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About the Editors XV
List of Contributors XVII
Preface XXIII
Part I: Fundamentals 1
1 Quantum Spin Hall Effect and Topological Insulators 3
Frank Ortmann, Stephan Roche, and Sergio O. Valenzuela
References 9
2 Hybridization of Topological Surface States and Emergent States 11
Shuichi Murakami
2.1 Introduction 11
2.2 Topological Phases and Surface States 12
2.2.1 Topological Insulators and Z2 Topological Numbers 12
2.2.2 Weyl Semimetals 13
2.2.3 Phase Transition between Topological Insulators and Weyl semimetals 15
2.3 Hybridization of Topological Surface States and Emergent States 19
2.3.1 Chirality of the Surface Dirac Cones 19
2.3.2 Thin Film 20
2.3.3 Interface between Two TIs 21
2.3.4 Superlattice 25
2.4 Summary 28
Acknowledgments 29
References 29
3 Topological Insulators in Two Dimensions 31
Steffen Wiedmann and Laurens W. Molenkamp
3.1 Introduction 31
3.2 2D TIs: Inverted HgTe/CdTe and Inverted InAs/GaSb Quantum Wells 33
3.2.1 HgTe/CdTe QuantumWells 33
3.2.2 The System InAs/GaSb 35
3.3 Magneto-Transport Experiments in HgTe QuantumWells 36
3.3.1 Sample Fabrication 36
3.3.2 Transition from n- to p-Conductance 37
3.3.3 Magnetic-Field-Induced Phase Transition 38
3.4 The QSHeffect in HgTe QuantumWells 40
3.4.1 Measurements of the Longitudinal Resistance 41
3.4.2 Transport in Helical Edge States 43
3.4.3 Nonlocal Measurements 44
3.4.4 Spin Polarization of the QSH Edge States 45
3.5 QSH Effect in a Magnetic Field 45
3.6 Probing QSH Edge States at a Local Scale 48
3.7 QSH Effect in InAs/GaSb QuantumWells: Experiments 49
3.8 Conclusion and Outlook 51
Acknowledgements 52
References 52
4 Topological Insulators, Topological Dirac semimetals, Topological Crystalline Insulators, and Topological Kondo Insulators 55
M. Zahid Hasan, Su-Yang Xu, and Madhab Neupane
4.1 Introduction 55
4.2 Z2 Topological Insulators 58
4.3 Topological Kondo Insulator Candidates 69
4.4 Topological Quantum Phase Transitions 74
4.5 Topological Dirac Semimetals 76
4.6 Topological Crystalline Insulators 84
4.7 Magnetic and Superconducting Doped Topological Insulators 89
Acknowledgements 95
References 96
Part II: Materials and Structures 101
5 Ab Initio Calculations of Two-Dimensional Topological Insulators 103
Gustav Bihlmayer, Yu. M. Koroteev, T. V.Menshchikova, Evgueni V. Chulkov, and Stefan Blügel
5.1 Introduction 103
5.2 Early Examples of 2D TIs 104
5.2.1 Graphene and the Quantum Spin Hall Effect 104
5.2.2 HgTe: Band Inversion and Topology in a 2D TI 108
5.3 Thin Bi and Sb Films 112
5.3.1 Bilayers 112
5.3.2 Thicker Layers 115
5.3.3 Alloyed Layers 118
5.3.4 Supported Layers 119
5.4 Compounds 121
5.4.1 Binary Compounds of A2B3 Type 122
5.4.2 Ternary Compounds: A′A2B4 and A′ 2A2B4 Types 124
5.5 Summary 125
Acknowledgments 126
References 126
6 Density Functional Theory Calculations of Topological Insulators 131
Hyungjun Lee, David Soriano, and Oleg V. Yazyev
6.1 Introduction 131
6.2 Methodology 132
6.2.1 Foundations of Density Functional Theory 132
6.2.2 Practical Aspects of DFT Calculations 136
6.2.3 Including Spin–Orbit Interactions 139
6.2.4 Calculating Z2 Topological Invariants 143
6.3 Bismuth Chalcogenide Topological Insulators: A Case Study 144
6.3.1 Bulk Band Structures of Bi2Se3 and Bi2Te3 144
6.3.2 Topologically Protected States at the (111) Surface of Bismuth Chalcogenides 148
6.3.3 Nonstoichiometric and Functionalized Terminations of the Bi2Se3 (111) Surface 151
6.3.4 High-Index Surfaces of Bismuth Chalcogenides 155
6.4 Conclusions and Outlook 156
References 157
7 Many-Body Effects in the Electronic Structure of Topological Insulators 161
Irene Aguilera, Ilya A. Nechaev, Christoph Friedrich, Stefan Blügel, and Evgueni V. Chulkov
7.1 Introduction 161
7.2 Theory 163
7.3 Computational Details 166
7.4 Calculations 167
7.4.1 Beyond the Perturbative One-Shot GW Approach 167
7.4.2 Analysis of the Band Inversion 169
7.4.3 Treatment of Spin–Orbit Coupling 170
7.4.4 Bulk Projected Band Structures 174
7.4.4.1 Bi2Se3 175
7.4.4.2 Bi2Te3 179
7.4.4.3 Sb2Te3 182
7.5 Summary 184
Acknowledgments 187
References 187
8 Surface Electronic Structure of Topological Insulators 191
Philip Hofmann
8.1 Introduction 191
8.2 Bulk Electronic Structure of Topological Insulators and Topological Crystalline Insulators 192
8.3 Bulk and Surface State Topology in TIs and TCIs 194
8.4 Surface Electronic Structure in Selected Cases 198
8.4.1 Bi Chalcogenite-Based Topological Insulators 198
8.4.2 The Group V Semimetals and Their Alloys 200
8.4.3 Other Topological Insulators 203
8.4.4 Topological Crystalline Insulators 203
8.5 Stability of the Topological Surface States 207
8.5.1 Stability with Respect to Scattering 207
8.5.2 Stability of the Surface States’ Existence 208
Acknowledgements 211
References 211
9 Probing Topological Insulator Surface States by Scanning Tunneling Microscope 217
Hwansoo Suh
9.1 Introduction 217
9.2 Sample Preparation Methods 219
9.3 STM and STS on Topological Insulator 220
9.3.1 Topography and Defects 221
9.3.2 STS and Band Structure of Topological Insulators 223
9.3.3 Landau Quantization of Topological Surface States 225
9.4 Conductance Map Analysis of Topological Insulator 229
9.4.1 Magnetically Doped Topological Insulator 233
9.4.2 Superconductor, Topological Insulator, and Majorana Zero Mode 235
9.5 Conclusions 236
References 237
10 Growth and Characterization of Topological Insulators 245
Johnpierre Paglione and Nicholas P. Butch
10.1 History of Bismuth-Based Material Synthesis 245
10.2 Synthesis and Characterization of Crystals and Films 246
10.3 Native Defects and Achieving Bulk Insulation 252
10.4 New Material Candidates and Future Directions 256
References 260
Part III: Electronic Characterization and Transport Phenomena 265
11 Topological Insulator Nanostructures 267
Seung Sae Hong and Yi Cui
11.1 Introduction 267
11.2 Topological Insulators: Experimental Progress and Challenges 268
11.3 Opportunities Enabled by Topological Insulator Nanostructures 270
11.4 Synthesis of Topological Insulator Nanostructures 271
11.4.1 Vapor-Phase Growth 271
11.4.2 Solution-Phase Growth 273
11.4.3 Exfoliation 273
11.4.4 Heterostructures 274
11.4.5 Doping and Alloying 275
11.5 Fermi Level Modulation and Bulk Carrier Control 276
11.6 Electronic Transport in Topological Insulator Nanostructures 279
11.6.1 Weak Antilocalization and Magnetic Topological Insulators 280
11.6.2 Shubnikov–de Haas Oscillations 280
11.6.3 Insulating Behavior at Ultrathin Limit 283
11.6.4 Aharonov–Bohm Effect and 1D Topological States 283
11.6.5 Superconducting Proximity Effect in TI Nanodevices 286
11.7 Applications and Future Perspective 286
11.8 Conclusion 288
References 289
12 Topological Insulator Thin Films and Heterostructures: Epitaxial Growth, Transport, and Magnetism 295
Anthony Richardella, Abhinav Kandala, and Nitin Samarth
12.1 Introduction 295
12.2 MBE Growth of Topological Insulators 297
12.2.1 HgTe 299
12.2.2 Bi and Sb Chalcogenides 300
12.2.2.1 Bi2Se3 303
12.2.2.2 Bi2Te3 303
12.2.2.3 Sb2Te3 304
12.2.2.4 (Bi1−xSbx)2Te3 305
12.2.2.5 Film Growth, Quality, and Stability 305
12.3 Transport Studies of TIThin Films 306
12.3.1 Shubnikov–de Haas Oscillations 308
12.3.2 Quantum Corrections to Diffusive Transport in 3D TI Films 309
12.3.3 Mesoscopic Transport in 3D TI Films 310
12.3.4 Hybridization Gaps in Ultrathin 3D TI Films 311
12.4 Topological Insulators Interfaced with Magnetism 313
12.4.1 Bulk Ferromagnetism 313
12.4.2 Ferromagnetic Insulator/Topological Insulator Heterostructures 315
12.5 Conclusions and Future Outlook 321
Acknowledgments 321
References 321
13 Weak Antilocalization Effect, Quantum Oscillation, and Superconducting Proximity Effect in 3D Topological Insulators 331
Hongtao He and Jiannong Wang
13.1 Introduction 331
13.2 Weak Antilocalization in TIs 331
13.3 Quantum Oscillations in TIs 340
13.4 Superconducting Proximity Effect in TIs 344
13.5 Perspective 353
References 353
14 Quantum Anomalous Hall Effect 357
Ke He, YayuWang, and Qikun Xue
14.1 Introduction to the Quantum Anomalous Hall Effect 357
14.1.1 The Hall Effect and Quantum Hall Effect 357
14.1.2 The Anomalous Hall Effect and Quantum Anomalous Hall Effect 359
14.2 Topological insulators and QAHE 360
14.3 Experimental Procedures for Realizing QAHE 362
14.3.1 Strategies for Experimental Observation of QAHE 362
14.3.2 Growth of Ultrathin TI Films by Molecular Beam Epitaxy 364
14.3.3 Band structure Engineering in (Bi1−xSbx)2Te3 ternary alloys 366
14.3.4 Ferromagnetism in Magnetically Doped Topological Insulators 367
14.3.5 Electrical Gate Tuning of the AHE 370
14.4 Experimental Observation of QAHE 371
14.5 Conclusion and Outlook 374
References 375
15 Interaction Effects on Transport in Majorana Nanowires 377
Reinhold Egger, Alex Zazunov, and Alfredo Levy Yeyati
15.1 Introduction 377
15.2 Transport through Majorana Nanowires: General Considerations 380
15.2.1 Model 380
15.2.2 Majorana–Meir–Wingreen Formula 381
15.2.3 Conductance for the Noninteracting M = 2 Case 382
15.3 Majorana Single-Charge Transistor 383
15.3.1 Charging Energy Contribution 383
15.3.2 Theoretical Approaches 384
15.3.3 Master Equation Approach 386
15.3.4 Coulomb Oscillations: Linear Conductance 388
15.3.5 From Resonant Andreev Reflection to Teleportation 389
15.3.6 Finite Bias Sidepeaks 389
15.3.7 Josephson Coupling to a Superconducting Lead 391
15.4 Topological Kondo Effect 392
15.4.1 Low-EnergyTheory 393
15.4.2 Majorana Spin 394
15.4.3 Renormalization Group Analysis 394
15.4.4 Topological Kondo Fixed Point 395
15.4.5 Conductance Tensor 396
15.5 Conclusions and Outlook 397
Acknowledgments 397
References 398
Index 401
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