Topological Insulators

Frank Ortmann is Head of the Computational Nanoelectronics group at the Institute for Materials Science at the Technische Universität Dresden, Germany. He is specialized on large-scale electronic transport simulations linked with ab initio electronic structure methods and on nanoelectronics of materials. Frank Ortmann studied physics at the University of Jena, Germany, where he received his PhD for a work on the topic of charge transport in organic crystals in 2009. He moved to the French Commissariat a l'Energie Atomique et aux Energies Alternatives Grenoble, France, for a postdoctoral stay funded by a Marie Curie fellowship from the European Commission. In 2011, he moved to the Catalan Institute of Nanotechnology Barcelona. Frank Ortmann was awarded with the Faculty Prize of the University of Jena, received a prestigious Emmy Noether Young Investigator grant from the DFG in 2014 and is author of several articles in high-impact journals.Stephan Roche is an ICREA Research Professor and Head of the group Theoretical and Computational Nanoscience at the Institut Catala de Nanociencia i Nanotecnologia (ICN2) in Barcelona, Spain. He studied Theoretical Physics at the Ecole Normale Supérieure, France, where a received his PhD after completion of his thesis at the French National Centre for Scientific Research in 1996. After several postdoctoral fellowships at universities in Japan, Spain, and Germany he was appointed Professor at the Joseph Fourier University, France, and became researcher at the French Commissariat a l'Energie Atomique et aux Energies Alternatives in 2004. He has published more than 130 scientific contributions, is member of various international nanotech conference committees and Head of the ICN2 in the Graphene Flagship initiative of the European Commission. In 2009, Stephan Roche was awarded with the Friedrich Wilhelm Bessel prize by the Alexander von Humboldt Foundation.Sergio O. Valenzuela is an ICREA Research Professor and Head of the group Physics and Engineering of Nanodevices at the Institut Catala de Nanociencia i Nanotecnologia (ICN2) in Barcelona, Spain. He received his PhD in Physics from the University of Buenos Aires, Argentina, in 2001. After a postdoctoral fellowship at Harvard University, he became a Research Scientist at the Massachusetts Institute of Technology in 2005, then moved to Barcelona in 2008. Valenzuela is interested in quantum computation, NEMS and superconductivity and has ample experience in the characterization of spintronic devices. He is editor of one book and several book chapters and author of more than 40 journal articles. In 2009, Sergio O. Valenzuela was honored with the Young Scientist award of the International Union of Pure and Applied Physics and, in 2012, received a highly renowned European Research Council Starting Grant.

• About the Editors XVList of Contributors XVIIPreface XXIIIPart I: Fundamentals 11 Quantum Spin Hall Effect and Topological Insulators 3Frank Ortmann, Stephan Roche, and Sergio O. ValenzuelaReferences 92 Hybridization of Topological Surface States and Emergent States 11Shuichi Murakami2.1 Introduction 112.2 Topological Phases and Surface States 122.2.1 Topological Insulators and Z2 Topological Numbers 122.2.2 Weyl Semimetals 132.2.3 Phase Transition between Topological Insulators and Weyl semimetals 152.3 Hybridization of Topological Surface States and Emergent States 192.3.1 Chirality of the Surface Dirac Cones 192.3.2 Thin Film 202.3.3 Interface between Two TIs 212.3.4 Superlattice 252.4 Summary 28Acknowledgments 29References 293 Topological Insulators in Two Dimensions 31Steffen Wiedmann and Laurens W. Molenkamp3.1 Introduction 313.2 2D TIs: Inverted HgTe/CdTe and Inverted InAs/GaSb Quantum Wells 333.2.1 HgTe/CdTe QuantumWells 333.2.2 The System InAs/GaSb 353.3 Magneto-Transport Experiments in HgTe QuantumWells 363.3.1 Sample Fabrication 363.3.2 Transition from n- to p-Conductance 373.3.3 Magnetic-Field-Induced Phase Transition 383.4 The QSHeffect in HgTe QuantumWells 403.4.1 Measurements of the Longitudinal Resistance 413.4.2 Transport in Helical Edge States 433.4.3 Nonlocal Measurements 443.4.4 Spin Polarization of the QSH Edge States 453.5 QSH Effect in a Magnetic Field 453.6 Probing QSH Edge States at a Local Scale 483.7 QSH Effect in InAs/GaSb QuantumWells: Experiments 493.8 Conclusion and Outlook 51Acknowledgements 52References 524 Topological Insulators, Topological Dirac semimetals, Topological Crystalline Insulators, and Topological Kondo Insulators 55M. Zahid Hasan, Su-Yang Xu, and Madhab Neupane4.1 Introduction 554.2 Z2 Topological Insulators 584.3 Topological Kondo Insulator Candidates 694.4 Topological Quantum Phase Transitions 744.5 Topological Dirac Semimetals 764.6 Topological Crystalline Insulators 844.7 Magnetic and Superconducting Doped Topological Insulators 89Acknowledgements 95References 96Part II: Materials and Structures 1015 Ab Initio Calculations of Two-Dimensional Topological Insulators 103Gustav Bihlmayer, Yu. M. Koroteev, T. V.Menshchikova, Evgueni V. Chulkov, and Stefan Blügel5.1 Introduction 1035.2 Early Examples of 2D TIs 1045.2.1 Graphene and the Quantum Spin Hall Effect 1045.2.2 HgTe: Band Inversion and Topology in a 2D TI 1085.3 Thin Bi and Sb Films 1125.3.1 Bilayers 1125.3.2 Thicker Layers 1155.3.3 Alloyed Layers 1185.3.4 Supported Layers 1195.4 Compounds 1215.4.1 Binary Compounds of A2B3 Type 1225.4.2 Ternary Compounds: A′A2B4 and A′ 2A2B4 Types 1245.5 Summary 125Acknowledgments 126References 1266 Density Functional Theory Calculations of Topological Insulators 131Hyungjun Lee, David Soriano, and Oleg V. Yazyev6.1 Introduction 1316.2 Methodology 1326.2.1 Foundations of Density Functional Theory 1326.2.2 Practical Aspects of DFT Calculations 1366.2.3 Including Spin–Orbit Interactions 1396.2.4 Calculating Z2 Topological Invariants 1436.3 Bismuth Chalcogenide Topological Insulators: A Case Study 1446.3.1 Bulk Band Structures of Bi2Se3 and Bi2Te3 1446.3.2 Topologically Protected States at the (111) Surface of Bismuth Chalcogenides 1486.3.3 Nonstoichiometric and Functionalized Terminations of the Bi2Se3 (111) Surface 1516.3.4 High-Index Surfaces of Bismuth Chalcogenides 1556.4 Conclusions and Outlook 156References 1577 Many-Body Effects in the Electronic Structure of Topological Insulators 161Irene Aguilera, Ilya A. Nechaev, Christoph Friedrich, Stefan Blügel, and Evgueni V. Chulkov7.1 Introduction 1617.2 Theory 1637.3 Computational Details 1667.4 Calculations 1677.4.1 Beyond the Perturbative One-Shot GW Approach 1677.4.2 Analysis of the Band Inversion 1697.4.3 Treatment of Spin–Orbit Coupling 1707.4.4 Bulk Projected Band Structures 1747.4.4.1 Bi2Se3 1757.4.4.2 Bi2Te3 1797.4.4.3 Sb2Te3 1827.5 Summary 184Acknowledgments 187References 1878 Surface Electronic Structure of Topological Insulators 191Philip Hofmann8.1 Introduction 1918.2 Bulk Electronic Structure of Topological Insulators and Topological Crystalline Insulators 1928.3 Bulk and Surface State Topology in TIs and TCIs 1948.4 Surface Electronic Structure in Selected Cases 1988.4.1 Bi Chalcogenite-Based Topological Insulators 1988.4.2 The Group V Semimetals and Their Alloys 2008.4.3 Other Topological Insulators 2038.4.4 Topological Crystalline Insulators 2038.5 Stability of the Topological Surface States 2078.5.1 Stability with Respect to Scattering 2078.5.2 Stability of the Surface States’ Existence 208Acknowledgements 211References 2119 Probing Topological Insulator Surface States by Scanning Tunneling Microscope 217Hwansoo Suh9.1 Introduction 2179.2 Sample Preparation Methods 2199.3 STM and STS on Topological Insulator 2209.3.1 Topography and Defects 2219.3.2 STS and Band Structure of Topological Insulators 2239.3.3 Landau Quantization of Topological Surface States 2259.4 Conductance Map Analysis of Topological Insulator 2299.4.1 Magnetically Doped Topological Insulator 2339.4.2 Superconductor, Topological Insulator, and Majorana Zero Mode 2359.5 Conclusions 236References 23710 Growth and Characterization of Topological Insulators 245Johnpierre Paglione and Nicholas P. Butch10.1 History of Bismuth-Based Material Synthesis 24510.2 Synthesis and Characterization of Crystals and Films 24610.3 Native Defects and Achieving Bulk Insulation 25210.4 New Material Candidates and Future Directions 256References 260Part III: Electronic Characterization and Transport Phenomena 26511 Topological Insulator Nanostructures 267Seung Sae Hong and Yi Cui11.1 Introduction 26711.2 Topological Insulators: Experimental Progress and Challenges 26811.3 Opportunities Enabled by Topological Insulator Nanostructures 27011.4 Synthesis of Topological Insulator Nanostructures 27111.4.1 Vapor-Phase Growth 27111.4.2 Solution-Phase Growth 27311.4.3 Exfoliation 27311.4.4 Heterostructures 27411.4.5 Doping and Alloying 27511.5 Fermi Level Modulation and Bulk Carrier Control 27611.6 Electronic Transport in Topological Insulator Nanostructures 27911.6.1 Weak Antilocalization and Magnetic Topological Insulators 28011.6.2 Shubnikov–de Haas Oscillations 28011.6.3 Insulating Behavior at Ultrathin Limit 28311.6.4 Aharonov–Bohm Effect and 1D Topological States 28311.6.5 Superconducting Proximity Effect in TI Nanodevices 28611.7 Applications and Future Perspective 28611.8 Conclusion 288References 28912 Topological Insulator Thin Films and Heterostructures: Epitaxial Growth, Transport, and Magnetism 295Anthony Richardella, Abhinav Kandala, and Nitin Samarth12.1 Introduction 29512.2 MBE Growth of Topological Insulators 29712.2.1 HgTe 29912.2.2 Bi and Sb Chalcogenides 30012.2.2.1 Bi2Se3 30312.2.2.2 Bi2Te3 30312.2.2.3 Sb2Te3 30412.2.2.4 (Bi1−xSbx)2Te3 30512.2.2.5 Film Growth, Quality, and Stability 30512.3 Transport Studies of TIThin Films 30612.3.1 Shubnikov–de Haas Oscillations 30812.3.2 Quantum Corrections to Diffusive Transport in 3D TI Films 30912.3.3 Mesoscopic Transport in 3D TI Films 31012.3.4 Hybridization Gaps in Ultrathin 3D TI Films 31112.4 Topological Insulators Interfaced with Magnetism 31312.4.1 Bulk Ferromagnetism 31312.4.2 Ferromagnetic Insulator/Topological Insulator Heterostructures 31512.5 Conclusions and Future Outlook 321Acknowledgments 321References 32113 Weak Antilocalization Effect, Quantum Oscillation, and Superconducting Proximity Effect in 3D Topological Insulators 331 Hongtao He and Jiannong Wang13.1 Introduction 33113.2 Weak Antilocalization in TIs 33113.3 Quantum Oscillations in TIs 34013.4 Superconducting Proximity Effect in TIs 34413.5 Perspective 353References 35314 Quantum Anomalous Hall Effect 357Ke He, YayuWang, and Qikun Xue14.1 Introduction to the Quantum Anomalous Hall Effect 35714.1.1 The Hall Effect and Quantum Hall Effect 35714.1.2 The Anomalous Hall Effect and Quantum Anomalous Hall Effect 35914.2 Topological insulators and QAHE 36014.3 Experimental Procedures for Realizing QAHE 36214.3.1 Strategies for Experimental Observation of QAHE 36214.3.2 Growth of Ultrathin TI Films by Molecular Beam Epitaxy 36414.3.3 Band structure Engineering in (Bi1−xSbx)2Te3 ternary alloys 36614.3.4 Ferromagnetism in Magnetically Doped Topological Insulators 36714.3.5 Electrical Gate Tuning of the AHE 37014.4 Experimental Observation of QAHE 37114.5 Conclusion and Outlook 374References 37515 Interaction Effects on Transport in Majorana Nanowires 377Reinhold Egger, Alex Zazunov, and Alfredo Levy Yeyati15.1 Introduction 37715.2 Transport through Majorana Nanowires: General Considerations 38015.2.1 Model 38015.2.2 Majorana–Meir–Wingreen Formula 38115.2.3 Conductance for the Noninteracting M = 2 Case 38215.3 Majorana Single-Charge Transistor 38315.3.1 Charging Energy Contribution 38315.3.2 Theoretical Approaches 38415.3.3 Master Equation Approach 38615.3.4 Coulomb Oscillations: Linear Conductance 38815.3.5 From Resonant Andreev Reflection to Teleportation 38915.3.6 Finite Bias Sidepeaks 38915.3.7 Josephson Coupling to a Superconducting Lead 39115.4 Topological Kondo Effect 39215.4.1 Low-EnergyTheory 39315.4.2 Majorana Spin 39415.4.3 Renormalization Group Analysis 39415.4.4 Topological Kondo Fixed Point 39515.4.5 Conductance Tensor 39615.5 Conclusions and Outlook 397Acknowledgments 397References 398Index 401