Skip to main content

Topological Insulators: Fundamentals and Perspectives

Topological Insulators: Fundamentals and Perspectives

Frank Ortmann, Stephan Roche, Sergio O. Valenzuela, Laurens W. Molenkamp (Foreword by)

ISBN: 978-3-527-33702-6

Jun 2015

432 pages

In Stock

$205.00

Description

There are only few discoveries and new technologies in physical sciences that have the potential to dramatically alter and revolutionize our electronic world. Topological insulators are one of them. The present book for the first time provides a full overview and in-depth knowledge about this hot topic in materials science and condensed matter physics. Techniques such as angle-resolved photoemission spectrometry (ARPES), advanced solid-state Nuclear Magnetic Resonance (NMR) or scanning-tunnel microscopy (STM) together with key principles of topological insulators such as spin-locked electronic states, the Dirac point, quantum Hall effects and Majorana fermions are illuminated in individual chapters and are described in a clear and logical form. Written by an international team of experts, many of them directly involved in the very first discovery of topological insulators, the book provides the readers with the knowledge they need to understand the electronic behavior of these unique materials. Being more than a reference work, this book is essential for newcomers and advanced researchers working in the field of topological insulators.

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