Topological insulators / Marcel Franz, University of British Columbia, Vancouver, Canada, Laurens Molenkamp, University of Würzburg, Würzburg, Germany.

Format:

Book

Contributor:

Franz, Marcel, editor.

Molenkamp, Laurens, editor.

Craig M. Merrihue Memorial Fund.

Series:

Contemporary concepts of condensed matter science ; v. 6.

Contemporary concepts of condensed matter science ; volume 6

Language:

English

Subjects (All):

Energy-band theory of solids.

Condensed matter.

Topological dynamics.

Physical Description:

xvi, 331 pages : illustrations ; 24 cm.

Edition:

First edition.

Place of Publication:

Amsterdam ; Boston ; Heidelberg ; London : Elsevier, 2013.

Contents:

Part I Theoretical Foundations

1 Topological Band Theory and the Z₂ Invariant / C.L. Kane Kane, C.L.

1 Introduction 4

2 Topology and Band Theory 4

2.1 Topology 5

2.2 Band Theory 6

2.3 Topological Band Theory and the Bulk-Boundary Correspondence 7

2.4 Berry Phase, and the Chern Invariant 7

3 Illustrative Example: Polarization and Topology in One Dimension 9

3.1 Polarization as a Berry Phase 9

3.2 Su, Schrieffer, Heeger Model 11

3.3 Domain Wall States and the Jackiw Rebbi Model 12

3.4 Thouless Charge Pump, and the Chern Invariant 14

4 Integer Quantum Hall Effect 14

4.1 Laughlin Argument, and the TKNN Invariant 15

4.2 Haldane Model 16

4.3 Chiral Edge States, and the Bulk Boundary Correspondence 18

5 Z₂ Topological Insulators 20

5.1 Quantum Spin Hall Insulator in Graphene 20

5.2 Z₂ Topological Invariant 22

5.3 Topological Insulators in Three Dimensions 26

6 Related Topics 29

6.1 Topological Crystaline Insulators 29

6.2 Topological Nodal Semimetals 30

6.3 Topological Superconductivity 31

6.4 Topological Defects 32

Acknowledgments 33

References 33

2 Theory of Three-Dimensional Topological Insulators / Joel E. Moore Moore, Joel E.

1 Introduction 35

2 Topological Properties of Band Structures 38

2.1 Building the 3D Topological Insulator from 2D 39

2.2 Materials Considerations 43

2.3 Berry Phases of Bloch Electrons and Chern-Simons Form of Z₂ Invariant 44

2.4 Time-Reversal Breaking, Surface Hall Effect, and Magnetoelectric Response 45

3 Transport in Topological Surface States and Real-Space Geometry 48

4 Consequences of Strong Electronic Interactions 50

4.1 Defining the 3D Topological Insulator with Interactions 51

4.2 Superconducting Proximity Effect 52

4.3 Fractional Topological Insulators 53

4.4 Related States in Three Dimensions 54

Acknowledgments 55

References 55

3 Models and Materials for Topological Insulators / Chaoxing Liu Liu, Chaoxing, Shoucheng Zhang Zhang, Shoucheng

1 Introduction 59

2 HgTe Quantum Wells and the Bernevig-Hughes-Zhang Model 60

3 Effective Model of the Three-Dimensional Topological Insulator 65

4 Helical Edge/Surface State of 2D/3D Topological Insulators 70

5 Physical Properties of Topological Edge/Surface States 73

5.1 Total Angular Momentum, Spin, and Orbital Texture of Helical Edge/Surface States 74

5.2 Topological Stability of Edge/Surface State 75

5.3 Topological Response of TR Breaking Mass Term 77

6 Topological Insulator Materials 79

6.1 Bi₂Se₃ Family and Related Materials 79

6.2 HgTe and Related Materials 82

6.3 Other Materials 84

Acknowledgments 86

References 86

4 Field-Theory Foundations of Topological Insulators / Xiao-Liang Qi Qi, Xiao-Liang

1 Introduction to Topological Field Theory 91

2 TFT Description of 3D Time-Reversal Invariant TI 97

2.1 Obtaining the Topological Term from General Considerations 97

2.2 Microscopic Derivation of the Topological Order Parameter 99

2.3 Physical Consequences of the TFT 107

3 TFT Description of More General Topological States 113

3.1 Phase Space Chern-Simons Theories 113

3.2 Further Investigation on Interacting Topological States 117

Acknowledgement 120

References 120

Part II Experimental Discoveries

5 Quantum Spin Hall State in HgTe / C. Brüne Brüne, C., H. Buhmann Buhmann, H., L.W. Molenkamp Molenkamp, L.W.

1 HgTe Quantum Wells 125

2 The Quantum Spin Hall Effect 128

3 Non-Local Transport in the Quantum Spin Hall State 131

4 Spin Polarization of the Quantum Spin Hall Edge States 135

5 Conclusion 141

References 141

6 Topological Surface States: A New Type of 2D Electron Systems / M. Zahid Hasan Hasan, M. Zahid, Su-Yang Xu Xu, Su-Yang, David Hsieh Hsieh, David, L. Andrew Wray Wray, L. Andrew, Yuqi Xia Xia, Yuqi

1 Introduction 144

2 The Birth of Momentum-Resolved Spectroscopy as a Direct Experimental Probe of Z₂Topological-Order 145

3 Separation of Insulating Bulk from Metallic Surface States Using Incident Photon Energy Modulated ARPES 147

4 Winding Number Count: Counting of Surface Fermi Surfaces Enclosing Kramers Points to Identify Topologically Non-Trivial Surface Spin-Textured States 151

5 Spin-Resolving the Surface States to Identify the Non-Trivial Topological Phase and Establish a 2D Helical Metal Protected from Backscattering 154

6 Identifying the Origin of 3D Topological Order Via a Bulk Band Gap Inversion Transition 158

7 Topological Protection and Tunability of the Surface States of a 3D Topological Insulator 165

8 Future Directions: Topological Superconductors and Topological Crystalline Insulators 168

Acknowledgments 172

References 172

7 Visualizing Topological Surface States and their Novel Properties using Scanning Tunneling Microscopy and Spectroscopy / Haim Beindenkopf Beindenkopf, Haim, Pedram Roushan Roushan, Pedram, Ali Yazdani Yazdani, Ali

1 Introduction 175

2 Scanning Tunneling Microscopy and Spectroscopic Mapping 176

3 Absence of Backscattering 177

4 Fluctuation of the Dirac Point in Doped Topological Insulators 187

5 Enhanced Transmission Through Defects 190

6 Conclusion and Outlook 195

Acknowledgments 196

References 196

8 Transport Experiments on Three-Dimensional Topological Insulators / Jeroen B. Oostinga Oostinga, Jeroen B., Alberto F. Morpurgo Morpurgo, Alberto F.

1 Introduction 200

2 Bulk Transport Through Bismuth-Based Compounds 201

2.1 Bi_1-xSb_x 202

2.2 Bi₂Se₃ and Bi₂Te₃ 203

2.3 Controlling the Bulk Conductivity 206

3 Identification of Surface Transport Using Bulk Single Crystals 209

3.1 Different Types of Charge Carriers 209

3.2 Angle-Dependent Shubnikov-de Haas Resistance Oscillations 211

3.3 Landau Level Indexing 213

4 Electronic Transport Through Nanofabricated Devices 215

4.1 Top-Down Approach: Mechanical Exfoliation of Macroscopic Crystals 216

4.2 Epitaxial Films, Nanoribbons, and Nanowires 217

4.3 Ambipolar Transport in Gated Devices 218

4.4 Gate-Tunable Shubnikov-de Haas Resistance Oscillations 220

4.5 Topological Surface States in Epitaxially Grown HgTe Layers 223

5 Miscellaneous Transport Properties 223

5.1 Aharonov-Bohm Effect in Bi₂Se₃ and Bi₂Te₃ nanowires 224

5.2 Josephson Junctions 224

5.3 Doped Topological Insulators 227

6 Conclusions and Outlook 228

References 229

Part III The Road Ahead

9 New Materials

Ke He / Xucun Ma Ma, Xucun, Xi Chen Chen, Xi, Qi-Kun Xue Xue, Qi-Kun

1 Three-Dimensional Topological Insulators 238

1.1 Early Discovered Three-Dimensional Topological Insulator Materials 238

1.2 Molecular Beam Epitaxy Grown Thin Films of Topological Insulators 240

1.3 Defects in Epitaxial Films of Bi₂Se₃ Family Topological Insulators 243

1.4 Chemical Potential Tuning 246

1.5 New Systems of Topological Insulator Materials 248

2 Two-Dimensional Topological Insulators 251

2.1 InAs/GaSb/AlSb Quantum Wells 252

2.2 Bi Thin Films 253

2.3 Single Atomic Layer of Silicon and Germanium 253

2.4 Thin Films of Three-Dimensional Topological Insulator 255

3 Magnetic Topological Insulators 256

Acknowledgments 259

References 260

10 Theoretical Design of Materials and Functions of Topological Insulators and Superconductors / Naoto Nagaosa Nagaosa, Naoto

1 Introduction 263

2 Magnetic and Magneto-Electric Phenomena Related to Topological Insulators 266

3 Correlated Topological Insulators 276

4 Topological Superconductors and Majorana Fermions 281

5 Discussion and Conclusions 288

Acknowledgments 289

References 289

11 Beyond Band Insulators: Topology of Semimetals and Interacting Phases / Ari M.

Turner Turner, Ari M., Ashvin Vishwanath Vishwanath, Ashvin

1 Part 1: Topological Semimetals 294

1.1 Topological Properties of Weyl Semimetals 296

1.2 Topological Semimetals: Generalizations 303

1.3 Candidate Materials 305

1.4 Other Directions 306

2 Part 2: Topology of Interacting Phases 307

2.1 One-Dimensional Topological Insulators 310

2.2 Topological SRE Phases in Higher Dimensions 317

2.3 Edge States and Topological Order 321

2.4 Outlook 322.

Notes:

Includes bibliographical references and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Craig M. Merrihue Memorial Fund.

ISBN:

0444633146

9780444633149

OCLC:

857347461

Publisher Number:

99958845977