Shen Topological Insulators

Dirac Equation in Condensed Matter
2. Auflage 2017
ISBN: 978-981-10-4606-3
Verlag: Springer Nature Singapore
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 187, 272 Seiten

Reihe: Springer Series in Solid-State Sciences

This new edition presents a unified description of these insulators from one to three dimensions based on the modified Dirac equation. It derives a series of solutions of the bound states near the boundary, and describes the current status of these solutions. Readers are introduced to topological invariants and their applications to a variety of systems from one-dimensional polyacetylene, to two-dimensional quantum spin Hall effect and p-wave superconductors, three-dimensional topological insulators and superconductors or superfluids, and topological Weyl semimetals, helping them to better understand this fascinating field. To reflect research advances in topological insulators, several parts of the book have been updated for the second edition, including: Spin-Triplet Superconductors, Superconductivity in Doped Topological Insulators, Detection of Majorana Fermions and so on. In particular, the book features a new chapter on Weyl semimetals, a topic that has attracted considerable attention and has already become a new hotpot of research in the community. 

Professor Shun-Qing Shen, an expert in the field of condensed matter physics, is distinguished for his research works on topological quantum materials, spintronics of semiconductors, quantum magnetism and orbital physics in transition metal oxides, and novel quantum states of condensed matter. He proposed topological Anderson insulator, theory of weak localization and antilocalization for Dirac fermions, spin transverse force, resonant spin Hall effect and the theory of phase separation in colossal magnetoresistive (CMR) materials. He proved the existence of antiferromagnetic long-range order and off-diagonal long-range order in itinerant electron systems. 

Professor Shun-Qing Shen has been a professor of physics at The University of Hong Kong since July 2007. Professor Shen received his BS, MS, and PhD in theoretical physics from Fudan University in Shanghai. He was a postdoctorial fellow (1992 - 1995) in China Center of Advanced Science and Technology (CCAST), Beijing, Alexander von Humboldt fellow (1995 - 1997) in Max Planck Institute for Physics of Complex Systems, Dresden, Germany, and JSPS research fellow (1997) in Tokyo Institute of Technology, Japan. In December 1997 he joined Department of Physics, The University of Hong Kong. He was awarded Croucher Senior Research Fellowship (The Croucher Award) in 2010.

Autoren/Hrsg.

Shen, Shun-Qing

Inhaltsverzeichnis

1;Preface to the Second Edition;6
2;Preface to the First Edition;7
3;Contents;9
4;1 Introduction;14
4.1;1.1 From the Hall Effect to the Quantum Spin Hall Effect;14
4.2;1.2 Topological Insulators as a Generalization of the Quantum Spin Hall Systems;19
4.3;1.3 Beyond Band Insulators: Disorder and Interaction;21
4.4;1.4 Topological Phases in Superconductors and Superfluids;22
4.5;1.5 Topological Dirac and Weyl Semimetals;24
4.6;1.6 Dirac Equation and Topological Insulators;25
4.7;1.7 Topological Insulators and Landau Theory of Phase Transition;25
4.8;1.8 Summary;26
4.9;1.9 Further Reading;27
4.10;References;27
5;2 Starting from the Dirac Equation;30
5.1;2.1 Dirac Equation;30
5.2;2.2 Solutions of Bound States;32
5.2.1;2.2.1 Jackiw-Rebbi Solution in One Dimension;32
5.2.2;2.2.2 Two Dimensions;35
5.2.3;2.2.3 Three and Higher Dimensions;36
5.3;2.3 Why not the Dirac Equation?;36
5.4;2.4 Quadratic Correction to the Dirac Equation;37
5.5;2.5 Bound State Solutions of the Modified Dirac Equation;38
5.5.1;2.5.1 One Dimension: End States;38
5.5.2;2.5.2 Two Dimensions: Helical Edge States;40
5.5.3;2.5.3 Three Dimensions: Surface States;42
5.5.4;2.5.4 Generalization to Higher-Dimensional Topological Insulators;44
5.6;2.6 Summary;44
5.7;2.7 Further Reading;45
5.8;References;45
6;3 Minimal Lattice Model for Topological Insulators;46
6.1;3.1 Tight Binding Approximation;46
6.2;3.2 Mapping from a Continuous Model to a Lattice Model;48
6.3;3.3 One-Dimensional Lattice Model;50
6.4;3.4 Two-Dimensional Lattice Model;53
6.4.1;3.4.1 Integer Quantum Hall Effect;53
6.4.2;3.4.2 Quantum Spin Hall Effect;55
6.5;3.5 Three-Dimensional Lattice Model;55
6.6;3.6 Parity at the Time Reversal Invariant Momenta;57
6.6.1;3.6.1 One-Dimensional Lattice Model;58
6.6.2;3.6.2 Two-Dimensional Lattice Model;59
6.6.3;3.6.3 Three-Dimensional Lattice Model;61
6.7;3.7 Summary;63
6.8;References;63
7;4 Topological Invariants;64
7.1;4.1 Bloch's Theorem and Band Theory;64
7.2;4.2 Berry Phase;65
7.3;4.3 Quantum Hall Conductance and the Chern Number;68
7.4;4.4 Electric Polarization in a Cyclic Adiabatic Evolution;72
7.5;4.5 Thouless Charge Pump;74
7.6;4.6 Fu--Kane Spin Pump;77
7.7;4.7 Integer Quantum Hall Effect: The Laughlin Argument;79
7.8;4.8 Time Reversal Symmetry and the Z2 Index;81
7.9;4.9 Generalization to Two and Three Dimensions;86
7.10;4.10 Phase Diagram of the Modified Dirac Equation;88
7.11;4.11 Further Reading;91
7.12;References;92
8;5 Topological Phases in One Dimension;93
8.1;5.1 Su--Schrieffer--Heeger Model for Polyacetylene;93
8.2;5.2 Topological Ferromagnet;98
8.3;5.3 p-Wave Pairing Superconductor;98
8.4;5.4 Ising Model in a Transverse Field;100
8.5;5.5 One-Dimensional Maxwell's Equations in Media;101
8.6;5.6 Summary;102
8.7;References;102
9;6 Quantum Anomalous Hall Effect and Quantum Spin Hall Effect;103
9.1;6.1 Quantum Anomalous Hall Effect;103
9.1.1;6.1.1 Two-Dimensional Dirac Model and the Chern Number;103
9.1.2;6.1.2 Haldane Model;104
9.1.3;6.1.3 Experimental Realization;107
9.2;6.2 From the Haldane Model to the Kane-Mele Model;110
9.3;6.3 Transport of Edge States;113
9.3.1;6.3.1 Landauer-Büttiker Formalism;114
9.3.2;6.3.2 Transport of Edge States;116
9.4;6.4 Stability of Edge States;119
9.5;6.5 Realization of the Quantum Spin Hall Effect in HgTe/CdTe Quantum Wells;121
9.5.1;6.5.1 Band Structure of HgTe/CdTe Quantum Wells;121
9.5.2;6.5.2 Exact Solution of Edge States;124
9.5.3;6.5.3 Experimental Measurement;127
9.6;6.6 Quantized Conductance in InAs/GaAs Bilayer Quantum Well;129
9.7;6.7 Quantum Hall Effect and Quantum Spin Hall Effect: A Case Study;130
9.7.1;6.7.1 Quantum Hall Effect (?=2);130
9.7.2;6.7.2 Quantum Spin Hall Effect;131
9.8;6.8 Coherent Oscillation Due to the Edge States;132
9.9;6.9 Further Reading;134
9.10;References;134
10;7 Three-Dimensional Topological Insulators;136
10.1;7.1 Family Members of Three-Dimensional Topological Insulators;136
10.1.1;7.1.1 Weak Topological Insulators: PbxSn1-xTe;136
10.1.2;7.1.2 Strong Topological Insulators: Bi1-xSbx;137
10.1.3;7.1.3 Topological Insulators with a Single Dirac Cone: Bi2Se3 and Bi2Te3;138
10.1.4;7.1.4 Strained HgTe;138
10.2;7.2 Electronic Model for Bi2Se3;140
10.3;7.3 Effective Model for Surface States;142
10.4;7.4 Physical Properties of Topological Insulators;145
10.4.1;7.4.1 Absence of Backscattering;145
10.4.2;7.4.2 Weak Antilocalization;146
10.4.3;7.4.3 Shubnikov-de Haas Oscillation;147
10.5;7.5 Surface Quantum Hall Effect;148
10.6;7.6 Surface States in a Strong Magnetic Field;151
10.7;7.7 Topological Insulator Thin Film;153
10.7.1;7.7.1 Effective Model for Thin Film;153
10.7.2;7.7.2 Structural Inversion Asymmetry;157
10.7.3;7.7.3 Experimental Data of ARPES;159
10.8;7.8 HgTe Thin Film;159
10.9;7.9 Further Reading;161
10.10;References;162
11;8 Impurities and Defects in Topological Insulators;164
11.1;8.1 One Dimension;164
11.2;8.2 Integral Equation for Bound State Energies;166
11.2.1;8.2.1 ?-Potential;167
11.3;8.3 Bound States in Two Dimensions;168
11.4;8.4 Topological Defects;172
11.4.1;8.4.1 Magnetic Flux and Zero Energy Mode;172
11.4.2;8.4.2 Wormhole Effect;174
11.4.3;8.4.3 Witten Effect;175
11.5;8.5 Disorder Effect on Transport;179
11.6;8.6 Further Reading;181
11.7;References;181
12;9 Topological Superconductors and Superfluids;183
12.1;9.1 Complex (p+ip)-Wave Superconductor for Spinless ƒ;184
12.2;9.2 Spin Triplet Pairing Superfluidity: 3He-A and -B Phases;188
12.2.1;9.2.1 3He: Normal Liquid Phase;189
12.2.2;9.2.2 3He-B Phase;189
12.2.3;9.2.3 3He-A Phase: Equal Spin Pairing;192
12.3;9.3 Spin-Triplet Superconductor: Sr2RuO4;194
12.4;9.4 Superconductivity in Doped Topological Insulators;195
12.5;9.5 Further Reading;196
12.6;References;196
13;10 Majorana Fermions in Topological Insulators;198
13.1;10.1 What Is a Majorana Fermion?;198
13.2;10.2 Majorana Fermions in p-Wave Superconductors;199
13.2.1;10.2.1 Zero Energy Mode Around a Quantum Vortex;199
13.2.2;10.2.2 Majorana Fermions in Kitaev's Toy Model;202
13.2.3;10.2.3 Quasi-One-Dimensional Superconductors;204
13.3;10.3 Majorana Fermions in Topological Insulators;207
13.4;10.4 Sau--Lutchyn--Tewari--Das Sarma Model for Topological Superconductors;208
13.5;10.5 4?-Josephson Effect;211
13.6;10.6 Non-Abelion Statistics and Topological Quantum Computing;213
13.7;10.7 Further Reading;215
13.8;References;215
14;11 Topological Dirac and Weyl Semimetals;216
14.1;11.1 Weyl Equations and Weyl Fermions;216
14.1.1;11.1.1 Weyl Equations;216
14.1.2;11.1.2 A Single Node and Magnetic Monopole;217
14.2;11.2 Emergent Dirac and Weyl Semimetals;218
14.2.1;11.2.1 Dirac Semimetal;219
14.2.2;11.2.2 Topological Dirac Semimetal;220
14.2.3;11.2.3 Topological Weyl Semimetal;221
14.3;11.3 Graphene: A Topological Dirac Semimetal;221
14.4;11.4 Two-Node Model;223
14.4.1;11.4.1 Model;224
14.4.2;11.4.2 The Chern Number and Fermi Arc;225
14.4.3;11.4.3 Quantum Anomalous Hall Effect;227
14.5;11.5 Tight-Binding Model and Topological Phase Transition;229
14.6;11.6 Chiral Anomaly;231
14.7;11.7 Exotic Magnetotransport;232
14.7.1;11.7.1 Three-Dimensional Weak Antilocalization;232
14.7.2;11.7.2 Negative Magnetoresistance;233
14.7.3;11.7.3 Linear Magnetoconductance Near the Weyl Nodes;236
14.7.4;11.7.4 High Mobility and Large Magnetoresistance;237
14.8;11.8 Further Reading;238
14.9;References;238
15;12 Topological Anderson Insulator;239
15.1;12.1 Band Structure and Edge States;239
15.2;12.2 Quantized Anomalous Hall Effect;241
15.3;12.3 Topological Anderson Insulator;243
15.4;12.4 Effective Medium Theory for Topological Anderson Insulator;245
15.5;12.5 Band Gap or Mobility Gap;246
15.6;12.6 Summary;248
15.7;12.7 Further Reading;248
15.8;References;249
16;13 Summary: Symmetries and Topological Classification;250
16.1;13.1 Ten Symmetry Classes for Non-interacting Fermion Systems;250
16.2;13.2 Physical Systems and the Symmetry Classes;252
16.2.1;13.2.1 Standard (Wigner--Dyson) Classes;252
16.2.2;13.2.2 Chiral Classes;253
16.2.3;13.2.3 Bogoliubov-de Gennes (BdG) Classes;253
16.3;13.3 Characterization in the Bulk States;254
16.4;13.4 Five Types in Each Dimension;255
16.5;13.5 Conclusion;256
16.6;13.6 Further Reading;257
16.7;References;257
17;Appendix A Derivation of Two Formulae;258
18;Appendix B Time Reversal Symmetry;264
19;Appendix C The Dirac Matrices and the Dirac Gamma Matrices;268
20;Index;269