal conductivity, and a quick phase transition to the normal conducting state under the influence of an increase in current, magnetic field and temperature. Fast-operating nonlinear SFCLs can increase their impedance rapidly, and limit high fault currents. A limitation time of just 100 ms has been reported for a resistive FCL with ratings of 10 kV, 2.3 kA (40 MV A), a peak short circuit current of 50 kA and a limited peak short circuit current of 13 kA, by Stemmle et al [29]. In 2017, Sokolovsky et al [30] proposed an inductive SFCL, which can be also called ‘shielded-core’ or ‘transformer type’, It is based on magnetic coupling between a superconducting element and a protected circuit that allows the cryogenic environment to remain mechanically isolated. The primary coil of this transformer is connected in series with the protected circuit (figure 4.21). Under normal conditions, the secondary coil is in the superconducting state. Under any shortcircuit conditions, the increased current in the secondary coil exceeds a critical value and the whole coil or at least some of its parts turn into a resistive normal state. If the dissipative resistance exceeds the inductive reactance of the coil, the induced current in the secondary coil is sharply reduced and the magnetic flux of the primary coil is 4-31

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Figure 4.21. Inductive (transformer type) SFCLs based on the ring-shaped bulk MgB2. It can measure AC losses, and can simulate a fault current. Reproduced with permission from [30]. Copyright IOP Publishing. All rights reserved.

Figure 4.22. SFCL made from pancake coils. On the right is its circuit diagram. Both reproduced with permission from [31]. Copyright IOP Publishing. All rights reserved.

no longer compensated. Consequently, the impedance of the SFCL increases and limits the fault current. A transformer type SFCL composed of pancake coils (figure 4.22) has the advantage that the amount of superconducting wire used is less, allowing the size of SFCL to be smaller than the solenoid coil type SFCL. A pancake coil SFCL limits small fault current with reactance [31]. But when fault current gets larger, a resistance component is also added and a larger impedance is generated to tackle the fault current. This transformer magnetic shield type SFCL consists of four REBCO pancake coils which are arranged co-axially. The two inside pancake coils are primary coils which are connected to the power systems. The outer two pancake coils are secondary coils, which are short-circuited. In the steady-state condition, both coils are in the superconducting state and the current through the secondary coil is induced to cancel the magnetic flux generated by the current of the primary coil. The circuit, shown on the right in figure 4.22 has a variable autotransformer, a load reactor (1.33 mH), a shunt resistor (0.25 mΩ), a magnetic switch and the SFCL. The SFCL is immersed in liquid N2. When the magnetic switch is closed at t = 0 s, fault current flows through the circuit by changing the voltage level across the variable autotransformer, and the switch opens at t = 0.1 s. When the voltage across 4-32

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the variable autotransformer is 10 Vrms, the current through the primary and secondary coil are smaller than critical current. Therefore, both coils are in the superconducting state. When the voltage across the variable autotransformer is 30 Vrms, or higher, the fault current gets larger than trigger current level. Thus, the secondary coil turns to the normal state while the primary coil is in the superconducting state. The peak value of fault current is then reduced by the SFCL.

4.13 Miscellaneous applications 4.13.1 Miniature antennas By employing superconductors, an antenna can be made tiny—just 5% of the size of a conventional antenna. For example, an HTSC antenna 6 cm long can replace the standard 130 cm long antenna used for commercial FM reception. 4.13.2 Interconnects Superconducting materials would keep interconnects from slowing the high-speed computers as miniaturization of electronics continues necessitating closer packing on chips. In any case, semiconductor chips perform better when operated at lower temperatures, say if cooled at >77 K rather than operating at 300 K. Jc values for HTSC films are adequate for interconnects. High-frequency signals traveling through such interconnects will undergo little attenuation or dispersion, providing improved performance for information storage systems. 4.13.3 Bolometers High-Tc bolometers in the form of shaped films can be especially useful for wavelengths longer than the 20 μm cut-off that the liquid nitrogen cooled photovoltaic detectors such as those made from HgCdTe provide. Potential applications of such HTSC bolometers are in far-infrared spectroscopy and for passively cooled observations of bright sources in outer space. 4.13.4 Magnetic shielding Because superconductors repel lines of magnetic flux, they can be used to create regions free of magnetic field or to shape the magnetic field. Such shields can be made more economically from HTSC materials extending their potential for a variety of applications, such as shielding the space vehicles upon re-entry into the Earth’s atmosphere, shielding security-related computers to protect data, shields for SQUID based equipment from stray fields, etc. 4.13.5 Passive microwave devices for signal processing and transmission The following are examples of low-loss high-Q passive microwave devices based on HTSCs for use in the telecommunications industry and defense-related areas such as radar, target detection, jamming, and communications: • high-Q resonators built from HTSCs can transmit more information, due to their lower noise. They can lead to improved resolution of radars; 4-33

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Figure 4.23. Schematic diagram of the Meissner motor. Figure courtesy, Dr V K Aswal.

• HTSC microstrips acting as bandpass filters can achieve the same performance as copper waveguides, although they are 90% smaller and lighter; • HTSC delay lines which maintain the integrity of the signal much better. 4.13.6 SC motors and bearings Magnet bearings made using superconducting materials show low-loss and selfcontrolled levitation. ISTEC has demonstrated high field trapped magnets, operating at 29 K, with Bt > 17 T [32]. Flux expulsion property of superconductors can be used to construct motors where blades of a rotor would keep their motion due to the Meissner effect, or noncontact magnetic bearings (figure 4.23). Use of HTSCs would make them also economical. These may find applications in designing new or improving the efficiency of existing machinery. An axial superconducting motor, with a high-Tc superconductor rotor, offers high power density, enhanced efficiency, and it is lighter in weight and occupies less volume [33].

4.14 High-field magnets using HTSCs 4.14.1 HTSC magnets for MRI Medical imaging (MRI) equipment based on HTSC magnets would make these units more economical and convenient to operate, vis-à-vis the units used currently that use He-cooled LTSC magnets. The magnetic field requirement for such units, viz. 2 T–3 T, are within the scope of the current R&D status of the HTSC oxides. To build a viable alternative to the LHe-cooled NbTi magnets, designers have evaluated the different options among the high-temperature superconductors (HTS) for building high-field magnets.

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Bi-2223 HTS tape has been used to design a conduction-cooled magnet operating at 20 K for a head-only 3 T MRI system [34]. However, the main difficulty in making such MRI magnets is faced during the processing of coil bundles from the brittle Bi-2223 ceramic material, to counter which one needs to use expensive silver, up to 70% content, during the making of tapes from Bi-2223. Besides, such HTSC magnets are not amenable to operating in a persistent mode, i.e. the superconducting current does not flow without attachment of such HTSC magnets to an external power supply. YBCO has also been considered, but the cost of this superconductor is still quite high and needs to come down considerably to be considered for commercial MRI magnets. Recently, Parkinson et al [35] have presented a second-generation YBCObased 1.5 T double pancake shape conduction-cooled magnet design operating at 20 K. The imaging volume of the MRI magnet is only 120 mm, with inhomogeneity of just 20 ppm. It is much smaller than the desirable value of 450 mm for the diameter spherical volume (DSV), now considered standard for whole-body MRI systems. Again, because low resistance joints have not been developed to join the pancake coils, the YBCO-based MRI magnet is also continuously driven by a power supply and not operated in an autonomous persistent mode [36]. All commercial high frequency NMR instruments working up to 1 GHz, employed in many areas of research in molecular biology, chemistry and physics use LTSC magnets. Currently, the highest field superconducting magnet is a state-of-the-art 4 inch bore Nb3Sn LTS magnet, operating at 21 T in persistent mode for use in a 900 MHz NMR instrument at NHFM lab in the USA. Ultra high-field magnets, if built successfully from HTSs would have great potential in several applications, including their use in superconducting cyclotrons, for producing intense neutron beams for the treatment of cancer. 4.14.2 Possibility of HTSC magnets for separation in industry High-field superconducting magnets have great potential in industrial applications, such as removal of toxic metals from water, removal of catalysts from chemical reactors, removal of sulfur oxides from stack effluents, separation of steel scrap, purification of ores and desulfurizing of coal (figure 4.24). LTSC magnet separators have been in use for kaolin clay purification. HTSC magnets would bring further economy and reliability to industrial separators. 4.14.3 Superconducting rotating machines and wind turbines A conventional wind turbine has a rotating magnet (rotor) built in a set of copper coils (stator), and the rotor rotates in the stator coil to generate a current. Currently, wind turbine generators of power use permanent magnets, mostly of the Nd–Fe-B type, which turn inside coils that transform magnetic power into electricity, like in a dynamo. However, these magnets not only make the structure heavy, but they also require substantial quantities of Nd, a rare earth metal which is expensive and mined mostly in China. 4-35

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Figure 4.24. Schematic of a magnetic separator using a superconducting magnet. Figure courtesy, Dr V K Aswal.

With higher and higher ratings, the wind turbines have become so big and bulky that their transport and installation are posing challenges. Generators for large wind turbines now weigh more than 200 tons. Even larger systems are being planned by the industry for future. By replacing permanent magnets with superconducting magnets, one can not only make significant savings in the size and weight of the wind turbine generators, thereby producing lighter and smaller wind turbines, but also cut their cost by doing away with the expensive rare earth element (Nd). A reduction in the price tag of turbines could bring down the cost of energy produced by them. Due to the advantage of weight reduction (by almost half) by employing superconducting wind turbines, one can build off-shore wind platforms that deliver high power with higher efficiency. For instance, one can quadruple the performance by using superconductors in 10 MW wind generators at 30 K, at 2.5 T field. Under an EU-funded project EcoSwing, the world’s first superconducting wind turbine was made in 2018 by replacing permanent magnets with HTSC magnets, The new generator is 4 m in diameter, 1.5 m smaller than a conventional one, and it sits inside an 88 m high 3.6 MW wind turbine in Thyboron, Denmark [37]. The superconducting generator developed under this project abandoned the permanent magnets used in the traditional generators, replacing them with coils made of ceramic strips and metal strips to develop a two-blade wind turbine generator based on high-temperature superconductors. The coil was built into the vacuum drum, which was cooled with a low-temperature gas from the cryo-cooler, to bring the superconducting conditions, under which the current passed through the coil in a resistance-less manner. The energy transmission efficiency of this superconducting generator is much higher than that of the conventional generator. The generator does not use Nd-oxide, and is 40% lighter in weight, and is, therefore, easier to transport and install. A conventional wind generator making

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1 MW of power uses roughly a tonne of Nd-oxide, costing over $45/kg, in its magnets. The new generator using Gd–Ba–Cu–O tapes use just about 1 kg of the rare earth Gd-oxide costing $18.70/kg. Therefore, conventional heavy-duty, expensive permanent-magnet direct-drive generators are modified to incorporate HTSC magnets made from a composite tape having a Gd–Ba–Cu–O ceramic superconducting layer. The superconducting layer sits on a steel ribbon for flexibility and strength. Layers of magnesium oxide, used to protect this superconducting tape from metal poisoning, also act as a template for the precise crystalline structure needed by the Gd–Ba–Cu–O. An outer copper layer offers electrical and thermal stabilization. Tens of kilometers of this tape sit inside the new wind turbine. The rotor is made up of two parts, which are thermally decoupled by a vacuum chamber. The part responsible for the bearing and the mechanical connection of the generator rotor is operated at ambient temperatures; the electromagnetic part of the generator rotor is designed to operate at 30 K using a closed-cycle gas cooling. Cooling consumes 100 kW of electricity—around three percent of the generator’s maximum output. Off-the-shelf cryo-coolers are used to cool the superconductor to −240 °C, the same coolers which are also used at times in hospital MRI machines. A single unit as discussed above generates 3 MW of electricity, enough to power 1000 homes. By making a further reduction in the weight and size of the wind turbine, it is planned to increase the power output of the wind turbine to over 10 MW.

4.15 Use of HTS in superconducting cavities for accelerators Continuous wave (CW) SC RF technology is used for light sources, viz.: A. Spallation neutron source (SNS): a short-pulse neutron source, driven by a proton accelerator. B. Superconducting linear accelerator (SCL) which accelerates beam from 186 to 1000 MeV. SCL consists of 81 independently-powered cavities in 23 cryomodules. Most operations are done at 4.2 K, though it can support operation at 2.1 K, too. Coating of the inside surface of cavities is a challenge. Among the HTS options which have been tried are: (i) YBaCuO thick films by plasma-spray method (3 GHz); (ii) BiSrCaCuO thick films by a screen-printing or spray-coating method (3GHz); (iii) YBaCuO thin films by a PLD method (16 GHz); (iv) MgB2 thin films by a PLD method (13.6 GHz). 4.15.1 RF cavities from MgB2 Compared to cuprates, MgB2 is cheaper, has lower anisotropy, and larger coherence length. It also has the transparency of grain boundaries to current flows. All this makes MgB2 attractive for RF applications. The reactive evaporation route can be

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used to deposit films of thickness 500 nm on LaAlO3 or sapphire substrates. RF surface resistance (Rs) for MgB2 films at 3.3 K and at 10 GHz is even lower than that of Nb [38]. Rs is comparable to Nb, even when MgB2 is kept at 20 K. Besides, the Rs for MgB2 film does not show a significant increase under applied fields of up to ∼400 Oe. One can coat a cavity by pulsed laser deposition (PLD) of MgB2. Substrates heated to 250 °C during under Ar atmosphere, at ∼120 mTorr, can be coated using a KrF excimer laser of ∼500 mJ/pulse, at 5–10 Hz. Films of controlled thickness grown thus can be annealed in situ at ∼650 °C for ∼10–15 min under ∼760 Torr argon [39]. An essential parameter during testing of MgB2 coated cavities is the RF critical magnetic field of MgB2.

4.16 Applications of MgB2 wires Although at 39 K, the Tc value of MgB2 is lower than those for high-temperature superconducting cuprate materials, it is considerably above the value of Nb3Sn (18 K). Besides, both Mg and B are abundant and not intrinsically expensive, which makes MgB2 appealing for use in superconducting devices wherever found suitable. Therefore, it was expected that MgB2 wires fabricated using classical deformation methods would be competitive for superconducting applications. MgB2 is also amenable to manipulation of its superconducting behaviour. For instance, a sizeable and reproducible enhancement was observed in the Jc value of MgB2 after partial substitution of B by carbon. However, this brings down the Tc of MgB2 almost linearly with the increase in C-content, falling to 30 K for MgB1.82C0.18. Modified to increase the pinning and upper critical field, MgB2 is considered as a viable material for MRI magnets and other applications [40, 41]. The availability of MgB2 in the form of multifilamentary round wire should make it suitable for the production of cables. Production of MgB2 wires have been attempted at the University of Geneva and Columbus Superconductors, and on an industrial scale by NIMS in Tsukuba (Japan), in collaboration with Hitachi. Basic inputs for this are pure elemental powders of B and Mg with small particle size, using which one can try either the ex situ route, the in situ routes, or even the internal Mg diffusion method to produce wires. In the powder-in-tube ex situ method, pre-reacted MgB2 powders are loaded into Nb tube to prepare MgB2 wires and drawn into wires/tapes, followed by short heat treatment at 965 °C for recrystallization. ex situ wires can be produced thus in km lengths and are very homogeneous, though their Jc values are not very high, being ∼ 3 × 103 A mm−2 at 4.2 K and 5 × 102 A mm−2 at 3–5 T, respectively [42]. The in situ method affords the reaction to MgB2 at much lower temperatures of about 650 ° C and wires made thus can exhibit Jc of 1 × 102 A mm−2 at 4.2 K under applied fields of 13.2 T.

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A high precision long level sensor for liquid hydrogen (LH2: 20 K) has been fabricated from MgB2 by M Takeda et al [43]. This can be installed in tanks of about 10 m diameter to transport large amounts of this renewable fuel across the world.

4.17 Other applications of superconductors Conventional gas-cycle refrigerators based on chlorofluorocarbons are inherently inefficient and have adverse effects on the Earth’s ozone layer. Refrigeration to produce ultralow temperatures for space and defense areas will increasingly depend on the magnetocaloric effect requiring SC magnets. SC electromagnetic coil-based launching systems could launch objects at much higher velocities than the current gas expansion systems. Possible applications include aircraft catapults, earth satellites, space vehicles, and defense.

4.18 Cryogenics Before ending this chapter, we would like to discuss cryogens, refrigerators, and cryostats briefly, which are essential to use with superconducting materials and devices. Novel physical properties are often observed at extremely low temperatures. Ability to sustain low temperatures of about 1–10 mK often requires measurements. Ideally, one would strive to approach absolute zero temperature, i.e. 0 K, which equals −273.15 °C, or −459.67 °F, at which any given system reaches its lowest possible energy or thermal motion. However, absolute zero temperature cannot be attained, in principle, because one would need to do an infinite amount of work, as per laws of thermodynamics, to remove heat from a material, as one approaches 0 K, simply because one has to work harder and harder to do so as we attain colder temperatures. Besides, even if one could achieve that state, quantum mechanics states that the atoms and molecules would still have some irreducible motion. Quantum states are mostly ‘fragile,’ and can get easily ‘shrouded by inherent lattice vibrations at higher temperatures’. Liquid helium undergoes a phase change upon further cooling into a superfluid, a liquid that flows without any resistance of friction. Superfluid He can spontaneously flow upwards and out of a container; seep through molecule-thin cracks; remain perfectly still while spinning at high speeds; and coalesce into one ‘super-atom,’ known as a Bose–Einstein condensate. Supercooling techniques such as the ones used in dilution refrigeration are critical for supporting the studies of a wide range of disciplines: gravitational wave research, superconductivity, spintronics, quantum computing, and other up-and-coming technologies. 4.18.1 Handling of cryogens. Safety risks—the danger of suffocation Size of cryogenic fluid storage vessels (called Dewar flasks) range from 1 liter flasks used in lab work to as big as 28 000 US gallons which are used to store liquid nitrogen, liquid oxygen, and liquid hydrogen for industrial use and in space-vehicle ground-support systems. Storage vessels are insulated thermally by using rigid foam or fibrous insulation, or even with multilayer evacuated insulations, in order that a minimum amount (say 0.1%) of cryo-liquid is lost from the storage vessel per day. 4-39

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In small laboratory Dewars, the ‘insulation’ consists of silvered surfaces and evacuation. Portable liquid helium Dewars are commercially marketed, in varying sizes, to store and carry liquid He amounts of 30–100 liters (https://www.cryofab.com/ producers/cmsh_series). The evaporation of cryogenic liquids in closed or badly ventilated rooms can lead to oxygen deficiency. Because most cryogens are odorless and colorless, this hazard cannot be detected without special equipment. Furthermore, argon and nitrogen are heavier than air and can, therefore, collect near the floor or in pits. The symptoms of oxygen deficiency (oxygen concentration in %) can be catastrophic and even fatal. Oxygen levels below 15% in ambient can lead to a fast beating of pulse, with deep breathing and a lack of coordination. Below 12% levels can lead to vertigo, or lips turning blue. Catastrophic symptoms occur with nausea, vomiting, or even unconsciousness if oxygen content falls to 10% or lower at 8%. Any lower content of oxygen in ambient has also to be seen in the context of time duration for which a person is exposed. For instance, 6%–8% levels can bring brain damage in just 4–8 min and a sure death within 8 min. Still lower levels like 4% oxygen can lead to coma in just 40 s and a quick loss of breathing and immediate death. 4.18.2 Cryogenics for frontline research 4.18.2.1 Femtosecond chemistry for lifetimes of states Femtochemistry techniques are crucial in accessing the short time scales necessary to probe transient intermediates in chemical reactions. However, one can take a new approach where one prolongs the lifetime of an intermediate by preparing reactant molecules in their lowest vibronic quantum state at ultralow temperatures. Relying on the substantial control attainable over the quantum states of the ultracold molecules, chemical reaction rates for specific reactions could perhaps be altered by orders of magnitude, merely by changing the nuclear spins of the reactants and entering quantum degeneracy. 4.18.2.2 Dynamics of intermediary reaction products at nanokelvin temperatures Using ionization spectroscopy and velocity map imaging of a trapped gas of KRb molecules at a temperature of 500 nK, Hu et al [44] have directly observed reactants, intermediates, and products of the reaction 40K87Rb + 40K87Rb→K2Rb2*→K2 + Rb2. Beyond observation of a long-lived, energy-rich intermediate complex, this technique opens doors to a new capability to study quantum-state-resolved reaction dynamics in the ultra-cold regime. 4.18.2.3 Improving wide-band telecommunication Wide-band telecommunications technology, which operates best at gigahertz frequencies, is beneficial for improving the efficiency and reliability of cell phones. Such frequencies are very difficult to achieve with semiconductor-based circuitry. However, using a rapid single flux quantum, or RSFQ, integrated circuit Hypres’s receiver, which operates with the aid of a liquid helium cryocooler, one can attain

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gigahertz frequencies easily. This technology is emerging in cell-phone receiver– transmitter towers. 4.18.2.4 Single-photon detection The optical response of high responsive YBCO microwires (Tc = 89 K, sharp transition width ∼ 2 K, and high Jc of 5.7 × 105 A cm−2 at 77 K) have shown potential for infrared single-photon detection using HTSCs [45].

References [1] Raine M J 2015 High field superconductors for fusion energy applications Thesis University of Durham [2] Sawada K 2009 Outlook of the superconducting Maglev Proc. IEEE 97 1881–5 [3] Escudero R, Morales F and Bernes S 2009 Specific heat studies of pure Nb3Sn single crystals at low temperature J. Phys. Condens. Matter 21 325701 [4] Zlobin A V and Schoerling D 2019 Superconducting magnets for accelerators Nb3Sn Accelerator Magnets: Designs, Technologies and Performance (Particle Acceleration and Detection) ed D Schoerling and A V Zlobin (Switzerland, AG: Springer) 3–22 ch 1 [5] Iwasa Y 2009 Case Studies in Superconducting Magnets: Design and Operational Issues (New York: Springer) [6] Bormio-Nunes C, Sandim M J R, Edwards E R and Ghivelder L 2006 Artificial pinning centre Nb-Ti superconducting wire for AC applications Supercond. Sci. Technol. 19 1063–7 [7] Wolski A 2014 Beam Dynamics in High Energy Particle Accelerators (London: Imperial College Press) [8] Wilson M N 1983 Superconducting Magnets (New York: Oxford University Press) [9] Johnston H 2017 Upgrade for European synchrotron Phys. World 30 11 [10] Allen R E 2014 The Higgs bridge Phys. Scr. 89 018001 [11] https://www.iter.org/mach [12] Padamsee H 2017 50 years of success for SRF accelerators – a review Supercond. Sci. Technol. 30 053003 [13] Schäfer N, Karabas N, Palakkal J P, Petzold S, Major M, Pietralla N and Alff L 2020 Kinetically induced low-temperature synthesis of Nb3Sn thin films J. Appl. Phys. 128 133902 [14] Edlow B L et al 2019 7 Tesla MRI of the exvivo human brain at 100 micron resolution Nat. Sci. Data 6 244 [15] De Cocker L J L, Lindenholz A, Zwanenburg J J M, van der Kolk A G, Zwartbol M, Luijten P R and Hendrikse J 2018 Clinical vascular imaging in the brain at 7 T NeuroImage 168 452–8 [16] Zubkov M A, Andreychenko A E, Kretov E I, Solomakha G A, Melchakova I V, Fokin V A, Simovski C R, Belov P A and Slobozhanyuk A P 2019 Ultrahigh field magnetic resonance imaging: new frontiers and possibilities in human imaging Physics - Uspekhi 62 1214–32 [17] Warner R 2016 Ultra-high field magnets for whole-body MRI Supercond. Sci. Technol. 29 094006 [18] Cookson E, Nelson D, Anderson M, Barsukov I and McKinney D L 2019 Exploring magnetic resonance with a compass Phys. Teach. 57 633 [19] Nishijima S et al 2013 Superconductivity and the environment: a Roadmap Supercond. Sci. Technol. 26 113001

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[20] Zhou D, Zhao L, Ke C, Hsieh C C, Cui C, Zhang Y and Zhao Y 2018 High-Tc superconducting Maglev prototype vehicle running at 160 km/h in an evacuated circular track IEEE J. Mag. 28 3600504 [21] Granados X, Puig T, Treva J, Mendoza E and Obradors X 2001 Quench behaviour of the switching elements of a hybrid HTS current limiter IEEE Trans. Appl. Supercond. 11 2406–9 [22] Bray J W 2008 Superconducting applications: present and future J. Supercond. Novel Magn. 21 335–41 [23] Hull J R 2003 Applications of high-temperature superconductors in power technology Rep. Prog. Phys. 66 1865–86 [24] Foltyn S R, Civale L, Macmanus-Driscoll J L, Jia Q X, Majorov B, Wang H and Maley M 2007 Materials science challenges for high-temperature superconducting wire Nat. Mater. 6 631–42 [25] Wei B, Zhou S, Sun Z and Wang Y 2020 Design of an online monitoring system for threephase belted HTS cables IOP Conf. Ser.: Earth Environ. Sci. 446 042076 [26] Haran K S et al 2017 High power density superconducting rotating machines—development status and technology roadmap Supercond. Sci. Technol. 30 123002 [27] Solovyov V and Farrell P 2017 Exfoliated YBCO filaments for second generation superconducting cable Supercond. Sci. Technol. 30 014006 [28] Mukoyama S, Amemiya N, Watanabe K, Iijima Y, Mido N, Masuda T, Morimura T, Oya M, Nakano T and Yamamoto K 2017 Study on AC loss measurements of HTS power cable for standardizing J. Phys.: IOP Conf. Seri. 897 012021 [29] Stemmle M, Allweins K, Merschel F, Noe M and Hobl A 2014 40 MVA HTS cable and fault current limiter installation in City Center, Ampa City Project IEEE/CSC Superconductivity News Forum (Global Edition), Invited Presentation 4LOr3B-01 given at ASC Conf. (Charlotte, VA, August 10–15, 2014) [30] Sokolovsky V, Prikhna T, Meerovich V, Eisterer M, Goldacker W, Kozyrev A, Weber H W, Shapovalov A, Sverdun V and Moshchil V 2017 MgB2-based superconductors for fault current limiters IOP Conf. Ser.: Mater. Sci. Eng. 171 012144 [31] Sakamoto D, Sakamoto T and Shirai Y 2020 Current limiting characteristics of a magnetic shielding type Superconducting Fault Current Limiter of REBCO pancake coils 14th European Conf. on Applied Superconductivity (EUCAS 2019) J. Phys.: Conf. Ser. 1559 012099 [32] Tomita M and Murakami M 2003 High-temperature superconductor bulk magnets that can trap magnetic fields of over 17 tesla at 29 K Nature 421 517–20 [33] Granados X, Lopez J, Bosch R, Bartolome E, Lloberas J, Maynou R, Puig T and Obradors X 2008 Low-power superconducting motors Supercond. Sci. Technol. 21 034010 [34] Terao Y, Ozaki O, Ichihara C, Kawashima S, Hase T, Kitaguchi H, Kobayashi S, Sato K, Nakajima I and Oonishi N 2013 Newly designed 3 T MRI magnet wound with Bi-2223 tape conductors IEEE Trans. Appl. Supercond. 23 4400904 [35] Parkinson B J, Slade R, Mallett M J and Chamritski V 2013 Development of a cryogen Free 1.5 T YBCO HTS Magnet for MRI IEEE Trans. Appl. Supercond. 23 4400405 [36] Baig T, Yao Z, Doll D, Tomsic M and Martens M 2014 Conduction cooled magnet design for 1.5 T, 3.0 T and 7.0 T MRI systems Supercond. Sci. Technol. 27 125012 [37] King A 2018 World first as wind turbine upgraded with high temperature superconductor Chemistry World 22 Nov. 2018

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[38] Moeckly B H, Kihlstrom K E, Findikoglu A T and Oates D E 2005 Microwave properties of MgB2 thin films grown by reactive evaporation IEEE Trans. Appl. Supercond. 15 3308–12 [39] Zhao Y, Ionescu M, Horvat J and Dou S X 2005 Off-axis MgB2 films using an in situ annealing pulsed laser deposition method Supercond. Sci. Technol. 18 395–9 [40] Ranot M and Kang W N 2012 MgB2 coated superconducting tapes with high critical current densities fabricated by hybrid physical–chemical vapor deposition Curr. Appl. Phys. 12 353–63 [41] Ballarino A and Flükiger R 2017 Status of MgB2 wire and cable applications in Europe J. Phys.: Conf. Ser. 871 012098 [42] Kario A, Grinenko V, Kauffmann A, Häßler W, Rodig C, Kováč P, Melišek T and Holzapfel B 2012 Isotropic behavior of critical current for MgB2 ex situ tapes with 5 wt.% carbon addition Physica C 483 222–4 [43] Takeda M, Inoue Y, Maekawa K, Matsuno Y, Fujikawa S and Kumakura H 2015 Superconducting characteristics of short MgB2 wires of long wire sensor for liquid hydrogen AIP Conf. Series: Mater. Sci. Eng. 101 012156 [44] Hu M-G, Liu Y, Grimes D D, Lin Y-W, Gheorghe A H, Vexiau R, Bouloufa- Maafa N, Dulieu O, Rosenband T and Ni K-K 2019 Direct observation of bimolecular reactions of ultracold KRb molecules Science 366 1111–5 [45] Xing X, Balasubramanian K, Bouscher S, Zohar O, Nitzav Y, Kanigel A and Hayat A 2020 Photoresponse above 85 K of selective epitaxy grown high-Tc superconducting microwires Appl. Phys. Lett. 117 032602

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Superconducting Materials and Their Applications An interdisciplinary approach Jatinder Vir Yakhmi

Chapter 5 Applications in Josephson junctions, SQUIDs, and MEG. Other low field applications

5.1 From quantum concepts to superconducting technology: Josephson junctions and SQUIDs The underlying mechanism of superconductivity, known as the BCS theory, was established in 1957 [1], and it applies well to the so-called low-Tc superconductors (LTSCs) like Nb3Sn. According to it, the superconducting state is characterized by the formation of pairs of conduction electrons (the Cooper pairs) which arise as a direct consequence of their interaction with the lattice. Above Tc, the thermal energy of the lattice overcomes the attraction between the partners of a Cooper pair, destroying the superconductivity. When a piece of metal is placed very close (within about 10−7cm) to a piece of another metal, conduction electrons have a finite probability of penetrating the potential barrier formed by the insulating layer between the two metals. It happens because electrons, owing to their wave nature, can tunnel through a thin insulating barrier between metals. Tunneling arises because the electron waves in metal do not cut off sharply at the surface but fall to zero within a short distance outside. Within that short distance, there is a small but finite probability that an electron will be found outside the metal. One could say that the electron wave leaks into the ‘forbidden’ barrier region. Zener [2] had already shown in 1934 that electrons could tunnel from the valence band into the conduction band of a semiconductor under the application of a large electric field. In 1958, Esaki [3] demonstrated a current tunneling between two semiconductors, for the first time, which led to the development of the tunnel diode. Superconductive tunneling was discovered by Giaever [4] in 1960 when he observed that the I–V characteristics of a normal metal–insulator–superconductor (NIS) and superconductor–insulator–superconductor (SIS) sandwich structures, were directly related to the excitation spectrum of the superconducting electrode.

doi:10.1088/978-0-7503-2256-0ch5

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Figure 5.1. A Josephson junction. Figure courtesy of Dr V K Aswal.

In 1962, Josephson [5] predicted that, in addition to the ordinary single-electron tunneling, the tunneling current between two superconductors should include a contribution from the tunneling of Cooper pairs, too. Thus, two superconducting thin films sandwiching a thin insulating layer (a barrier, of about ~20 Å thickness), made of silicon or of an oxide material, comprise what is known as a Josephson junction (figure 5.1). The superconductors on either side of the barrier are weakly coupled, i.e. the wave function describing a Cooper pair in superconducting film ‘1’ has a significant overlap with that of the other superconducting film ‘2’, across the insulating layer. The ‘size’ of the wave function is determined by the coherence length ξ of the Cooper pairs. The coherent quantum mechanical wave associated with the Cooper pairs leaks from the superconductor on each side into the insulating region. If the insulating barrier is sufficiently thin, the waves on each side must overlap, and their phases should lock together. Therefore, the Cooper pairs can tunnel through the barrier without breaking up, i.e. the two electrons forming a Cooper pair maintain their momentum pairing across the insulating gap and so the junction acts as a weak superconducting link, providing an ideal Josephson junction viz. two superconductors separated by a thin insulating layer.

5.2 Josephson junction electronics, computers and detectors Josephson tunneling of Cooper pairs through a barrier led to the emergence of the field of superconducting electronics. This is because while predicting that a superconducting current can tunnel through a thin insulating barrier between two superconductors without any resistance, Josephson also showed that the amount of current able to tunnel across the barrier had a maximum value that could be controlled by a very small magnetic field. A ‘Josephson junction’ (J.J.), therefore, acts as an ultrafast ‘switch’, a device that can operate much faster than the best semiconductor devices. The Josephson effect established that a supercurrent can tunnel across an insulating layer ‘O’ in between two superconductors A and B, without dissipation, and without losing the coherence of the wave function. The amount of supercurrent is related to the difference in the phases of the two superconductors θA and θB.

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This current flow is usually known as a continuous Josephson effect, and it is very sensitive to an external magnetic field. On the other hand, it is also possible to induce in the junction SCA–O–SCB an alternating current by applying a continuous voltage to the insulating layer. This alternating Josephson effect is currently used in a variety of superconducting electronic devices including radiation detectors, devices to manipulate high-frequency signals or fast-switching devices such as the ones used in computers and metrology. Switching voltage for J.J.’s is 100 times smaller than those encountered in semiconductor technology, allowing for miniaturization. Ultimate switching time of high-temperature superconductor (HTSC)-based J.J.’s could be 10−13–10−14s. Conventional semiconductor technology cannot approach such speeds. This could lead to building of ultrafast computers. The use of HTSC J.J.’s could extend the frequency detection range to 1012 Hz, which can have potential in high-resolution radar and space applications. Giaever tunneling of current does not occur, unlike Josephson tunneling, until a specific voltage is reached. Commercial ultrafast analog-to-digital converters could be made available on the principle that specific voltages, when applied to a superconductor, could switch it very rapidly (within a few picoseconds) from the Josephson tunneling regime to the Giaver tunneling regime.

5.3 Measurement of ultra-low magnetic fields by SQUIDs A device called SQUID (superconducting quantum interference device), which exploits the J.J. technology, is a magnetic field sensor of unparalleled sensitivity, approaching the limits allowed by the physical laws. A SQUID offers a sensitivity of ~fT (femto-Tesla) for the detection of very feeble magnetic signals, which cannot be measured by any other sensors [6]. A SQUID is essentially a superconducting ring, usually of size 1 mm or smaller, which is interrupted by one, or two thin insulating barriers (weak links). A SQUID is indeed a powerful tool using which measurements of magnetic flux of the order of 10−5 ϕ0 (where ϕ0 denotes one flux quantum) can be carried out in a bandwidth of 1 Hz. A SQUID (of the DC kind, described in what follows) can detect magnetic fields as low as 5 × 10−15 T. Accordingly, it can measure current as small as 10−18 A (only a few electrons per second), OR a potential difference as small as 10−18 V, and also operate much faster than the best semiconductor devices. SQUIDs find applications in diagnostics (biomagnetism), in magneto-telluric detection, in search of oil basins, and of course, in basic research involving the precise study of magnetic properties of materials. Before we look into the working mechanism of a SQUID, and its potential for applications in different areas, it is essential to underline that prior to the development of SQUIDs, it was a huge challenge to detect very small magnetic fields, which was attempted either by using Hall probes or by using what are called fluxgate sensors. The Hall probe was based on measuring the Hall voltage across a semiconducting element and had a sensitivity of ~mT, which was quite poor, and therefore, had only limited applications. A fluxgate sensor, on the other hand, 5-3

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offered a much higher sensitivity of ~nT, and to use it, one passed an AC through a coil wound around a magnetic core and measured the output voltage of the pickup coil. However, the drawback presented by a fluxgate sensor was that its output voltage was comprised of components of several frequencies, arising from the nonlinearities of the magnetization curve of the ferromagnetic core. The external magnetic field to be detected is given by the second harmonic component, measured in a phase-sensitive manner. It is a tough task to make this measurement because the fluxgate sensor needs to be driven in and out of saturation, repeatedly, to get rid of any measurable magnetic hysteresis. Besides, getting a good linearity of the fluxgate sensor requires a feedback loop, which runs a compensation current through a compensation coil to bring the magnetic field incident on the fluxgate sensor back to zero [7].

5.4 Types of SQUIDs The magnetic flux contained within a superconducting ring is quantized. Electrons tunneling through the Josephson junctions show quantum interference dependent on the strength of the magnetic field. Tiny changes in the magnetic field make the junctions behave like a resistor, and so enable the measurement of such tiny changes. There are two types of SQUIDS: the RF SQUID and the DC SQUID. The RF SQUID employs only one Josephson junction, i.e. a superconducting ring is interrupted by just one insulating barrier, as shown in figure 5.2. RF current is applied via a tank circuit inductively coupled to the SQUID loop. The damping of the RF tuned circuit is dependent on the magnetic flux passing through the ring. The energy resolution of an RF SQUID is, however, limited. The DC SQUID (direct current SQUID) has a superconducting loop interrupted by two insulating layers (weak links), as shown in figure 5.4. In other words, it has two J.J.s, connected in parallel. A DC SQUID has much higher sensitivity than an RF SQUID, but the fabrication of an RF SQUID is easier, requiring only one, rather than two, well-matched weak links1. The SQUID is said to be operated in a current bias mode, when one passes a DC current through it, which produces across it a voltage V depending in a nonlinear way on the magnetic flux threading the SQUID loop. To operate it in a voltage bias the voltage across the SQUID is kept constant and the current I through the SQUID is sensed. The voltage developed between the two limbs of the ring, when a fixed current is passed, is dependent on the magnetic flux impinging on it. The I–V characteristics of The flux through the ring is quantized and the flux can only take on values that are integer multiples of a basic quantum of magnetic flux ϕ0 = h/2e ≈ 2 × 10−7 gauss cm2. In a SQUID, the periodic flux variations are exploited to measure the current in the superconductor. Typically, the ring is inductively coupled to a radiofrequency circuit that both supplies a known bias field and serves as the detector output. Changes in the field can be measured by counting the peaks that are a result of the flux quantization, or a feedback loop can be employed to lock the radio-frequency circuit onto a single peak. The feedback current is then a measure of the ambient field. One can also form a DC SQUID by employing two Josephson junctions in the ring. When the two weak links are matched properly through design, the current in the ring has a DC response to the flux going through it [8]. 1

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Figure 5.2. An RF SQUID device reproduced from [8] (IOP).

Figure 5.3. SQUID voltage as a function of the applied flux, Φa. W is the working point. Reproduced with permission from [9]. Copyright IOP Publishing. All rights reserved.

Figure 5.4. Basic FLL circuit with direct readout. The DC SQUID is drawn as a circle with two crosses indicating the Josephson junctions. Everything inside the dashed box are at cryogenic temperature. Reproduced with permission from [9]. Copyright IOP Publishing. All rights reserved.

the DC SQUID get modulated by magnetic flux ϕ (one flux quantum being ϕ0 = h/ 2e = 2 ×10−15 T m2 or = 2.068 × 10−15 V s. Figure 5.3 shows the periodic dependence of the SQUID voltage V on applied flux ϕa, the period being the flux quantum ϕ0. The peak-to-peak modulation Vpp of the voltage across the SQUID is small, typically between 10 μV and 50 μV. A SQUID converts the flux threading its loop into a parameter detectable by a subsequent electronic circuit. The SQUID electronics amplifies the small SQUID signal to an acceptable level without adding noise, and it linearizes the transfer function of the SQUID in order to provide sufficient dynamic range. To operate a SQUID one needs a readout electronics, the main task of which is to amplify the weak voltage across the SQUID without adding (too much) noise. To obtain a linear transfer function, the SQUIDs are operated in a flux-locked loop (FLL) [9], as shown in figure 5.4.

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Due to its inherent capacity to sense very weak magnetic fields, a DC SQUID can provide useful magnetic signatures of fields several orders of magnitude smaller than the Earth’s magnetic field. A SQUID magnetometer employs a single wire loop and is the most basic sensor. However, to measure ultra-low magnetic fields such as those associated with a beating human heart, one has to enclose the SQUID magnetometer in a shielded room in order to shut out signal from the Earth’s magnetic field, which interferes, as a noise larger than the signal to be measured, by orders of magnitude. Magnetically shielded rooms are made from mu-metal.

5.5 Applications of SQUID magnetometers and gradiometers Gradiometers are used to suppress remote signals. A gradiometer is essentially a combination of two or more loops with antiparallel orientation, which allows the SQUID to measure the derivative of the field, B. This system ignores plane waves emitted from distant sources and focuses attention on local sources. There are two types of gradiometers, axial and planar. In axial gradiometers, the coils are placed above each other, while in planar gradiometers, they are in the same plane, as indicated in figure 5.5. Gradiometers measure changes in the magnetic field along their latitude. As the magnetic field of a dipole (at a distance ‘r’) decreases with r−2, the gradient of this field decreases with r−3. So, depending on their baseline (the distance between the two pickup coils), gradiometers behave like spatial highpass filters and damp signals from distant sources. SQUIDs magnetometers and gradiometers find applications, in the following broad areas: i. In biomagnetism—to study the magnetic fields produced by the electrical currents flowing in body tissues like skeletal muscles, heart, and brain. The

Figure 5.5. (a) Typical MEG measurement for detection of cerebral magnetic fields. The bottom of the He Dewar, with the flux-transformer pickup coils near its tip, is brought as close to the head of the patient as possible. (b) and (c) show two superconducting flux transformers employed in brain research: the axial gradiometer (b) and the planar gradiometer (c), which detect and record fields in different directions. Reproduced with permission from [12]. Copyright (1993) by the American Physical Society.

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ii.

iii. iv.

v. vi. vii. viii.

magnetic field of the nerve signals in the human brain is not distorted by the skull, unlike their electric field. Magnetoencephalography using SQUIDs (figure 5.5) is, therefore, increasingly employed to locate, say, epileptic centers, etc. In geophysics, to survey the ground for oil, water, and ore deposits by detecting anomalies in the Earth’s magnetic field. Prospecting hidden groundwater sources by monitoring geomagnetic signals is an activity of great societal benefit. The flow of water through rock generates a small magnetic signal produced by the electro-kinetic effect. SQUID magnetometry has the potential to allow passive studies of groundwater changes in complex systems. Survey of minerals buried deep in the Earth can be traced by carrying a SQUID sensor in a plane/helicopter and monitoring any magnetic field signatures coming from minerals which have better conductivity than the bare soil [10]. In magnetotellurics—to detect sources of geothermal energy. In palaeomagnetism—to determine the geological history of rock samples by studying their remanent magnetic fields. It helps to locate geological faults, also. In high energy physics—to detect exotic particles such as quarks, gravitons, and magnetic monopoles. In defense—to detect submarines lurking beneath the sea. In metallurgy—to detect tiny ion currents resulting from the process of corrosion of a metal. In civil structures like bridges to evaluate their functional safety by using SQUID sensors in nondestructive testing [11].

5.6 SQUID sensors for magnetoencephalography and biomagnetic applications 5.6.1 General SQUIDs offer unrivaled sensitivity in sensing very weak magnetic signals. A uniquely successful application of SQUIDs is for measurements of the tiny magnetic fields produced by the firing neurons in a human brain, using a technique known as magnetoencephalography (MEG) (figure 5.5). Just a few years after the invention of the SQUID, among its first applications was to conduct MEG of neuronal currents by David Cohen in 1972 [13]. MEG was conceptually demonstrated already by him in 1968 by using Faraday type detection with induction coils [14]. Currently, a stateof-the-art MEG system employs a helmet-shaped Dewar incorporating several hundred SQUID sensors (figure 5.6). The use of SQUID magnetometry for MEG has revolutionized the field of neuroscience and has proved to be a boon for conducting pre-surgical mapping of brain functions affected by brain tumors [17], to locate epileptic foci [18], and, for basic research in neuroscience [19]. Figure 5.7 depicts the comparative strengths of different biomagnetic signals from a human being which a Squid sensor can pick up, even in the presence of much stronger environmental signals. The magnetic fields used for MRI are, of course, orders of magnitude higher in comparison, as shown. 5-7

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Figure 5.6. On left side is shown the commercial whole-head MEG systems marketed by Elekta Neuromag® TRIUX, reproduced from Korber et al [15]. The helmet used by this system, reproduced from Penna et al [16], is shown on right side. It consists of 306 channels arranged in 102 sampling positions. Each measurement module consists of two orthogonal planar gradiometers and one coplanar magnetometer all integrated into a single chip. Copyright IOP Publishing. Reproduced with permission. All rights reserved.

Figure 5.7. The very weak biomagnetic signals which a SQUID sensor can pick up are shown. The tesla is the SI unit of the magnetic field, For comparison, the Earth’s field ranges between approximately 25 000 and 65 000 nT (0.25–0.65 G), and a strong refrigerator magnet has a field of about 10 000 000 nT (100 G). Figure courtesy, Dr V K Aswal.

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Figure 5.8. An ULF-MR SQUID setup with low-noise Dewar. Reproduced from [15]. Copyright IOP Publishing. Reproduced with permission. All rights reserved.

An ULF (ultra-low field)-MRI system prepolarizes the volume of interest using a field of about 100 mT, so that the MR signal can be recorded at a still lower field of tens to hundreds of μT, with un-tuned SQUID detection. Such systems are based on coupling a superconducting pick-up coil inductively to a SQUID, so that one can use it for recording both MEG and ULF MRI [20]. To investigate spiking activity by MEG, Korber et al [15] have designed a new system (figure 5.8) using a shield made of alumina to reduce noise substantially to record both ULF MRI and high frequency MEG signals. It employs a first order gradiometer. NMR/MRI, when done in ultra-low magnetic fields, has advantages of economy and patient convenience. Besides, it has the potential to provide enhanced contrast of cancerous tissue to healthy tissue without using a contrast agent. 5.6.2 Magnetocardiography (MCG) SQUIDs are useful to conduct magnetocardiography (MCG), i.e. to measure the magnetic fields produced by the human heart. A multichannel SQUID system can

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Figure 5.9. A magneto-cardiogram (MCG) being recorded using a 37 channel MCG unit built indigenously at Indira Gandhi Centre for Atomic Research (IGCAR), Kalpakkam (India). It is used to study the electrophysiology of human heart and cardiac dysfunctions. Using an array of SQUID sensors mounted inside a liquid-He cryostat installed in a magnetically shielded room, this unit can record extremely weak magnetic fields (100 fT to 100 pT) with a resolution of 10 fT. On the right is shown an 86 channel system, also assembled indigenously and used for MEG measurements. Figure reproduced with permission from IGCAR.

monitor the currents flowing in the heart muscle (figure 5.9), which has a unique advantage in the case of a fetal MCG [21]. To date, the only technique available for reliable determination of the ‘His’ventricular (HV) interval, an important index of atrioventricular conduction, has been electrophysiology (EP), which is invasive. The signal produced by the activation of the bundle of ‘His’ is of very small magnitude, which cannot be seen on an ECG. Due to the high sensitivity offered by SQUID sensors in the measurement of weak cardiac magnetic fields inside magnetically shielded rooms, SQUIDbased magnetocardiography (MCG) is emerging as a direct non-invasive technique which can successfully track the ‘His’-bundle signals as against the body surface potential measurements, or even the high-resolution ECG [22].

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5.6.3 Specific biomagnetic applications of SQUID sensors in human health Clinical: 1. Pre-surgical screening of brain tumors (evoked response); and 2. Location of epileptic foci (spontaneous signals). Research: 1. Language mapping in the brain; 2. Diagnostics of schizophrenia in patients; 3. Identification of patients with dyslexia; 4. To investigate Alzheimer’s disease and Parkinson’s disease; and 5. To evaluate neurological recovery following a stroke or hemorrhage. 5.6.4 Study of brain processes non-invasively by imaging of brain functions The first methods to image brain functioning were positron emission tomography (PET) and single photon emission computer tomography (SPECT). In both of them, a patient is administered radioactive molecules which are known to increase their concentration in metabolically active areas. The detection of emitted gamma-radiation (i.e. photons) gives useful information about metabolic processes. The major drawback of these techniques is that they are invasive since administering radioactive substances is a must. Compared to PET or SPECT, high spatial resolution can be achieved with fMRI. However, all these three methods are based on indirect measurements of neuronal activity, implicating a temporal delay to the observed parameters. Studying brain processes more directly is possible with electro- or magnetoencephalography (EEG/MEG). With these completely noninvasive techniques, electric potentials or magnetic fields are measured, respectively. They are generated by tiny currents in activated neurons and make neuronal processes visible with high temporal resolution (millisecond). The spatial resolution, however, is usually lower than that of PET and fMRI [23]. 5.6.5 MEG in comparison to EEG, fMRI, and fNIRS Reprinted in part from [24] with permission from Elsevier. As explained above, MEG is an invaluable tool allowing researchers to study brain activity by recording the magnetic fields generated by the electrical activity of neurons. MEG can be used for diagnostics by studying brain activity in the functional and dysfunctional body and brain states. MEG systems are based on highly sensitive SQUID sensors that non-invasively record—outside of the human head—minute magnetic fields that are generated by neural activity in the brain. Current state-of-the-art, whole-head systems use about 300 sensors that are spatially arranged in a helmet-shaped Dewar (cryogenic storage container) (figure 5.6). The Dewar is filled with liquid helium at a temperature of about −269 °C, just four degrees Celsius above absolute zero temperature. Current commercial, whole-head systems using SQUID sensors can measure very weak magnetic fields in the femto-tesla range [12]. Each SQUID is coupled to a pickup coil and measures the 5-11

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changing magnetic flux through this coil. Typical MEG signals recorded from the brain have an amplitude of the order of 100 femtotesla (fT), which is 7–8 orders of magnitude lower than the Earth’s magnetic field and even about three orders of magnitude smaller than the magnetic field generated by the heart [24]. MEG systems are operated in a magnetically shielded room to avoid interference from ambient magnetic fields. MEG relies on the fundamental physical principle that electrical currents are always associated with magnetic fields. In the brain, these currents are produced during neural activity by the movement of ions in intra- and extracellular space. Ion currents linked to postsynaptic potentials are the most significant contributors to the MEG signal. Pre-synaptic neurotransmitter release leads to postsynaptic dendritic trans-membrane currents. When primary intra-cellular current and extracellular return currents in the opposite direction flow simultaneously across neighboring neurons with a similar dendritic orientation, synchronous activation of a few tens of thousands of neurons leads to robust detectable signals, corresponding to individual magnetic fields which add up to detectable field strength, that can be recorded by MEG sensors near the scalp. Current sophisticated MEG systems featuring nearly 300 sensors to cover the whole scalp qualify as appropriate for the study of large-scale brain dynamics because these SQUID systems have capabilities to provide: i. whole-brain coverage; ii. a silent and noninvasive recording; iii. excellent temporal resolution; iv. good spatial resolution; v. low sensitivity to uncertainties about tissue conductivities; and vi. direct coupling of the recorded signal to neural activity independent of neurovascular coupling. High temporal resolution of MEG is particularly advantageous as it helps to characterize the spatiotemporal progression of stimulus-related neural processes throughout the brain. MEG scans have already made valuable contributions to our understanding of the relationship between the (rhythmic) dynamics of large-scale brain activity and human behavior in health and disease. MEG data, when acquired in combination with other signals, can, at times, lead to novel applications that can potentially make significant contributions to neuroscience. Examples are recording both MEG and the electrooculogram (EOG) to facilitate the identification of artifacts related to eye movements or blinks. MEG is also recorded sometimes together with the electromyogram (EMG), which records muscle activity. Similarly, it is beneficial to record MEG alongside electrodermal activity (EDA), or with the electrocardiogram (ECG), or the electrogastrogram. Cognitive neuroscience inputs can be obtained by recording MEG, simultaneously with transcranial electric stimulation (TES) or deep-brain stimulation (DBS). MEG data combined with other useful data, computational brain network modeling and neuro-stimulation is poised to gain mechanistic insights into brain function or dysfunction. 5-12

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Figure 5.10. Resolution (temporal and spatial) of MEG, compared with functional other brain imaging techniques, including magnetic resonance spectroscopy (MRS) and invasive EEG (IEEG). Figure courtesy Dr V K Aswal.

MEG has a high temporal resolution (like EEG) when compared to fMRI (functional magnetic resonance imaging) or fNIRS (functional near-infrared spectroscopy). The spatial resolution provided by MEG is about the best (figure 5.10). MEG can have sensors covering most of the scalp, while fMRI does not have this limitation, whereas fNIRS has limited coverage. MEG/EEG signals are more directly related to neuronal activity compared to fNIRS and fMRI. While making an inter-comparison of different techniques, one finds that in comparison with EEG, the MEG signals are less distorted by changes in tissue conductivities. MEG, EEG, and fNIRS are silent recording techniques in contrast with fMRI, where gradient coils produce noise during data acquisition. A positive with MEG is that it is not affected by the problems commonly caused by intermediate processes, such as neurovascular coupling in fMRI or fNIRS. This is because there is a direct relationship between the recorded magnetic field under MEG and the underlying neuronal currents. In recent times, the availability of optically-pumped magnetometers (OPMs), have made possible to have a motion-robust MEG device, such that the MEG-OPM sensors can be integrated into more mobile MEG systems, as reported by Hill et al [25]. Cost-wise, fMRI systems are the most expensive, followed by MEG, and more affordable EEG and fNIRS systems [24]. 5.6.6 Origin of electromagnetic signals and role of MEG for neurophysiology A neuronal cell, like the pyramidal cell of the human cortex shown in figure 5.11, consists of many dendrites, the cell body, and an axon and is connected to other neurons by synapses. Information is received by the dendrites and relayed via the axon. Within a neuron, signals are carried electrically, whereas information transfer between different neurons, muscles, or sensory receptors takes place chemically. Inside a neuron, at rest, there is a surplus of potassium ions (K+) and a deficit of sodium ions (Na+). Additionally, the cell has a resting potential of −70 mV compared to the extracellular space. 5-13

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Figure 5.11. A pyramidal neuronal cell, and its three magnified synapses. Reproduced with permission from reference [12]. Copyright (1993) by the American Physical Society.

When a signal from an axon reaches the synapse (figure 5.11), it leads to an output of certain chemicals into the synaptic cleft. This opens ion channels at the adjacent neuronal cell, and the ion flow builds up a postsynaptic potential (PSP) across its membrane. The PSP can increase the potential difference between intracellular and extracellular space, which is inhibitory and hyperpolarizing, or it can decrease the potential difference, in which case it is excitatory and depolarizing. If an excitatory PSP exceeds a certain threshold at the axon hillock, an action potential is created in this cell and will be transported further through its axon to other cells. The action potential of about +30 mV activates the neuronal cell and opens channels in the membrane to enable Na+-ions to get in. A depolarization wavefront travels along the axon. Compensation of electrical charges is achieved through K+-ions flowing out, leading to repolarization. Due to the disturbed K+–Na+ equilibrium, now K+-ions have to be pumped into, and Na+-ions out of the cell. This process of restoring the original ion distribution, consumes energy and takes some time, during which no further signals can be passed. Both the action potential and the PSP cause intra-cellular current flow, the socalled primary currents. Due to the conservation of electrical charges, extracellular secondary or volume currents can be observed, too. A large number of simultaneous potentials are needed to create an extra-cranially detectable signal, because the single contributions are so small to detect.

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Figure 5.12. Zoom of a part of the cortex, illustrating different dipole orientations under radial and tangential sources, generating a negligible (Φr) and a detectable (Φt) flux, respectively. Volume currents and radial sources do not contribute to the magnetic field external to the head. This makes MEG an ideal technique to catch only neuronal activity not distorted by volume properties. Reproduced with permission from: [16]. Copyright IOP Publishing. All rights reserved.

The action potentials are relatively short in time (about 1 ms). The traveling depolarization and repolarization waves produce two opposite currents, which can be seen as a quadrupolar current from a distance. For these reasons, the action potentials in different cells are rather unlikely to occur synchronously. The extracranial fields are mainly generated by the excitatory PSPs, which are spatially less distributed and present for about 10 ms. Thus, the apical dendrites of the cortical pyramidal cells, which are aligned in parallel, are considered to be the principal generators of both MEG and EEG signals. The center of these neuronal sources can be treated as an equivalent current dipole (ECD), since the measured field patterns are similar to the field of a current dipole, like a small source viewed from a remote position. The currents flow perpendicular to the cortical surface, and because of the convoluted structure of the cortex, the orientations of the currents change (figure 5.12). It should be noted that the MEG can detect magnetic fields of dipoles lying only tangentially to the skull surface because these fields leave and re-enter the head, whereas the fields of radial sources do not. The radial sources are magnetically silent, relatively, because they exist in exact spherical symmetry, as in realistically shaped head models, and they produce signals five to ten times smaller than the tangential sources. 5.6.7 Brief details about MEG instrumentation and operation Neuronal magnetic fields are very small and lie in a typical range between fT and a few pT. Measurement of these tiny biomagnetic signals is indeed tough since these signals due to neuronal activity are much smaller than the fields prevalent in the 5-15

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surrounding environment. For instance, the signal to be measured is one billion to one million times weaker than the Earth’s magnetic field of 50 μT, and orders of magnitude smaller than the fields exerted by other external noise sources (figure 5.7). To measure MEG signals, therefore, one employs sensitive detectors and elaborate noise reduction methods [12, 26]. Currently, these tiny neuromagnetic signals are measured using SQUIDs, exclusively. The SQUIDs are coupled to small conductor loops, called flux transformers, which consist of a pickup coil and a coupling coil. The field change perpendicular to the face of the pickup coil induces a voltage. Since the whole flux transformer is superconducting, this voltage causes a loss-free current, which produces a magnetic field within the coupling coil, and the SQUIDs detect this field. The SQUIDs and the flux transformers are both superconducting and have to be operated at very low temperatures. Therefore, they are kept in a thermally insulated Dewar, which is cooled with liquid helium (4.2 K). Usually, the entire MEG system is surrounded by a magnetically shielded chamber to minimize environmental interference. Today’s whole-head MEG systems can comprise various pickup coil arrangements leading to different sensor types [16]. As an example, the 306 channel VectorView device of Elekta Neuromag Oy (Helsinki, Finland), comprises 102 magnetometers and 204 planar gradiometers (shown in figure 5.6), and each of its 102 sensor chips, contains one magnetometer and two orthogonal gradiometers.

5.7 High-Tc SQUIDs Both high-Tc and low-Tc superconducting materials can be used for fabricating SQUIDs, having typical operation temperatures of 77 K (liquid nitrogen) and 4.2 K (liquid helium), respectively. Although the magnetic field sensitivity of a low-Tc SQUID is superior to its high-Tc equivalent, there are several essential advantages of high-Tc technology. Firstly, liquid nitrogen systems at 77 K require less thermal insulation than liquid helium systems operating at 4.2 K. This advantage leads to a reduction of the spacing between the cold sensor and a room-temperature sample such as a human scalp, to just a few mm compared with 2–4 cm, typical for a liquid helium system supported low-Tc SQUID. A liquid nitrogen system is also more flexible than a liquid helium system (figure 5.13). For MEG, the rigid helmet Dewar that does not fit arbitrary head shapes could be replaced by a flexible array of SQUIDs mounted in novel cooling systems. As discussed before, the SQUID sensors are made of SNS (superconductor/ normal metal/superconductor) junctions. Sensitivities of the SQUID system based on SNS junctions operating in a superconducting magnetic shield are more than 100 times those of the same SQUID system in a magnetically shielded room of permalloy. The neuromagnetic experiments indicate that one of the most important applications of a high-Tc superconductor, in future, would be to provide a superconducting magnetic shield for SQUID systems. A superconducting magnetic shield, having a diameter is 65 cm and length 60 cm, has been fabricated successfully, a few years ago, from the high-Tc superconductor Bi(Pb)–Sr–Ca–Cu–Ox (Tc = 103 K). 5-16

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Figure 5.13. A model high-Tc SQUID-based MEG system, showing a subject’s head surrounded by an array of single-sensor cooling modules. Typically, a distance of ~10 mm should suffice between the pickup loop of each high-Tc SQUID and the subject’s brain, as shown in the inset. In view of the liquid nitrogen Dewar to be used (T ~77 K), a single cooling module with outer vacuum enclosure and insulation space, can, in principle allow the sensor to be just 1 mm away from the head surface, and can outperform a typical low-Tc array despite higher levels of sensor noise in a high-Tc SQUID. Reproduced with permission from [15]. Copyright IOP Publishing. All rights reserved.

For this, the inside wall of a nickel cylinder was coated with a 0.5 mm thick film of Bi(Pb)–Sr–Ca–Cu–Ox, deposited by high-temperature spray-coating [27]. The complete system was used successfully to measure somatosensory evoked magnetic field of human brains in the HTSC magnetic shield.

References [1] Bardeen J, Cooper L N and Schrieffer J R 1957 Theory of superconductivity Phys. Rev. 108 1175–204 [2] Zener C 1934 A theory of the electrical breakdown of solid dielectrics Proc. R. Soc. A 145 523–9 [3] Esaki L 1958 New phenomena in narrow germanium p-n junctions Phys. Rev. 109 603–4 [4] Giaever I 1960 Energy gap in superconductors measured by electron tunneling Phys. Rev. Lett. 5 147–8 Also see Nobel Lecture by I Giaever (1973) [5] Josephson B D 1962 Possible new effects in superconducting tunneling Phys. Lett. 1 251–3 [6] Janawadkar M P et al 1999 SQUIDs—highly sensitive magnetic sensors Curr. Sci. 77 759–69 https://www.jstor.org/stable/24102687 [7] DRV425 Fluxgate Magnetic-Field Sensor, Texas Instruments, SBOS729A—Oct. 2015– Revised March 2016. http://www.ti.com/lit/ds/symlink/drv425.pdf [8] Edelstein A 2007 Advances in magnetometry J. Phys.: Condens. Matter 19 165217 [9] Drung D 2003 High-Tc and low-Tc dc SQUID electronics Supercond. Sci. Technol. 16 1320–36 [10] Foley C P et al 1999 Field trials using HTS SQUID magnetometers for ground-based and airborne geophysical applications IEEE Trans. Appl. Supercond. 9 3786–92 [11] Krause H-J and Kreutzbruck M 2002 Recent developments in SQUID NDE Physica C 368 70–9 [12] Hamalainen M, Hari R, Ilmoniemi R J, Knuutila J and Lounasmaa O V 1993 Magnetoencephalography—theory, instrumentation, and applications to noninvasive studies of the working human brain Rev. Mod. Phys. 65 413–97

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[13] Cohen D 1972 Magnetoencephalography: detection of the brain’s electrical activity with a superconducting magnetometer Science 175 664–6 [14] Cohen D 1968 Magnetoencephalography: evidence of magnetic fields produced by alpharhythm currents Science 161 784–6 [15] Körber R et al 2016 SQUIDs in biomagnetism: a roadmap towards improved healthcare Supercond. Sci. Technol. 29 113001 [16] Penna S D, Pizzella V and Romani G L 2014 Impact of SQUIDs on functional imaging in neuroscience Supercond. Sci. Technol. 27 044004 [17] Roberts T P L, Ferrari P, Perry D, Rowley H A and Berger M S 2000 Presurgical mapping with magnetic source imaging: comparisons with intraoperative findings Brain Tumor Pathol. 17 57–64 [18] Ray A and Bowyer S 2010 Clinical applications of magnetoencephalography in epilepsy Ann. Indian Acad. Neurol. 13 14–22 [19] Hansen P C, Kringelbach M L and Salmelin R (ed) 2010 MEG: An Introduction to Methods (New York: Oxford University Press) [20] Zotev V S, Matlachov A N, Volegov P L, Urbaitis A V, Espy M A and Kraus R H 2007 SQUID-based instrumentation for ultralow-field MRI Supercond. Sci. Technol. 20 367–73 [21] Koch H 2001 SQUID magnetocardiography: status and perspectives IEEE Trans. Appl. Supercond. 11 49–59 [22] Sengottuvel S, Selvaraj R J, Patel R, Santhosh S, Gireesan K, Janawadkar M P and Radhakrishnan T S 2017 Non-invasive determination of HV interval using magnetocardiography PACE 40 568 [23] Baillet S, Mosher J C and Leahy R M 2001 Electromagnetic brain mapping IEEE Signal Process Mag. 18 14–30 [24] Gross J 2019 Magnetoencephalography in cognitive neuroscience: a primer Neuron 104 189–204 [25] Hill R M et al 2020 Multi-channel whole-head OPM-MEG: Helmet design and a comparison with a conventional system Neuroimage 219 116995 [26] Vrba J and Robinson S E 2001 Signal processing in magnetoencephalography Methods 25 249–71 [27] Ohta H, Matsui T and Uchikawa Y 2007 A whole-head SQUID system in a superconducting magnetic shield IEEE Trans. Appl. Supercond. 17 730–33

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Superconducting Materials and Their Applications An interdisciplinary approach Jatinder Vir Yakhmi

Chapter 6 Applications in the areas of diagnostics and neuroscience

In chapter 4, we have discussed applications based largely on bulk superconducting materials, such as wires/cables for the power sector dealing with energy transmission and storage, as high-field magnets wound from superconducting cables/wires, such as for MRI machines, maglev, particle accelerators and fusion reactors; or as thin films, such as in RF cavities. The largest commercial market for superconducting magnets has, of course, been for their application in MRI scanners. In chapter 5, we described the low field applications of superconductors, such as the use of sensitive SQUID sensors (figure 5.7) in mapping the very low magnetic fields generated by the human heart using the technique called magnetocardiography (MCG), or in the brain known as magneto-encephalography (MEG). We also tried to focus on the specific capabilities of MEG, when compared with other scanning techniques such as EEG, fMRI, and fNIRS and other functional brain imaging techniques, including magnetic resonance spectroscopy (MRS) and invasive EEG (iEEG) (figure 5.8). In this short chapter, we endeavor to take up the recent progress in brain imaging techniques based on superconducting materials, such as MRI and MEG, to investigate how brain function supports mental activities, i.e. cognitive neuroscience. For instance, we shall discuss how rt-fMRI-NF (real-time functional magnetic resonance imaging neurofeedback) has been emerging, not just as a diagnostic tool, but also for therapy, i.e. treatment of neuro-psychiatric disorders; and, the recent dramatic growth of human brain-mapping after the advent of fMRI BOLD (‘blood oxygen level dependent contrast’) imaging. Similarly, psycho-physiological MEG studies are beginning to assume a role in suppressing the spontaneous brain activity in favor of the evoked activity.

doi:10.1088/978-0-7503-2256-0ch6

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6.1 Brain imaging and cognitive neuroscience Cognitive neuroscience deals with the study of how brain function supports mental activities. Among the different brain imaging techniques, the oldest is x-ray computed tomography (CT), which was introduced in 1971 by Godfrey Hounsfield. It deals with obtaining three-dimensional transaxial tomographic images by passing highly focused x-ray beams through the brain and recording their attenuation [1]. However, CT is an anatomical tool, whereas ‘functional brain imaging’ for humans falls in the purview of the techniques known as positron emission tomography (PET), functional magnetic resonance imaging (fMRI), electroencephalography (EEG), electrocorticography (ECoG), magnetoencephalography (MEG) and, optical imaging with nearinfrared spectroscopy (NIRS). MEG employs the unique sensitivity of SQUID magnetometry, using which magnetic fields of the order of 10−11 Oe can be detected, which translates into measurement of magnetic flux with a resolution of the order of 10−5 ϕ0 in a bandwidth of 1 Hz. MEG has unique applications in diagnostics through brain imaging related to neuro-disorders, plus as a general tool for biomagnetism. SQUID magnetometry also finds applications in magneto-telluric detection, in the search for oil basins and in basic research for precise study of magnetic properties. Both PET and MRI (explained in chapter 4), have the capability to do functional brain imaging because any changes in the cellular activity cause local blood flow changes in the brain, quite similar to the earlier non-tomographic techniques. Positron emission tomography (PET) employs radionuclides with short half-lives, viz. 15O (2 min), 13N (10 min), 11C (20 min) and 18F (110 min), which decay by emission of positrons, providing a link between biology and medicine, fortuitously, because carbon, nitrogen and oxygen are the building blocks of most biological molecules and fluorine can be substituted for hydrogen in some instances. While working with these positron-emitting radionuclides, if an image of the density of a transverse section of the body could be reconstructed from the measured attenuation of highly-focused x-ray beams projected through the section (i.e. x-ray CT), then the distribution of a radionuclide within the section (especially ones that decayed by positron emission) could be accurately and quantitatively reconstructed from its emissions, which became the basis of PET. MRI gained quick popularity because it doesn’t use any ionizing radiation and yields superb images of the human body with much greater detail and variety than CT because of its high sensitivity to soft tissues. Owing to the existence of a correlation between the neuronal activation and cerebral blood flow, the use of any region of the brain leads to (calls upon) an increased blood flow to that region of the brain. The fMRI (functional MRI), which measures brain activity by detecting changes associated with blood flow, has turned out to be a serious player in the functional mapping of the human brain, as discussed in an overview by Glover [2]. 6.1.1 rt-fMRI-NF In recent years, a non-invasive MRI-based technique called rt-fMRI-NF (real-time functional magnetic resonance imaging neurofeedback) has been emerging as a tool 6-2

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for the treatment of neuro-psychiatric disorders. Under rt-fMRI-NF, we have, perhaps for the first time, the potential to use a neuroscience-based intervention to train human brain function towards healthier patterns [3]. Real-time functional magnetic resonance imaging neurofeedback (rt-fMRI-NF) presents fMRI signals to participants in a real-time manner to change their behaviors. Any resultant alterations in comportments observed after real-time fMRI as neurofeedback are postulated to be caused by neural plasticity driven by the induction of specific targeted activities at the neuronal level (targeted neural plasticity model). 6.1.2 Blood oxygenation level dependent (BOLD) MRI Using contrast agents and rapid data acquisition strategies, one can use MRI to measure changes in brain blood volume produced by physiological manipulations of brain blood flow. High contrast MRI images relevant to functional mapping of the human brain can yield excellent results when combined. However, one can administer a contrast agent only a limited number of times. This limitation could be addressed due to the property of deoxyhemoglobin itself in a magnetic field. The magnetic susceptibilities of oxygenated and deoxygenated hemoglobin differ significantly. Unlike oxyhemoglobin, the deoxyhemoglobin is paramagnetic and, hence, can function as an MRI contrast agent. The deoxygenated hemoglobin that is present in the veins acts like a little magnet due to its paramagnetic behavior. Under a magnetic field, such as during an MRI scan, owing to the presence of the exposed iron in the hemoglobin molecule, and its presence in large veins in the resting state, the deoxygenated hemoglobin makes the veins stand out as dark lines. However, the presence of oxygen in the oxygenated hemoglobin, found in arteries, ‘neutralizes’ this effect of the iron such that oxygenated blood can be present in a magnetic field without disrupting it. BOLD imaging, however has its limitations because the cerebral blood flow (CBF), being an indirect marker of activity cannot visualize the active cortex directly. Besides, any increased activity of the brain takes time (about 5 s) to generate increased CBF, and further, the blood flow can be regulated in only a small region (a few mm dia). Functional brain imaging with PET, or with fMRI are both based on changes in the circulation in the brain, and on metabolisms that are associated with activity changes in both neurons and astrocytes. The profile of these changes was first detailed by PET, which showed that increases in blood flow and glucose utilization far exceeded that of oxygen utilization. Consequently, the amount of oxygen available in the brain increases, causing the relative percentage of paramagnetic deoxyhemoglobin to decrease. The fMRI signal arises because of this change in the relative amount of deoxyhemoglobin (deoxyHb). Dark areas of veins (containing deoxyHb) disappear when the subject breathes on 100% oxygen. In the human fMRI experiment, deoxyHb can decrease when blood flow increases more than oxygen consumption, leading to an enhancement of the fMRI BOLD signal. While on 100% oxygen, the venous structures disappear, which is called the ‘blood oxygen level dependent contrast’ or BOLD contrast, as discussed by Ogawa et al [4], which provides

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an additional feature to magnetic resonance imaging. The human brain-mapping has seen a dramatic growth, since the advent of fMRI BOLD imaging.

6.2 Neuro-diseases 6.2.1 Tourette syndrome Although the critical potential of rt-fMRI-NF is quite general, being applicable to treat conditions arising from depression to Parkinson’s disease, it is quite useful as a clinical intervention for Tourette syndrome (TS). TS is a neurodevelopmental disorder characterized by childhood onset of motor and vocal tics affecting an estimated 14/1000 children, with peak severity afflicting adolescents, who undergo repetitive movements or vocalizations known as tics. Recently, Yale researchers trained 21 adolescents aged 11 to 19 years with TS to control their tics through rtfMRI-NF, which allows them to monitor the function of their own brain in real time. TS has been linked with dysfunction in motor corticostriatal–thalamo-cortical loops, and the supplementary motor area (SMA) is particularly a key node in the dysfunctional neural circuit underlying the chronic tics of TS. Stimulation of the SMA can produce movements as well as urges to move, similar to tics and the premonitory urges experienced by patients with TS. The imaging technique rt-fMRI-NF has been used by Sukhodolsky et al [5] to track the feedback from the supplementary motor area (SMA), the brain region associated with tics in Tourette syndrome. To date, the tics in TS are treated using behavior therapy and pharmaceuticals, but not every case responds to those efforts. The rt-fMRI-NF intervention has great potential, therefore, for treating TS, since NF can potentially harness feedback learning to train targeted control over the neural circuitry underlying tic generation. Neuro-feedback is a low-risk, drug-free treatment, and although functional neuroimaging is expensive, the time commitment for neurofeedback scans is less than that spent on a course of behavioral therapy for tics. Being a new technique, the neurofeedback protocol is yet to be optimized, and the efficacy of this intervention for TS is expected to increase with time. Neurofeedback lets patients see activity in a particular brain region while thinking of specific cues. In this way, a patient learns which cues trigger the most activity, and can therefore trigger the development of more connections. As a brain scanner measures brain activity, the patients imagine motor tasks while looking at a bar representing activity in the SMA region. Neurofeedback training may increase brain connectivity in patients with Huntington’s disease (HD), too, even after some degeneration, with chances to improve behavior and movement abnormalities. 6.2.2 rt-fMRI-NF for ADHD Critical underlying neurofunctional deficits can be targeted by using fMRI-NF [6], which teaches participants (even children) to self-regulate ‘blood oxygen level dependent’ (BOLD) response in specific brain regions based on real-time feedback of their brain activation [7]. 6-4

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The advantages of fMRI-NF are no known side effects and potential longer-term neuroplastic effects. Neurofeedback using fMRI has several advantages over EEGneurofeedback. Due to its superior spatial resolution, it can target key neurofunctional biomarkers, such as the inferior frontal cortex or the basal ganglia, which cannot directly be reached with EEG-Neurofeedback, as observed by Rubia [6]. Although more costly per session, self-regulation is typically achieved much faster with fMRI-neurofeedback than with EEG-neurofeedback. The comparison between pre- and post-fMRI-neurofeedback of a typically dysfunctional frontal region in ADHD adolescents showed a significant decrease in the ADHD symptoms. To rule out behavioral changes in conventional real-time fMRI neurofeedback studies due to any alternative accounts, including the placebo effect and physiological artifacts, a decoded neurofeedback (DecNef) system has been developed by Shibata et al [8] by an integration of implicit neurofeedback and fMRI multivariate analysis. DecNef provides strong evidence for the targeted neural plasticity and refutes the possibility of any artifacts causing it. It has also been shown by employing DecNef that the targeted neural plasticity occurs at the neuronal level during DecNef training.

6.3 The salience network (SN) A collection of parts of the human brain, comprising the anterior insula (AI) and dorsal anterior cingulate cortex (dACC), is known as the salience network (SN), or more technically, the cingulo-opercular network. Along with its interconnected brain networks, the SN plays an important role in the conduct of complex human behavioral functions, such as communication, self-awareness and social behavior by collating cognitive, sensory and emotional information. Several psychiatric disorders, such as schizophrenia, Alzheimer’s disease, post-traumatic stress disorder, anxiety disorders and frontotemporal dementia have been linked with the dysfunction of the SN [9]. During anxiety disorders, the anterior insula (AI) node of the SN may become hyperactive which can lead to a worried state of mind. A reduction of salience of social stimuli related to eyes, gaze and face in the case of autistic people is thought to be responsible for relatively impaired social skills in them, as observed by Menon [10]. fMRI studies have, in fact, pointed to the severely affected SN across several psychiatric disorders, because the SN coordinates the neural resources of the brain in response to the detection of the behaviorally relevant stimuli by it [11].

6.4 SN and the mesolimbic dopamine system Dopamine neurons also play a role in the identification of behaviorally relevant environmental stimuli. Mesolimbic dopamine neurons are instrumental in assigning salience to relevant environmental stimuli [12, 13]. Dysfunction of this system is also observed in many neuropsychiatric illnesses [14, 15]. Mesolimbic dopamine signaling plays a role in the modulation of the salience network which, therefore, calls for the development of an integrative understanding of SN and the mesolimbic dopamine system. Using positron emission tomography (PET) to measure dopamine 6-5

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release capacity and dopamine synthesis capacity in the ventral striatum; and resting-state fMRI to investigate salience network functional connectivity in some individuals, it has been shown that the dopamine synthesis capacity is associated with greater salience network connectivity, particularly for the brain regions that act as information-processing hubs. In contrast, the dopamine release capacity was associated with weaker salience network connectivity. These findings demonstrate a close relationship between the salience network and mesolimbic dopamine system, and its relevance to neuropsychiatric illnesses which produce aberrant functioning of both these systems, as reported by McCutcheon et al [16].

6.5 Magnetic resonance perfusion In patients with risk factors for coronary artery disease, a common strategy employed for diagnosis is invasive angiography to visualize the presence and extent of coronary artery disease, supported by the assessment of fractional flow reserve (FFR) to guide the need for subsequent revascularization. One can alternately go for a noninvasive test for the detection of coronary artery disease, viz. myocardialperfusion cardiovascular magnetic resonance imaging (MRI), which has a high concordance with FFR for ischemia detection, as explained by Nagel et al [17]. Cardiovascular MRI has been associated with a lower incidence of invasive angiography than testing based on clinical risk assessment. In the group undergoing cardiovascular-MRI, myocardial perfusion cardiovascular MRI was performed with the use of scanners that had a magnetic field strength of 1.5 T. Myocardial perfusion was assessed with the first pass of gadobutrol (in the form of Gadovist, from Bayer, Germany) typically at a dose of 0.075 mmol kg−1 of body weight during adenosine infusion.

6.6 BIO-interface 6.6.1 Studies on dog brains and function Humans have bred different lineages of domestic dogs for different tasks, like hunting, herding, guarding, or companionship. In a first study of its kind, scientists have documented how brain structure varies across dog breeds and corresponds to the specific behavior each breed is known for. These behavioral differences have arisen from their underlying neuro-anatomical differences, which were the subject of an MRI study made in 2019 by Hecht et al [18]. It hints that though the brain structure is related to function, there does exist an interaction between genetically determined neuro-anatomy and learned behavior. 6.6.2 Plant biomechanics As the fruit of a witch hazel plant dries out, the top part of the woody capsule around the seed splits open. The middle part of the capsule constricts, as if it were squeezed by fingers, until the seed, about the size of a pumpkin seed, breaks free and flies out at about 28 miles h−1. Just before it shoots out, one hears the sound of a crack which is caused by a squeezing, because there is no other explosive mechanism to 6-6

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it. As it flies, the seed is spinning fast at about 12 000–25 000 revolutions per minute, which enables the seed to travel far, landing several yards away. Interestingly, the seeds from different fruits on the same witch hazel plant can spin in different directions! In addition to using high-speed cameras to study the seeds flying out, the researchers have also put the plants inside MRI machines, recently [19], to examine the hidden structures within the hazel plant and the fruit without having to cut it apart, and to get insights into the ballistic seed dispersal. By studying how the witch hazel launches its seeds by applying a torque to make them spin, one could inspire engineers to design a sensor that can detect when the humidity falls below a critical level, resulting in the opening of a valve. Repetitive MRI scans on the same plant as it grows over time can give a lead on the mechanism of the movements of other plants, too, such as that of the Venus flytrap that is famous for catching bugs to trap and eat them.

6.7 Signal-space projection/separation for MEG data Raw MEG data are a combination of brain activity, biological interference, and technical noise from outside. The signals that are not brain-related are widely suppressed by recording data in a magnetically shielded room, filtering it, and with software noise cancellation. Two prevalent methods for the suppression of external interference are signal-space projection [20], and signal space separation [21, 22]. A digital highpass filter eliminates possible baseline drifts, and by band-pass filtering the focus is put on a certain frequency range. The brain signals themselves can arise from two sources: (a) spontaneous activity, and, (b) activity elicited by a stimulus, in the case of neurocognitive experiments. Spontaneous activity is ongoing and can be measured without external stimulation. The challenge lies in trying to separate the stimulus-related brain signals from spontaneous activity signals, because both originate in the brain. Stimulus-related activity can, however, be distinguished by making a comparative analysis of the responses obtained under evoked activity and induced activity, as discussed below.

6.8 Evoked and induced responses Evoked responses have a fixed latency and are phase-locked to a stimulus. The stimulus can either be external, presented visually or auditorily, or it can be any response of the subject, like a button press or an eye blink, for example. To compute the generators of the event-related field (ERF), averaging proves to be useful. It is a standard procedure in data processing of many psycho-physiological MEG studies that has been applied very successfully to suppress spontaneous brain activity in favor of the evoked activity. Induced responses have a variable latency and are not necessarily phase-locked, so averaging them might lead to an attenuation. The brain does not always respond identically to repeated stimuli and there might be a great deal of information in the data which gets lost during the averaging process.

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6.9 Consequences of deprivation of sleep Acute deprivation of sleep can have disastrous effects, and even cause death. Researchers have investigated electromyograms (EMG), electroencephalograms (EEG) and also electrooculograms (EOG) to study both the rapid eye movement (REM) and non-REM (NREM) sleep phases [23], to investigate the origin and functions of sleep. Sleep-induced changes in the brain are thought to correlate with consciousness changes in the brain. Sleep is vitally important to the body’s regulation of oxidation, mainly in the gut. Deprivation of sleep has been seen to be associated with building up of reactive oxygen species (ROS) in the intestines [24, 25]. MEG holds promise to elucidate the hidden causes of acute lack of sleep in some people.

6.10 Non-destructive imaging of soft tissue using synchrotron radiation The synchrotron light source is about a hundred billion times more intense than the x-ray equipment that we come across in a hospital. Synchrotron radiation (SR) is emitted from an electron traveling at almost the speed of light when a magnetic field bends its path. Storage ring based synchrotron light sources offer synchrotron radiation, i.e. x-ray beams which have brightness and coherence boosted orders of magnitude over conventional x-ray sources. It allows high-resolution observations across multiple length scales, within very short and concise time spans. Other than deep x-ray penetration power and wide x-ray energy tunability, the improved brightness of the state-of-the-art synchrotron sources offers microscopic and imaging modalities. Synchrotron x-ray sources are now being used as a microscope to conduct virtual histology, because SR can be tuned to much shorter wavelengths than that of the normal light in a room, allowing synchrotron x-rays to make cellular level study of soft tissue, without making any incisions. For the first time, peripheral nerve samples from different subjects: a healthy person, a type 1 diabetes patient, and a type 2 diabetes patient have been studied using x-ray phase contrast holographic nano-tomography at European Synchrotron Radiation Facility (ESRF) at Grenoble, using an x-ray beam of 17 keV energy [26]. Such studies hold significance in how diabetes affects the growth of nerve fibers in the arms and legs, an important aspect in diabetes neuropathy. With the availability of compact synchrotrons, additional insights on such topics will unfold in the coming years.

6.11 Carbon-ion radiotherapy In order to treat a deep-seated tumor with well-localized dose distributions, carbon ions obtained from a superconducting synchrotron are considered to be a good candidate for heavy-ion radiotherapy. The carbon-beam intensity, which depends on the volume and shape of the target, and the efficiency of the irradiation method, needs to be a few 108 particles per second in order to obtain a biological dose rate of 5 Gy E min−1, which roughly equates to a physical dose of 2 Gy min−1 [27, 28]. 6-8

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The National Health Insurance scheme of Japan has approved carbon-ion radiotherapy (C-RT) for treating ‘bone and soft tissue tumor’, ‘prostate tumor’ and ‘head and neck tumor’.

References [1] Raichle M E 2008 A brief history of human brain mapping Trends Neurosci. 32 118–26 [2] Glover G H 2011 Overview of functional magnetic resonance imaging Neurosurg. Clin. N. Am. 22 133–9 [3] Linden D E J and Turner D L 2016 Real-time functional magnetic resonance imaging neurofeedback in motor neurorehabilitation Curr. Opin. Neurol. 29 412–8 [4] Ogawa S, Lee T M, Kay A R and Tank D W 1990 Brain magnetic resonance imaging with contrast dependent on blood oxygenation Proc. Natl. Acad. Sci. 87 9868–72 [5] Sukhodolsky D G et al 2020 Randomized, sham-controlled trial of real-time fMRI neurofeedback for tics in adolescents with Tourette syndrome Biol. Psychiatry 87 1063–70 [6] Rubia K 2018 Cognitive neuroscience of attention deficit hyperactivity disorder (ADHD) and its clinical translation Front. Hum. Neurosci. 12 1–23 [7] Rubia K, Criaud M, Wulff M, Alegria A, Brinson H, Barker G, Stahl D and Giampietro V 2019 Functional connectivity changes associated with fMRI neurofeedback of right inferior frontal cortex in adolescents with ADHD Neuroimage 188 43–58 [8] Shibata K, Lisi G, Cortese A, Watanabe T, Sasaki Y and Kawato M 2019 Toward a comprehensive understanding of the neural mechanisms of decoded neurofeedback NeuroImage 188 539–56 [9] Menon V 2011 Large-scale brain networks and psychopathology: a unifying triple network model Trends Cogn. Sci. 15 483–506 [10] Menon V 2015 Salience network Brain Mapping: An Encyclopedic Reference vol 2 ed A W Toga (Cambridge, MA: Academic) pp 597–611 [11] McTeague L M, Huemer J, Carreon D M, Jiang Y, Eickhoff S B and Etkin A 2017 Identification of common neural circuit disruptions in cognitive control across psychiatric disorders Am. J. Psychiatry 174 676–85 [12] Howes O D and Nour M M 2016 Dopamine and the aberrant salience hypothesis of schizophrenia World Psychiatry 15 3–4 [13] Takahashi Y K, Batchelor H M, Liu B, Khanna A, Morales M and Schoenbaum G 2017 Dopamine neurons respond to errors in the prediction of sensory features of expected rewards Neuron 95 1395–405 [14] Volkow N D, Wise R A and Baler R 2017 The dopamine motive system: implications for drug and food addiction Nat. Rev. Neurosci. 18 741–52 [15] Salamone J D and Correa M 2012 The mysterious motivational functions of mesolimbic dopamine Neuron 76 470–85 [16] McCutcheon R A et al 2018 Mesolimbic dopamine function is related to salience network connectivity: an integrative positron emission tomography and magnetic resonance study Biol. Psychiatry 85 368–78 [17] Nagel E et al 2019 Magnetic resonance perfusion or fractional flow reserve in coronary disease New Engl. J. Med. 380 2418–28 [18] Hecht E E, Smaers J B, Dunn W D, Kent M, Preuss T M and Gutman D A 2019 Significant neuroanatomical variation among domestic dog breeds J. Neurosci. 39 7748–58

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[19] Poppinga S et al 2019 A seed flying like a bullet: ballistic seed dispersal in Chinese witchhazel (Hamamelis mollis OLIV., Hamamelidaceae) J. R. Soc. Interface 16 20190327 [20] Uusitalo M A and Ilmoniemi R J 1997 Signal-space projection method for separating MEG or EEG into components Med. Biol. Eng. Comput. 35 135–40 [21] Taulu S, Kajola M and Simola J 2003 The signal space separation method Abstract Book of the NFSI2003 Conf. (Chieti, Italy) p A79 [22] Taulu S and Kajola M 2005 Presentation of electromagnetic multichannel data: the signal space separation method J. Appl. Phys. 97 124905-1–10 [23] Hobson J A 2005 Sleep is of the brain, by the brain and for the brain Nature 437 1254–6 [24] Greenwood V 2020 Why sleep deprivation kills Quanta https://www.quantamagazine.org/ why-sleep-deprivation-kills-20200604/ [25] Vaccaro A, Dor Y K, Nambara K, Pollina E A, Lin C, Greenberg M E and Rogulja D 2020 Sleep loss can cause death through accumulation of reactive oxygen species in the gut Cell 181 1307–28 [26] Dahlin L B, Rix K R, Dahl V A, Dahl A B, Jensen J N, Cloetens P, Pacureanu A, Mohseni S, Thomsen N O B and Bech M 2020 Three-dimensional architecture of human diabetic peripheral nerves revealed by x-ray phase contrast holographic nanotomography Sci. Rep. 10 7592 [27] Malouff T D, Mahajan A, Krishnan S, Beltran C, Seneviratne D S and Trifiletti D M 2020 Carbon ion therapy: a modern review of an emerging technology Front. Oncol. 10 82 [28] Ohno T et al 2011 Carbon ion radiotherapy at the Gunma University Heavy Ion Medical Center: new facility set-up Cancers 3 4046–60

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Superconducting Materials and Their Applications An interdisciplinary approach Jatinder Vir Yakhmi

Chapter 7 Concluding remarks. Slow progress in the commercialization of potential HTS devices. New hopes. Emerging new applications

This is a short but important chapter in which we discuss two seemingly opposing issues, namely, the unabated excitement that continues to be generated by new findings about superconductors on a regular basis, juxtaposed against the continued delay in the commercialization of several applications of the high-Tc superconductors, which technically are within the reach of the modern technology.

7.1 Why is superconductivity so exciting? Superconductivity has been a very fertile field of discoveries, research and applications. Hardly a decade has passed since the discovery of the phenomenon of superconductivity in 1911, when new superconducting materials, or new phenomena related to superconductivity were not discovered. After the discovery of superconductivity in mercury in 1911, and a few other elements from the periodic table (figure 1.6) quickly thereafter, exciting discoveries were made on superconductivity in type II Nb–Ti and A-15 compounds, and, following it up with oxides, Chevrel phase compounds, organic charge-transfer superconductors, RE-borides, heavy-Fermion materials, high-Tc cuprates, MgB2, Fe-based pnictides and hydrides. Most recently, superconductivity has been discovered for the first time in 2020 in meteorites [1], specifically in grains embedded in two distinct meteorites: (a) in Mundrabilla, a very large FeS-rich meteorite discovered in Australia in 1911; and (b) in GRA 95205, a ureilite meteorite which was found in Antarctica a quarter-century ago. This proves that extreme formation conditions of meteorites make them good candidates for investigating superconducting behavior in them.

doi:10.1088/978-0-7503-2256-0ch7

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Using materials informatics aided by machine learning (ML) methods, an ML model has been developed which can predict the possible Tc-values for new layered materials by a choice of inputs such as the average atomic mass of a compound, the average number of electrons in an unfilled shell, the average ground state atomic magnetic moments, the maximum difference of electro-negativity, etc. For known high-Tc superconductors, this model predicts Tc values with over 92% confidence. After application of this model to about 2500 layered materials in the inorganic crystal structure database, 25 of them are predicted to be superconductors not known before, including 12 cuprates, seven iron-based crystals, and six others, with Tc ranging from ~32 K to ~138 K, by Liu et al [2]. Excitement in discovering new phenomena amongst superconductors, too, never ceased. Some path-breaking phenomena and applications based on them discovered were Meissner effect, high-field Nb–Ti magnets for particle-accelerators and later for MRI machines; Josephson tunneling and the development of SQUID sensors based on it, etc. For theoreticians, superconductors offered a novel collective phenomenon (called Bose-condensation) at low temperatures, the physics of understanding of which is so fascinating. Besides, there is no single theory yet, despite the BCS theory which explains the LTSCs well but not the HTSCs, and some other strongly correlated systems. Relevance of application of GLAG (Ginzburg–Landau–Abrikosov– Gor’kov) theory as applicable to the superconducting properties of Nb3Sn has been established, recently [3]. Superconducting materials have shown potential in a variety of novel applications such as power storage (persistent current), magnetic levitation, high field magnets, MRI magnets, SQUID magnetometers, and Josephson junction electronics. Superconductivity continues to have potential to impact substantially, at least three sectors of our lives, namely, (a) energy: with applications in generators and motors, power transmission and distribution, energy storage systems, and magnets for fusion power and for magneto-hydrodynamic power; (b) transportation: superconducting magnets for levitated trains, ship propulsion, and for automobiles; and (c) healthcare: magnetic resonance imaging, MEG, etc. Before we move on to two important sections, 7.2 and 7.3, of this chapter, we consider it worthwhile to provide for the convenience of the more inquisitive reader, a list of a number of excellent books on superconductivity and superconducting materials, from literature, which emphasize different aspects of underlying superconducting characteristics exhibited by them in detail, as well as features which correlate with the potential of a variety of superconducting materials for applications [4–14].

7.2 Factors hampering the commercial applications of high-Tc superconductors High-Tc cuprate superconductors can carry extremely high amounts of electricity and can generate, in principle, magnetic fields of about 100 T at relatively warm temperatures. Thus, the HTS technology when used for magnets offers life-changing 7-2

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ideas in several sectors such as medicine and energy. Superconducting devices for most of the applications discussed in chapters 4 and 5 were already under advanced stages of development as LTSC-devices before the discovery of the new ceramic HTSCs. But the use of liquid He refrigerant was always an obstacle, except in strategic areas where cost is not a constraint. The economy and convenience of HTSCs is definitely a scoring point. And if current efforts to develop superconductors with Tc values near room temperature bear fruit, they would revolutionize modern technology. However, the oft-repeated question in the context of several commercial applications of high-Tc superconductors which have not been realized after nearly three decades of their discovery is: ‘What is blocking the progress of marketing/ commercializing several potential devices, which are known and discussed, but not exploited thus far?’ To answer this, one has to appreciate that the HTSCs present some features which make them less compliant to practical usage. Two prime barriers that work against the use of superconducting materials in wideranging applications are a critical temperature, Tc, characteristic of the material, above which its superconducting behavior disappears, making it a normal conductor; and a critical magnetic field, Hc, which may be an externally applied one, or internally generated in a superconductor in view of the large flow of current passed through it under its zero-resistance conditions, above which, too the material turns into a normal conductor. Thus, the usefulness of a superconducting material is restricted by the upper limits of the triumvirate: the Tc, Hc2 and Jc, each of which is influenced by the magnitude of the other two (figure 1.14). Unlike the metallic low-Tc superconductors, HTSCs do not have a sharply defined critical current. At higher temperatures and fields, there is a ‘flux flow’ region, where the material is resistive—although still superconducting. The boundary between flux pinning and flux flow is called the irreversibility line, discussed earlier in chapter 1 (see figure 1.15). Another difficulty with REBCO (rare earth barium copper oxide), or BSCCO (bismuth strontium calcium copper oxide)—is that they consist of several elements that must be painstakingly measured, mixed and baked into a high-quality endmaterial. Besides, being ceramic, they are not malleable like copper, but brittle. Transforming these ceramic superconductors into a tape of perfectly aligned crystals, which can be spooled into a coil to make an electromagnet, has not been a simple challenge, though incremental successes have been made over the years. It is still a challenge to process them successfully into long wires for use in SC magnets. The high-Tc cuprates are also susceptible to degradation under certain environmental and applied field conditions. They are also ‘anisotropic’, i.e. they conduct current along a particular direction in proportion to the degree of alignment of crystallites in that direction. Consequent upon intense R&D efforts in thin-film development of HTSCs, most of the thin film related problems such as low Jc or substrate interaction have either been solved or are nearing solution. As thermal processes for making high-quality HTSC thin films develop further, their advantage in terms of high Jc and higher Tc will be translated into reliable and economic devices. In this context, Tl-based HTSC 7-3

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thin film devices appear to have a better future. Futuristic hybrid chips combining the best of the advantages of opto-, micro- and superconducting electronic technologies and MET (magnetic field-effect transistor) are examples of new HTSC thin film devices, under development. Long after the discovery of high-Tc cuprates, the HTS technology revolution has remained elusive. However, after three decades of hard work in several labs, the HTS technology is finally appearing on the horizon. NHFM lab has produced a test magnet that, using HTS materials in part and some very clever engineering [15], provides a world-record magnetic field (>45.5 T) that is promising for a host of applications. Even until now, a majority of applications of superconducting materials in modern technology require the use of liquid helium, which has a boiling point, Tb, of 4.2 K. Handling of liquid He requires special conditions and cost, which is the major hurdle in the exploitation of superconductors for many useful applications. The development of high-temperature superconductors, mainly the cuprates, have definitely brought certain applications closer to reality, with the help of using liquid nitrogen as a coolant with a Tb of 77.4 K, and liquid oxygen at Tb = 90 K. However, for all new generation superconductors the cooling-down needs to be such that it would not consume more energy than what could theoretically be saved by, say, transmitting electricity via cables made from them, making them economically unviable. It is quite clear that production of high temperature superconductors with a high critical temperature (Tc ~ 273 K = 0 °C) would be of immense technical significance.

7.3 Limitations of hydride and organic superconductors to be overcome before their applications Both hydrides and organic superconductors have potential to offer superconductivity at temperatures much higher than established thus far for high-Tc cuprates, namely at and above room temperature conditions (>300 K) for the organic materials with excitonic superconductivity; or at 260 K, at 288 K, at 294 K or even at 550 K (though just signatures) for hydrides, as shown in figure 3.8, albeit under high pressure conditions. To make use of the full potential of the exciton mechanism for attraction between electrons, one may have to suppress the electron– phonon interaction, as much as possible. There is little chance for this to happen in the case of a three-dimensional structure. A thin film has a better chance, since the electron gas in it can be treated as two-dimensional, and the distance between energy levels corresponding to transverse motion of the electrons can be larger than the Fermi energy. It is quite clear that production of high temperature superconductors with a critical temperature around room temperature (290 K or so), such as hydrides, would be of immense technical significance. But they should work under ambient pressure conditions, unlike at present.

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7.4 New emerging applications, including those of HTSCs As discussed in section 4.4 in chapter 4, the magnet system in the nuclear fusion reactor ITER is going to be the largest and most integrated superconducting magnet system ever built (https://www.iter.org/mach), involving ten thousand tonnes of magnets (of both Nb–Ti and Nb3Sn conductors), to produce the magnetic fields that will initiate, confine, shape and control the ITER plasma. But ITER is only a demonstrator project, which too, is expected to fire up only in 2035. The actual nuclear fusion power reactors to deliver electrical power into the grid, would take another 15–20 years to be built from the know-how gained from ITER. Notwithstanding, the ITER and the subsequent commercial nuclear fusion tokamaks would be the biggest users of superconducting magnets based on LTSCs. What is exciting is that, in parallel, fusion energy projects (discussed in section 4.4) are at present being built on the principle of more compact spherical tokamaks that use HTSCs to contain the plasma in a very strong magnetic field. HTSC magnets are now poised to power high-definition MRIs, bringing into focus individual nerve fibers and cells. Today’s MRIs image only the hydrogen in our bodies, but future HTS-based machines will allow doctors to image any of the elements, say imaging sodium to learn if chemotherapy is successfully killing tumor cells, and oxygen to track glucose metabolism in tumors. High-field MRI machines will reveal the intricacies of the cell wall structures of viruses, helping the scientists to design molecular missiles to infiltrate them. They will track lithium in batteries, hydrogen in fuel cells and photosynthesis in plants, giving scientists clues on how to build better solar cells and energy storage devices. These possibilities plus the recent successes in building high-field magnets using HTSC, partly, at National High Magnetic Field Laboratory (USA) have been highlighted in a blog in 2019 by Gregory S Boebinger, its Director [15], entitled, The ‘Woodstock of Physics’ is finally living up to its promise! Similarly, the title of a feature article by Jamie Durrani published recently in Chemistry World is: Room temperature superconductivity is now within touching distance—but it won’t change the world yet [16]. We close this chapter on a positive note by listing a few promising new recent successes highlighting development of new superconductors and their applications: (a) High efficiency single photon detectors have been fabricated using a nanowire of superconducting (Tc = 3.4 K) WSi operating at 2.5 K [17]. (b) A Josephson quantum phase battery, which can provide a controlled, localized phase bias, has been reported. Such a battery can be used in superconducting flux and hybrid qubits, in superconducting quantum memories, and in superconducting rectifiers [18] (c) Superconductivity in metallic twisted bilayer graphene has been stabilized by WSe2 [19]. Tuning superconductivity in graphene—the wonder 2D-carbon material, has potential for applications in several modern technologies. (d) Ultra-fast vortex motion has been demonstrated at velocities of 10–15 km s−1 in a directly written Nb–C superconductor with a close-to-perfect edge barrier [20]. Nb–C is a candidate material for fast single-photon detectors.

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(e) A magnetically controllable superconducting diode effect has been reported in an artificial [Nb/V/Ta]n superlattice, without a centre of inversion [21]. This establishes potential for the construction of superconducting devices for non-dissipative electronic circuits. (f) Current research in the understanding of cognition is more and more focused on the identification of human brain responses simultaneously in space and time. This is being done non-invasively by linking multivariate response patterns of the human brain recorded with functional magnetic resonance imaging (fMRI) and with magneto- or electroencephalography (M/EEG) [22]. (g) A research group has reported the detection of a second harmonic generation after shining an ultrashort laser pulse, with a width of just 6 fs (6 × 10−15 s), on an organic superconductor, κ-(BEDT-TTF)2Cu[N(CN)2]Br, which is centro-symmetric [23]. The observation of a non-linear, polarized petahertz current, driven by the ultrashort laser pulse is a novel observation, though it violates the Ohm’s law according to which a net current cannot be induced by an oscillating electric field of light. The scattering-free current increases near the superconducting transition temperature (Tc = 12 K). The light-driven petahertz (1015 Hz) current has the potential for realizing on–off switching at petahertz, and thereby leads to the development of high-speed computers which are one million times faster than conventional ones. (h) Cooper pairs bear a close analogy to the Higgs field, which in high-energy physics, couples to gauge bosons and fermions and gives mass to their elementary excitations. ‘Higgs spectroscopy’ reveals the dynamics of paired electrons in superconductors. Recent observations of phase-resolved Higgs response in superconducting cuprates [24] indicate coupling of the Higgs mode to other collective modes and potentially a nonzero pairing amplitude above Tc. (i) As shown in chapter 3 (figure 3.8), different hydride materials have shown a lot of exciting results very recently, with the observation of superconductivity at Tc values of over 200 K, and even at room temperature or still higher, though under application of quite high pressures of over 150 GPa. There have been theoretical calculations that YH10 with a stable fcc structure can attain a Tc value of 305–326 K at 250 GPa [25]. The observation of signatures of superconductivity at 550 K, though under high applied pressures, and after several thermal excursions, has instilled a new enthusiasm about superconducting materials and their promise for applications, though all that would require bringing the applied pressures to ambient by making some very clever chemical-pressure inducing substitutions in hydride systems. For now, it appears that the route to stabilizing superconductivity at and above room temperature, may likely be to look for it in CH4-intercalated H3S hydride perovskites [26].

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References [1] Wampler J, Thiemens M, Cheng S, Zhu Y and Schuller I K 2020 Superconductivity found in meteorites Proc. Natl. Acad. Sci. 117 7645–9 [2] Liu Z-L, Kang P, Zhu Y, Liu L and Guo H 2020 Material informatics for layered high-Tc superconductors APL Mater. 8 061104 [3] Li Y and Gao Y 2017 GLAG theory for superconducting property variations with A15 composition in Nb3Sn wires Sci. Rep. 7 1133 [4] Poole C P 2007 Superconductivity (New York: Academic) pp 636 [5] Blundell S J 2009 Superconductivity: A Very Short Introduction (Oxford: Oxford Univ. Press) pp 168 [6] Tinkham M 2004 Introduction to Superconductivity 2nd edn (New York: Dover) pp 480 [7] Mangin P and Kahn R 2017 Superconductivity—An Introduction (Berlin: Springer) pp 379 [8] Cooper L N 2010 BCS: 50 Years (Singapore: World Scientific) pp 575 [9] Ginzburg V L 2004 Superconductivity (Singapore: World Scientific) pp 92 [10] Kresin V Z and Little W A 1991 Organic Superconductivity (Berlin: Springer) pp 386 [11] Ireson G 2012 Discovering Superconductivity: An Investigative Approach (New York: Wiley) pp 182 [12] Ginzburg V L 2009 On Superconductivity and Superfluidity—A Scientific Autobiography (Berlin: Springer) pp 232 [13] Sharma R G 2015 Superconductivity—Basic and Applications to Magnets (Berlin: Springer) pp 414 [14] Orlando T P 1991 Foundations of Applied Superconductivity (Reading, MA: AddisonWesley) pp 584 [15] Boebinger G 2019 The ‘Woodstock of Physics’ is finally living up to its promise Sci. Am. https://blogs.scientificamerican.com/observations/the-woodstock-of-physics-is-finally-livingup-to-its-promise/ [16] Durrani J 2020 Room temperature superconductivity is now within touching distance—but it won’t change the world yet Chem. World https://chemistryworld.com/holy-grails/the-grails/ room-temperature-superconductors [17] Verma V B, Korzh B, Bussières F, Horansky R D, Lita A E, Marsili F, Shaw M D, Zbinden H, Mirin R P and Nam S W 2014 High-efficiency WSi superconducting nanowire singlephoton detectors operating at 2.5 K Appl. Phys. Lett. 105 122601 [18] Strambini E et al 2020 A Josephson phase battery Nat. Nanotechnol. 15 656–60 [19] Arora H S et al 2020 Superconductivity in metallic twisted bilayer graphene stabilized by WSe2 Nature 583 379–84 [20] Dobrovolskiy O V, Vodolazov D Y, Porrati F, Sachser R, Bevz V M, Mikhailov M Y, Chumak A V and Huth M 2020 Ultra-fast vortex motion in a direct-write Nb-C superconductor Nat. Commun. 11 3291 [21] Ando F, Miyasaka Y, Li T, Ishizuka J, Arakawa T, Shiota Y, Moriyama T, Yanase Y and Ono T 2020 Observation of superconducting diode effect Nature 584 373 [22] Cichy R M and Oliva A 2020 A M/EEG-fMRI fusion primer: resolving human brain responses in space and time Neuron 107 772–81 [23] Kawakami Y et al 2020 Petahertz non-linear current in a centrosymmetric organic superconductor Nat. Commun. 11 4138

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[24] Chu H et al 2020 Phase-resolved Higgs response in superconducting cuprates Nat. Commun. 11 1793 [25] Liu H, Naumov I I, Hoffmann R, Ashcroft N W and Hemley R J 2017 Potential high-Tc superconducting lanthanum and yttrium hydrides at high pressure Proc. Natl. Acad. Sci. USA 114 6990–5 [26] Cui W, Bi T, Shi J, Li Y, Liu H, Zurek E and Hemley R J 2020 Route to high-Tc superconductivity via CH4-intercalated H3S hydride perovskites Phys. Rev. B 101 134504

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