SQUID - Superconducting Quantum Interference Devices and their Applications: Proceedings of the International Conference on Superconducting Quantum Devices, Berlin (West), October 4–8, 1976 9783110887495, 9783110068788

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SQUID Superconducting Quantum Interference Devices and their Applications

SQUID Superconducting Quantum Interference Devices and their Applications Proceedings of the International Conference on Superconducting Quantum Devices Berlin (West), October 5-8,1976 Editors H.D.Hahlbohm • H.Lubbig

W G DE

Walter de Gruyter • Berlin • New York 1977

Editors H. D. Hahlbohm H. Lübbig Institut Berlin der Physikalisch-Technischen Bundesanstalt, 1000 Berlin (West), Germany

CIP-Kurztitelaufnahme der Deutschen Bibliothek SQUID: superconducting quantum interference devices and their applications; proceedings of the Internat. Conference on Superconducting Quantum Devices Berlin (West), October 5 - 8 , 1976/ed. H.-D. Hahlbohm; H. Lübbig. - 1. Aufl. - Berlin, New York: de Gruyter, 1977. ISBN 3-11-006878-8 NE: Hahlbohm, Hans-Dieter [Hrsg.]; International Conference on Superconducting Quantum Devices

Library of Congress Cataloging in Publication Data International Conference on Superconducting Quantum Devices, 1st, Berlin, 1976 SQUID, superconducting quantum interference devices and their applications. Includes bibliographical references and indexes. 1. Superconducting quantum interference devices - Congresses. I. Hahlbohm, H. D., 1930 II. Liibbig, H., 1932 - III. Title. TK7872.S8157 1976 621,39 77-5409 ISBN 3-11-006878-8

©Copyright 1977 by Walter de Gruyter & Co. Berlin 30. All rights reserved, including those of translation into foreign languages. No part of this book may be reproduced in any form - by photoprint, microfilm, or any other means - nor transmitted nor translated into a machine language without written permission from the publisher. Printing: Karl Gerike, Berlin. - Binding: Liideritz & Bauer, Buchgewerbe GmbH, Berlin. Printed in Germany.

PREFACE

I n form of the proceedings of a first international devoted to Superconducting Quantum Interference

conference

Devices

(SQUID's), in this volume extended papers are published concerning specialized topics of fundamentals and applications of weak

superconductivity.

B e i n g the basis, the Josephson effect of phase-coherence

in

weakly connected superconductors brought insight into superconductivity in the presence of fields, and simultaneously, became starting point for revolutionary progress in a great number of technical applications, metrology and computer techniques for instance. The output accumulated in more than one decade suggested to attempt a n international interchange

bet-

w e e n scientists working in this area. The aim was to summarize the development, to give a survey over the present state, w i t h respect to results as well as w i t h respect to problems, and to estimate future aspects. This aim could be achieved only partially, since it soon became clear that it would be impossible to cover within four days the whole area of what may be called SQUID fundamentals and applications. Thus important applications as medical

and

geophysical ones could not be included. Fourtyseven papers were presented at this meeting. The delegates represented thirteen countries including Austria, CSSR, Denmark, Finland, France, Great Britain, Italy, Japan, The Netherlands, Sweden, Switzerland, United States of America and Germany. Together with the contributed papers nine invited lectures demonstrated the h i g h level of weaK-superconductivity research. However, it becomes clear as well that theory and application in several branches are just at the beginning.

VI Hence it might be expected that the next years will be characterized by further intensive research activities. The conference has b e e n inspired by the European Physical Society. The edition of the proceedings is a good occasion to acknowledge once more the generous support of the conference by the President of the Deutscher Bundestag, the B e r l i n Senate, the President of the Physikalisch-Technische

Bundesanstalt,

the Deutsche Physikalische Gesellschaft e.V., Fachausschuß Tiefe Temperaturen and the Siemens AG. Furthermore, we are indebted to the De Gruyter Publishing Company for its valuable cooperation in preparing these p r o ceedings. Berlin, February 1977

H.-D. Hahlbohm H. Lübbig

CONTENTS

THEORY OF SUPERCONDUCTING PHASE COUPLING Theory of phase coherence in SQUID'S. H. Lubbig

1

Investigation of the validity of generalizations of the adiabatic Josephson equation for a local junction by asymptotic expansions.

W.A. Schlup

29

A self-consistent model of the Josephson junction. H. Ohta

35

Order parameter relaxation and Josephson effects in superconducting weak links.

A. Baratoff, L. Kramer....

51

JUNCTION FABRICATION TECHNIQUES Junction fabrication techniques.

T. Van Duzer...

63

Preparation of variable thickness microbridges using electron beam lithography and ion etching. R.D. Sandell, G.J. Dolan, J.E. Lukens

93

REAL JUNCTION PROPERTIES Properties of real junctions.

J.E. Mercereau.

Some properties of long superconducting threads V v „ formed in monocrystallme silicon. S. Benacka, " * L. Bezakova, S. Gazi , J. Palaj.....

101

133

AC Josephson effect in long superconducting threads "

v

in static magnetic field. S. Benacka, S. TakScs, v * , L. Bezakova, S. Gazi......

147

VIII Voltage current characteristics of superconducting to normal metal point contacts in an rf-field. U. Kaiser-Dieckhoff

165

Measurement of the cos

term in Josephson tunneling.

M.R. Halse, J.C. Taunton...............................

171

Effects in high critical current density Josephson tunnel junctions.

J. Niemeyer, V. Kose................

179

Supercurrent interference patterns in a tunneling junction structure.

E.P. Balsamo, G. Paternö,

A. Barone, M. Russo, R. Vaglio

193

Anomalous thermoelectric effects in point contact tunnel junctions.

N.K. Welker, F.D. Bedard

199

LOW FREQUENCY APPLICATIONS Current performance of superconducting quantum interference devices. J. Clarke.

213

A variable temperature high sensitivity SQUID magnetometer.

J.A. Good.

225

Flux creep of superconductors measured with a SQUID system.

W. Ludwig, H. Gessinger.......................

239

A magnetic excited state in oxy haemoglobin A detected with an rf-SQUID-magnetometer.

H.E. Hoenig,

K. Gersonde............................................

249

High temperature application of SQUID voltmeter. M. Konishi, T. Fujita, T. Ohtsuka......................

255

Use of persistent supercurrents in SQUID current stabilisers and their application to a resistivity measurement on niobium and a portable voltage standard. J.C. Gallop............................................ The use of resistive SQUIDs for calorimetry.

2C7

IX Possible cryocoolers for SQUID magnetometers. J.E. Zimmerman, R. Radebaugh, J.D, Siegwarth....

287

On limiting magnetic field sensitivity of superconducting quantum interferometer with two Josephson junctions.

S.I. Bondarenko.................... .

• «

297

An integrated thin film gradiometer based on a dc SQUID. G.B. Donaldson, M.B. Ketchen, J. Clarke, W. Goubau.....

303

A cryodevice for induction monitoring of dc electron or ion beams with nano-ampere resolution. K. Grohmann, D. Hechtfischer, J. Jakschik..............

311

A SQUID comperator bridge for low-tc-cryoresistor measurements.

D. Andreone, E. Arri, G. Boella,

G.C. Marullo, ¿.P. Balsamc, U. Michi. ........

......

317

HIGH FREQUENCY APPLICATIONS Superconducting devices for millimeter and submillimeter wavelengths.

P.L. Richards............................

323

A closed loop broadband microwave operated SQUID. Ho Rogalla, C. Heiden...

...........................

339

A numerical treatment of the lumped model of an rf biased SQUID by means of a hybrid computer.

S.N. Erne,

H. Luther..............................................

349

Rf power measurements using quantum interference in superconductors.

D.B. Sullivan, N.V. Frederick,

R.T. Adair.............................................

355

An analysis of the low inductance ac-SQUID operated as a dc-magnetometer in a mixing mode.

O.H. Soerensen.

365

High frequency properties of stable Nb-Nb oxide-Pb Josephson tunnel junctions.

T.F. Finnegan, J. Wilson,

J. Toots...............................................

381

X NOISE Noise limitations of rf SQUIDs.

R.A. Buhrman

395

Optimum response and damping of Josephson junctions. C.D. Andriesse

433

COMMUNICATION SYSTEMS SQUID magnetometers for submarine communications at extremely low frequencies.

J.R. Davis, M. Nisenoff....

439

SIGNAL PROCESSING Complete linear equivalent circuit for the SQUID. G.J. Ehnholm. ......

......

485

Two junction SQUID using a sampling technique. P. Gutmann

501

Rf SQUID in the non hysteretic mode: the phase modulation of the tank voltage.

S.N. Ernê.

511

COMPUTER ELEMENTS SQUIDs as computer elements.

P. Wolf

519

Switching between two different vortex modes in Josephson junctions.

S. Hasuo, T, Imamura, K. Dazai...

541

Switching dynamics of Josephson junction logic circuits. H.W. Chan, B.T. Ulrich, T. Van Duzer

555

Superconducting neuromime: a Josephson junction model neuron.

B.T. Ulrich..............

567

Dynamics of flux transitions in the SQUID for the hysteretic case.

S.N. Ernê, H. Liibbig...

579

XI SUMMARY AND CONCLUSIONS Summary and conclusions.

J. Clarke

587

Subject Index

595

Author Index

605

LIST OF PARTICIPANTS Adde, R.

Institut d'Electronique Fondamentale, Università Paris-Sud, Bat. 220, 91405 Orsay, France

Albrecht, H.

2. Physikalisches Institut, Technische Hochschule Aachen, Templergraben 56, 5100 Aachen 1, Germany

Andreone, D„

Istituto Elettrotecnico Nazionale Galileo Ferraris, Corso Massimo D'Azeglio 42,

Andriesse, C.

10125 Torino, Italy

Kapteyn Astronomical

Institute,

University of Groningen, Space Research, P.O. Box 800, Groningen, The Netherlands Arri, E.

Istituto Elettrotecnico Nazionale Galileo Ferraris, Corso Massimo D'Azeglio 42,

Arons, R.R.

10125 Torino, Italy

Institut für Festkörperforschung, Kernforschungsanlage Jülich, Postfach 365, 5170 Jülich, Germany

Balsamo, P.E.

Comitato Nazionale per l'Energia Nucleare, Laboratori Nazionali di Frascati, C.P.N. 70, 00044 Frascati, Roma, Italy

Bannink, G„

Twente University of Technology, Lintveldebrink 262, Enschede, The Netherlands

Baratoff, A.

IBM Research Laboratory Zürich, Säumerstraße 4, 8803 Rüschlikon, Swi tzerland

XIII Barone, A.

Laboratorio di Cibernetica del CNR, Via Toiano 2, 80072 Arco Felice (Napoli), Italy

Berchier, J.-L.

University of Geneve, Institut de Physique, DPMC, 32 Bd. d'Yvoy, CH 1211 Geneve 4, Switzerland

Berlincourt, T.G.

Office of Naval Research, Physical Sciences Division, 800 N Quincy St. Arlington, Virginia 22217, USA

Beyer, J.

Department of Electrical and Computer Engineering, University of WisconsinMadison, Madison 53706, USA

Brandt, R,

Office of Naval Research, 1030 East Green Street, Pasadena, California 91106, USA

Buchholz, Fol.

Physikalisch-Technische Bundesanstalt, Bundesallee 100, 3300 Braunschweig, Germany

Buhrman, R.A.

School of Applied and Engineering Physics, Cornell University, Clark Hall, Ithaca, New York 14853, USA

Carelli, P.

Laboratorio di Elettronica dello Stato Solido del CNR, Via Cineto Romano 42, 00156 Roma, Italy

Clarke, J.

Department of Physics, University of California, Berkeley, California 94720, USA

Colegrove, F.D.

Texas Instruments Inc., Mail Station 266, P.O. Box 6015, Dallas, Texas 75222, USA

XIV Crum, D.B.

S.H.E. c/o Klaus Schäfer GmbH, Postfach 488, 6078 Neu-Isenburg, Germany S.H.E. Corporation, 4174 Sorrento Valley Blvd., San Diego, California 92121, USA

Daalmans, G.M.

Laboratorium voor Technische Natuurkunde, Technische Hogeschool Delft, Lorentzweg 1, Delft, The Netherlands

Davis, R.J.

U.S. Naval Research Lab., Code 5460, Washington D.C. 20375, USA

Daunt, J.G.

Cryogenics Center, Stevens Institute of Technology, Hoboken, N.J. 07030, USA

Donaldson, G.B.

Department of Applied Physics, John Anderson Building, University of Strathclyde, Glasgow G4 ONG, Great Britain

Dousselin, G.

I.N.S.A., Department de Physique, 20, Av. des Buttes de Coesmes, 35031 Rennes-Cedex, France

Dünajski, Z.

Technische Hogeschool Twente, Campuslaan 36, Enschede, The Netherlands

Durcansky, G.

Institut für Festkörperforschung, Kernforschungsanlage Jülich, Postfach 365, 5170 Jülich, Germany

Duret, D.

Institut d'Electronique Fondamentale, Université Paris-Sud, Bat. 220, 91405 Orsay, France

Ehnholm, G.J.

Helsinki University of Technology, Department of Technical Physics, SF-02150 Otaniemi, Finland

XV Ernfe, S . N .

Physikalisch-Technische

Bundesanstalt,

Institut Berlin, Abbestraße 1 0 0 0 B e r l i n 10, Pinnegan,

T„F„

Institut for B a s i c Standards,

Natio-

n a l B u r e a u of S t a n d a r d s , R o o m

A-247,

Bldg„ Fujita,

T.

2-12,

Germany

220, W a s h i n g t o n D.C. 20234,

D e p a r t m e n t of P h y s i c s , T o h o k u sity, K a t a h i r a Sendai, 980,

Gallop,

J.

National

Univer-

Japan

Physical Laboratory,

Queens

Road, Teddington, Middlesex TW11 Great Geisler,

R.

USA

OLW,

Britain

I n s t i t u t für G e o p h y s i k u . Technische Universität Mendelssohnstr.

Meteorologie

Braunschweig,

la, 3 3 0 0

Braunschweig,

Germany Giovannini,

B.

U n i v e r s i t y of G e n e v e , D e p a r t m e n t Physics,

32, B o u l e v a r d

CH-1211 Geneve Good , J.A.

4,

L o n d o n W3 Greidanus,

F.J.A.M.

K.

231 The

7QS, Great

Kamerlingh Onnes Nieuwsteeg

Grohmann,

Switzerland

Cryogenic Consultants Ltd., store Building,

Laboratorium, The

Physikalisch-Technische

F.

Physikalisches

Netherlands

Bundesanstalt,

Institut Berlin, Abbestraße

Gross,

Metro-

Vale,

Britain

18, L e i d e n ,

1 0 0 0 B e r l i n 10,

2-12,

Germany Institut,

Graz, Universitätsplatz

Universität 5, 8 0 1 0

Austria G u d r e t , P„

IBM Research L a b o r a t o r y Säumerstraße Swi t z e r l a n d

of

d'Yvoy,

4, 8 8 0 3

Zürich,

Rüschlikon,

Graz,

XVI Gundlach, K.

Max-Planck-Institut für Physik und Astrophysik, Föhringer Ring 6, 8000 München 40, Germany

Gutmann, P.

Physikalisch-Technische Bundesanstalt, Bundesallee 100, 3300 Braunschweig, Germany

Hahlbohm, H.-D.

Physikalisch-Technische Bundesanstalt, Institut Berlin, Abbestraße 2-12, 1000 Berlin

Hahn, D.

10, Germany

Physikalisch-Technische Bundesanstalt, Institut Berlin, Abbestraße 2-12, 1000 Berlin 10, Germany

Halse, H.R.

Physics Department, University of Kent, Giles Lane, Canterbury, Kent CTL 7NR, Great Britain

Hansen, J.

2. Physikalisches Institut, Universität Köln, Universitätsstraße 14, 5000 Köln 41, Germany

Hasuo, S.

Advanced Technology Lab., Fujitsu Lab» Ltd., Nakahara-ku, 1015 Kamikodanaka, Kawasaki 211, Japan

Hechtfischer, D.

Physikalisch-Technische Bundesanstalt, Institut Berlin, Abbestraße 2-12, 1000 Berlin 10, Germany

Heiden, C.

Institut für Angewandte Physik, Universität Giessen, Heinrich-EuffRing 15, 6300 Giessen, Germany

Hillenbrand, B.

Research Laboratories of Siemens AG, FL MET 11, G. Scharowsky Str. 2, 8520 Erlangen, Germany

Hoenig, H.E.

Physikalisches Institut, Universität Frankfurt, Robert-Mayer-Str. 2-4, 6000 Frankfurt/M., Germany

XVII Hoffmann, A.

Physikalisch-Technische Bundes ans t.al t Institut Berlin, Abbestraße 2-12, 1000 Berlin 10, Germany

¿•"ablonski, H.

Fa. Klaus Schäfer GmbH., Postfach 488 6078 Neu-Isenburg, Germany

Jakschik, J.

Physikalisch-Technische

Bundesanstalt

Institut Berlin, Abbestraße 2-12, 1000 Berlin 10, Germany Jutzi, W.

Institut für elektronische der Informatik,

Grundlagen

Universität.Karlsruhe

7500 Karlsruhe, Germany Kadlec, J.

Max-Planck-Institut für Physik und Astrophysik, Föhringer Ring 6, 8000 München 40, Germany

Kaiser-Dieckhoff, U.

Physikalisches Institut, Universität Würzburg, Röntgenring 8, 8700 Würzburg, Germany

Kessel, Wo

Physikalisch-Technische

Bundesanstalt

Bundesallee 100, 3300 Braunschweig, Germany Kirschman, R.K.

Jet Propulsion Lab., California Insti tute of Technology, 4800 Oak Grove Drive, Pasadena, California

91103,

USA Klein, K.D.

Physikalisch-Technische

Bundesanstalt

Institut Berlin, Abbestraße 2-12, 1000 Berlin 10, Germany Klipping, G.

Fritz-Haber-Institut der Max-Planck.Gesell schaf t, Faradayweg 4-6, 1000 Berlin 33, Germany

Kose, V.

Phys ik ali sch-Techni s che Bundes ans talt Bundesallee 100, 3300 Braunschweig, Germany

XVIII Kurkijärvi, J.

Helsinki University of Technology, Low Temperature Laboratory, SF-02150 Otaniemi, Finland

Kurti, N.

Clarendon Laboratory, University of Oxford, Parks Road,Oxford 0X1 3PJ, Great Britain

Kusayanagi, E.

Department of Electronics, Kyushu University, Fukuoka, Japan

Leppin, H.P.

2. Physikalisches Institut, Universität Köln, Zülpicher Straße 77, 5000 Köln 41, Germany

Levinsen, M.T.

H» C„ 0rsted Institute, Physics Laboratory I, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen 0, Denmark

Lindelof, P.E,

H.C. 0rsted Institute, Physics Laboratory I, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen 0, Denmark

Lindsay, N.M.

Cryogenic Consultants Ltd., Metrostore Building, 231 The Vale, London W3 7QS, Great Britain

Locatelli, M.

Centre d'Etudes Nucléaires de Grenoble Service des Basses Temperatures 85X, Av. des Martyrs, 38041 Grenoble-Cedex, France

Lübbig, H.

Physikalisch-Technische Bundesanstalt, Institut Berlin, Abbestraße 2-12, 1000 Berlin 10, Germany

Lüders, K.

Institut für Atom- und Festkörperphysik, Freie Universität Berlin, Königin-Luise-Str„ 28, 1000 Berlin 33, Germany

XIX Ludwig, W.

Max-Planck-Institut für Metallforschung, Institut für Physik, Büsenauer Str. 171, 7000 Stuttgart 80, Germany

Lukens, J.E»

Department of Physics, State University of New York, Stony Brook, New York 11794, USA

Lundgren, L.

Solid State Division, Institute of Technology, Box 534, 75121 Uppsala, Sweden

Luther, H.

Physikalisch-Technische Bundesanstalt, Institut Berlin, Abbestraße 2-12, 1000 Berlin 10, Germany

Malassis, R.

C.N.A.M., 292 Rue Saint Martin, Paris III, France

Matisoo, J.

IBM Thomas J. Watson Research Center, P.O. Box 218, Yorktown Heights/N.Y. 10598, USA

Mercereau, J.E,

California Institute of Technology, Low Temperature Physics, mail code 63-37, Pasadena, California 91125, USA

Meredith, D.F.

Physics Department, University of Lancaster, Lancaster LAI 4YW, Great Britain

Meyer, J.-D.

I. Physikalisches Institut, Universität Göttingen, Bunsenstraße 9, 3400 Göttingen, Germany

Modena, I.

Laboratorio di Elettronica dello Stato Solido del CNR, Via Cineto Romano 42, 00156 Roma, Italy

XX Mooij, J.E.

Laboratorium voor Technische Natuurkunde, Technische Hogeschool Delft, Lorentzweg 1, Delft, The Netherlands

Niemeyer, J.

Physikalisch-Technische Bundesanstalt, Bundesallee 100, 3300 Braunschweig, Germany

Nisenoff, M.

U.S. Naval Research Laboratory, Cryogenic and Superconductivity Branch, Code 6435, Washington D.C. 20375, USA

Ohta, H.

The Institute of Physical and Chemical Research, Hirosawa

2-1, Wako-shi,

Saitama, 351, Japan Orr, P.D.A.

University of Cambridge, 21 St. Regis Chesterton Road, Cambridge CB4 IB4, Great Britain

Pace, S„

Istituto di Fisica, University of Salerno, Via Vernieri 42, 84100 Salerno, Italy

Pals, J.A.

Philips Research Laboratories, Eindhoven, The Netherlands

Park, J» Go

The Blackett Laboratory, Imperial College of Science and Technology, Prince Consort Road, London SW7 2BZ, Great Britain

Pascal, Do

Institut d'Electronigue Fondamentale, Universi té Paris-Sud, Bat. 220, 91405 Orsay, France

Paterno, G.

Comitato Nazionale per L'Energia Nucleare, Laboratori Nazionali di Frascati, 00044 Frascati, Roma, Italy

XXI Pegrum, C.M.

Department of Applied Physics, John Anderson Building, University of Strathclyde, Glasgow G4 ONG, Great Britain

Pierre, J.

Centre d'Etudes Nucleaires de Grenoble, Service des Basses Temperatures 85X, Av. des Martyrs, 38041 GrenobleCedex, France

Ramin, H.

Institut für Fernmeldetechnik, Technische Universität Berlin, Einsteinufer 29, 1000 Berlin 10, Germany

Ricci, F,

Richards, P.L,

Istituto di Fisica "G. Marconi", Università Degli Studi di Roma, Piazzale Delle Scienze No. 5, Roma 00100, Italy Department of Physics, University of California, Berkeley, California 94720, USA

Rogalla, H.

Institut für Angewandte Physik, Universität Münster, Roxeler Str.7072, 4400 Münster/Wstf., Germany

Romani, Go

Istituto di Fisica "G. Marconi", Università Degli Studi di Roma, Piazzale Delle Scienze No. 5, Roma 00100, Italy

Russo, M.

Laboratorio di Cibernetica del CNR, Via Toiano 2, 80072 Arco Felice, (Napoli), Italy

Sandel1, R.D,

Department of Physics, State University of New York, Stony Brook, New York 11794, USA

XXII Sanitas,

Bureau National de Metrologique, 21 Rue Casimir Perier, 75007 Paris, France

Sauerbrey, G.

Physikalisch-Technische Bundesanstalt, Institut Berlin, Abbestraße 2-12, 1000 Berlin 10, Germany

Saur, E.

Institut für Angewandte Physik, Universität Giessen, Leihgesterner Weg 106, 6300 Giessen, Germany

Sauzade, M.

Institut d'Electronique Fondamentale, Université Paris-Sud, Bat. 220, 91405 Orsay, France

Soerensen, O.H.

Technical University of Denmark, Physical Laboratory I, 2800 Lyngby, Denmark

Suhr, H.

Physikalisch-Technische Bundesanstalt, Institut Berlin, Abbestraße 2-12, 1000 Berlin 10, Germany

Sullivan, D.B.

Cryogenics Division, Institute for Basic Standards, National Bureau of Standards, Boulder, Colorado 80302, USA

Swithenby, S.J.

University of Oxford, Department of Physics, Clarendon Laboratory, Oxford 0X1 3PU, Great Britain

Schäfer, G.

Fa. Leybold-Heraeus GmbH. u. Co. KG, Bonner Str. 504, 5000 Köln 51, Germany

Schlup, W.

IBM Research Laboratory Zürich, Säumerstraße 4, 8803 Rüschlikon, Switzerland

XXIII Schultz, G.

Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 5300 Bonn 1, Germany

Schultz-DuBois, E.O.

Institut für Angewandte Physik, Universität Kiel, 2300 Kiel, Germany

Schuster, G.

Physikalisch-Technische Bundesanstalt, Institut Berlin, Abbestraße 2-12, 1000 Berlin 10, Germany

Schwarz, W.

Institut für Experimentelle Kernphysik, Universität Karlsruhe, Postfach 3640, 7500 Karlsruhe, Germany

Takàcs, S„

Slovak Academy of Science, Institute of Electrical Engineering, Dubravska Cesta, Bratislava 80932, CSSR

Tidecks, R.

I. Physikalisches Institut, Universität Göttingen, Bunsenstraße 9, 3 400 Göttingen, Germany

Ulrich, B.T„

Physics Department, University of Nijmegen, Toernooiveld, Nijmegen, The Netherlands

Vaglio, R.

Istituto di Fisica, Università di Salerno, Via Vernieri 42, 84100 Salerno, Italy

Van Duzer, T.

Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, California 94720, USA

Van Haeringen, W.

Philips Research Laboratories, Eindhoven, The Netherlands

Van Maaren, H.H.

Philips Research Laboratories, Eindhoven, The Netherlands

XXIV Walker, E 0 A 0

Physics Department, University of Lancaster, Lancaster LAI 4YW, Great Britain

Walter-Peters, M.

Afdeling der Technische Natuurkunde, Technische Hogeschool Twente, Postbus 217, Enschede, The Netherlands

Welker, N.

Laboratories for Physical Sciences, 4928 College Av., College Park, Maryland 20740, USA

Wolf, P.

IBM Research Laboratory Zürich, Säumerstraße 4, 8803 Rüschlikon, Switzerland

Zenatti, D.

Centre d'Etudes Nucleaires de Grenoble, B.P. No. 85, 38041 GrenobleCedex, France

Zimmerman, J„E„

Cryogenics Division, National Bureau of Standards, Boulder, Colorado 80302, USA

THEORY OF SUPERCONDUCTING PHASE COUPLING

THEORY OP PHASE COHERENCE IN SQUID'S

H. Liibbig Physikalisch-Technische Bundesanstalt, Institut B e r l i n , Abbestr. 2-12, D-IOOO B e r l i n 10, Germany 1

INTRODUCTION

Superconducting microstructures, capable for carrying phase gradients in the presence of currents and fields, as well as electromagnetic circuits, based essentially upon the non-linearity of their current phase characteristic have now been studied over a range of fifteen years. A large number of geometrical different weak link configurations, spreading the range from tunnel contacts w i t h discontinuous gap structure to thin film microbridges

connecting

two superconductors in a continuous way, have b e e n developed, evolving a multifarious picture of phase coherence effects. F o r tunnel junctions, the original analysis of

B.D. J0SEPHS0N

and its version due to N.R. WERTHAMER provide an unified thorough description of the constitutive current-phase

rela-

tionship, including the complete dynamical response. I n microbridges the situation is more complicated. U p to now the appearance of phase gradients in various thin film structures is well understood only under static conditions. A dynamic description of phase coherence effects in microbridges has come into focus only in the last years, but no unified theory is available. O n the side of the electromagnetic circuits, the SQUID configuration, in particular, is characterized by the direct relation between the phase difference,

, which is enclosed in the twofold connected

2 topology containing the weak link. As a consequence, the electromagnetic behaviour of the SQUID, i.e. the exchange of flux between the SQUID and the surrounding circuit, is determined essentially by the current-phase relationship of the weak link. Thus, the dynamics of flux transition, being reversible or irreversible, involves both the response of the weak link and the dispersion due to the macroscopic circuit elements. A SQUID response theory, restricted to frequencies small in comparison with the characteristic energy-gap frequency, has been developed in recent years, a detailed thorough description of the SQUID dynamics, however, is not available at present. As an introduction, this paper is concerned to the theory of phase coherence in tunnel junctions with isolating barriers and in thin film microbridges. By reason of simplicity, the links are treated in the one-dimensional limit by assuming the transvers dimensions to be smaller than twice the coherence length and the penetration depth. Through the whole article, the superconductors are assumed to be in thermal equilibrium. In a final section an approach is reported to treat the low frequency behaviour of an rf-SQUID as an example for a circuit analysis. 2

TUNNELING STRUCTURE

Several microscopic concepts of the theory of electron-tunneling through thin isolating barriers separating two bulk superconductors have been developed using different mathematical methods; e.g. pertubation theory [1,2 J, GREEN'S function method [3J, GINZBURG-LANDAU theory, [4J. Concerning the pertubation method, the system is described by an effective Hamiltonian, [5>6j, H = H1 + H2+ H t + y U

•

(1)

The Hamiltonians H^ and H^ are defined to describe the characteristics of the unperturbed system consisting of the two seperated superconductors 1 and 2. Bringing the two superconductors into interaction, their wave functions

3 become overlapping within the isolating barrier constituting a connection between electron states on both sides of the barrier. An effective Hamiltonian H T is introduced to describe this interaction. The properties of the contact structure are included in the matrix elements of H,p. The linked superconductors are assumed to be in thermal equilibrium. One may think of H^, H^ as BCS Hamiltonians for the case of weak-coupling superconductors. The case of strong-coupling superconductors has been investigated in r e f{7>8]. The influence of the external circuit in this model is taken into account by means of the voltage V applied across the junction leading to the chemical potential^, equ.(l). Under physical conditions the junction is subject to an impressed current. Consequently, the voltage arising across the contact controlls the balance of the different additive terms involved in the expression of the tunneling current. Therefore, it seems intuitively consequent, to visualize the physical meaning of the distinguishable contributions of the total current by means of describing their interdependence due to their voltage dependence. 2.1 TIME-INDEPENDENT VOLTAGE In the case that a time-independent voltage V Q is assumed the resulting tunneling current I shows periodic behaviour with respect to the time I(t)

=

I

Cf(t)

=

-

K t )

31 e< (

W

M

SWt T(pit) + I ( Vc e T ) CCS ( f i t ) + I (Vor)

3Z