Glide-Symmetric Z2 Magnetic Topological Crystalline Insulators (Springer Theses) 9789811690761, 9789811690778, 9811690766

Table of contents :
Supervisor’s Foreword
Acknowledgements
Contents
1 Introduction
1.1 Background
1.2 Outline of Thesis
References
2 Topology, Symmetry, and Band Theory of Materials
2.1 Band Theory and Topology
2.1.1 Physics of Berry Phase, Berry Connection, and Berry Curvature
2.1.2 Bloch Hamiltonian
2.1.3 Chern Number
2.1.4 Hybrid Wannier Centers
2.1.5 Photonic Crystal
2.2 Symmetry Analysis and Notation
2.2.1 Internal Symmetry: Ten-Fold Classification
2.2.2 Space-Group Symmetry
2.2.3 Little Group of k (k-Group) and Its Representation
2.2.4 Compatibility Relations
2.2.5 Wyckoff Positions
2.2.6 Topological Invariant: Symmetry-Based Indicator
2.3 Topological Phases of Matter
2.3.1 Chern Insulator
2.3.2 Topological Insulators
2.3.3 Topological Crystalline Insulators
2.3.4 Topological Semimetals; Weyl, Dirac, and Nodal-Line Semimetals
2.3.5 Topological Photonics and Other Topological Phases
References
3 Weyl Semimetals and Spinless Z2 Magnetic Topological Crystalline Insulators with Glide Symmetry
3.1 General Theory: Phase Transition for the Glide-Symmetric Magnetic Systems
3.1.1 Z2 Topological Invariant for Glide-Symmetric Magnetic Systems
3.1.2 TCI-NI Phase Transition and Weyl Semimetal
3.1.3 Effective Model for the Pair Creation/Annihilation of Weyl Nodes
3.2 Model Calculation: 3D Fang-Fu Lattice Model with an Additional Term
3.2.1 Model
3.2.2 Trajectories of Weyl Nodes
3.2.3 Evolution of the Surface States
3.2.4 φ= 0 Case: Additional C2x Symmetry
3.3 Conclusion and Discussion
References
4 Interplay of Glide-Symmetric Z2 Magnetic Topological Crystalline Insulators and Symmetry: Inversion Symmetry and Nonprimitive Lattice
4.1 Preliminaries
4.1.1 Previous Works on Topological Phases for Glide-Symmetric Systems with and Without Inversion Symmetry in Class A
4.1.2 Brief Review of Sewing Matrices and Monodromy
4.2 Redefinition of the Glide-Z2 Invariant
4.2.1 Gauge Dependence of the Glide-Z2 Invariant
4.2.2 Redefinition of the Glide-Z2 Invariant
4.3 Glide-Symmetric Magnetic Topological Crystalline Insulators …
4.3.1 Topological Invariants for Space Group 13
4.3.2 Topological Invariants for 14
4.4 Glide-Symmetric Magnetic Topological Crystalline Insulators …
4.4.1 Motivation
4.4.2 Relation Between Hamiltonians in 9 and 7
4.4.3 Derivation of the Formula of the Z2 Topological Invariant for 9
4.4.4 Topological Invariants for 15
4.5 Symmetry-Based Indicators and K-Theory
4.6 Spinful Systems
4.7 Conclusion and Discussion
Appendix
References
5 Topological Invariants and Tight-Binding Models from the Layer Constructions
5.1 Topological Invariants from the Layer Construction for Class A
5.1.1 Setup
5.1.2 Topological Invariants for Glide-Symmetric Systems with Inversion Symmetry
5.1.3 Invariants for Layer Constructions
5.1.4 Elementary Layer Constructions
5.1.5 Convention Dependence of Topological Invariants
5.2 Tight-Binding Models Constructed from the Layer Construction
5.2.1 Tight-Binding Models Constructed from the Layer Construction for 13
5.2.2 Tight-Binding Models Constructed from the Layer Construction for 14
5.2.3 Tight-Binding Models Constructed from the Layer Construction for 15
5.3 Conclusion and Discussion
Appendix
References
6 Glide-Symmetric Z2 Topological Crystalline Insulators in Magnetic Photonic Crystals
6.1 Previous Work: Z2 Topological Photonic Crystal with Glide Symmetry …
6.2 Symmetry Consideration for Band Theory of Glide-Symmetric …
6.2.1 Representations at the High-Symmetry Points
6.2.2 Singularity of Photonic Bands
6.2.3 The Glide-Z2 Invariant for the Photonic Crystal
6.3 Manipulations for Topological Photonic Crystals with Glide Symmetry
6.3.1 Perturbation Theory
6.3.2 Photonic Band Structures Based on Wyckoff Positions
6.3.3 Designing for Topological Photonic Crystals Based on Wyckoff Positions
6.4 Conclusion and Discussion
References
7 Conclusion and Outlook
Appendix Curriculum Vitae
Education
Research Experience