Advanced Topological Insulators

This book is the first pedagogical synthesis of the field of topological insulators and superconductors, one of the most exciting areas of research in condensed matter physics. Presenting the latest developments, while providing all the calculations necessary for a self-contained and complete description of the discipline, it is ideal for researchers and graduate students preparing to work in this area, and it will be an essential reference both within and outside the classroom. The book begins with the fundamental description on the topological phases of matter such as one, two- and three-dimensional topological insulators, and methods and tools for topological material's investigations, topological insulators for advanced optoelectronic devices, topological superconductors, saturable absorber and in plasmonic devices. Advanced Topological Insulators provides researchers and graduate students with the physical understanding and mathematical tools needed to embark on research in this rapidly evolving field.

Autorentext

Huixia Luo received her PhD in physical materials science from Leibniz University, Hanover, Germany in 2012. After a postdoc period at Princeton University, she joined the School of Materials Science and Engineering at Sun Yat-Sen University, Guangzhou, China in 2016. She has published more than 30 peer-reviewed papers in SCI journals. Professor Luo is engaged in searching for the novel functional inorganic materials (oxygen transport membrane materials) and the condensed physical materials (such as new superconductor, magnetic material, topological insulators, Dirac and Weyl semimetals, etc).

Klappentext
Advanced Topological Insulators provides researchers and graduate students with the physical understanding and mathematical tools needed to embark on research in this rapidly evolving field. Topological insulators is one of the most exciting areas of research in condensed matter physics. Topological insulators are materials with nontrivial symmetry-protected topological order that behaves as insulators in their interior but whose surface contains conducting states, meaning that electrons can only move along the surface of the material. During the past decade, myriad reliable theoretical and experimental data have been accumulated on topological insulators. The time is now right to gather together this information into a handbook to make it readily available for researchers and students preparing to work in this area of condensed matter physics, quantum information and materials science. Presenting the latest developments, this book covers most introductory experiments and applications in topological insulators and provides a foundation for understanding the field. Some of the topics covered in this groundbreaking book are:

• Shows how to use topological insulator materials for advanced optoelectronic devices.
• Explains what topological insulator thin films and artificial topological superconductors are.
• Discusses dimensional crossover of topological properties in thin films of topological insulators (TI) and Weyl semimetals, electronic properties on the surface of TI nanoparticles and TI nanowires as a constrained electronic system. The effects of disorder are also highlighted.
• Demonstrates that a purely local interaction can cause topological transitions by renormalizing kinetic energy terms alone, without phase transitions associated with order parameters. Disorder is also a means of changing the topology of Chern insulators as it localizes every state except for those carrying the topological invariant.
• Presents two Q-switched Erbium-doped fiber lasers utilizing topology insulators as a saturable absorber.
• Introduces several statistical aspects related to the critical phenomena of topological phase transitions. Audience The book is written for researchers from diverse backgrounds across chemistry, physics, materials science and surface engineering.

Inhalt
Preface xv

**1 Characterization of Phase Transition Points for Topological Gapped Systems 1
**Linhu Li and Shu Chen

1.1 Introduction 2

1.2 General Definition of Topological Invariant of Phase Transition Points 3

1.2.1 A 1D Example: the Su-Schrieffer-Heeger Model 3

1.2.2 General Characterization of Topological Phase Transition 7

1.3 Phase Transition Points of One-Dimensional Systems 9

1.3.1 Z -Type Topological Gapped Systems 10

1.3.1.1 Class BDI: An Extended Version of the SSH Model 14

1.3.1.2 Class AIII: The Creutz Model 16

1.3.2 Z2 Topological Gapped Systems 17

1.3.2.1 Class D: An Extended Version of the Kiteav Model 21

1.3.2.2 Class DIII: An Example Model 23

1.3.3 A Non-Topological Example of 1D Insulating Systems 26

1.4 Phase Transition Points of Two-Dimensional Systems 26

1.4.1 The Haldane Model 28

1.4.2 An Extended Version of the Qi-Wu-Zhang Model 33

1.5 An Example of 3D Topological Insulators 36

References 41

**2 Topological Insulator Materials for Advanced Optoelectronic Devices 45
**Zengji Yue, Xiaolin Wang and Min Gu

2.1 Excellent Electronic Properties 46

2.1.1 Quantum Spin Hall Effect 46

2.1.2 Topological Magnetoelectric Effects 47

2.1.3 Magnetic Monopole Image 47

2.1.4 Topological Superconductors 48

2.1.5 Quantum Anomalous Hall Effects 49

2.1.6 Giant Magnetoresistance Effects 49

2.1.7 Shubnikov-De Haas Effects 50

2.2 Excellent Optical Properties 50

2.2.1 Ultrahigh Bulk Refractive Index 50

2.2.2 Near-Infrared Transparency 52

2.2.3 Faraday Rotation and Unusual Electromagnetic Scattering 53

2.2.4 Ultra-Broadband Plasmon Excitations 54

2.2.5 Polarized Light Induced Photocurrent 56

2.2.6 Broadband Optical Nonlinear Response 56

2.3 Advanced Optoelectronic Devices 57

2.3.1 Plasmonic Solar Cells 57

2.3.2 Nanometric Holograms 57

2.3.3 Ultrathin Flat Lens 59

2.3.4 Near-Infrared Photodetector 59

2.3.5 Saturable Absorber 60

2.4 Conclusion and Outlook 62

References 63

**3 Topological Insulator Thin Films and Artificial Topological Superconductors 71
**Hao Zheng, Yaoyi Li and Jin-Feng Jia

3.1 Theoretical Background 72

3.1.1 Berry Phase and Topology in Condensed Matter Physics 72

3.1.2 Topological Insulator 73

3.1.3 Topological Superconductor and Majorana Fermionic Mode 75

3.2 Introduction of the Experimental Methods 78

3.2.1 Molecular Beam Epitaxy 78

3.2.2 Scanning Tunneling Microscopy 80

3.3 Topological Insulator Thin Films 82

3.4 Artificial Two-Dimensional Topological Superconductor 88

3.5 Discovery of Majorana Zero Mode 94

3.5.1 Identification of a Majorana Zero Mode Base on Its Lateral Extension 95

3.5.2 Identification of a Majorana Zero Mode Based on Its Spin 99

3.6 Summary 102

References 103

**4 Topological Matter in the Absence of Translational Invariance 109
**Koji Kobayashi, Tomi Ohtsuki and Ken-Ichiro Imura

4.1 Introduction 109

4.2 Topological Insulator and Real-Space Topology 114

4.2.1 Cylindrical Topological Insulator 115

4.2.2 Spherical Topological Insulator 115

4.2.3 Protection of the Surface States: Berry Phase Point of View 118

4.3 Layer Construction: Dimensional Crossovers of Topological Properties 119

4.3.1 Time-Reversal Invariant (Z2) Type Lattice Model: STI/WTI 119

4.3.2 Time-Reversal Broken (Z) Type Lattice Model: WSM/CI 120

4.3.3 Similarity Between Two Phase Diagrams 121

4.3.4 Stacked QSH/QAH Model 122

4.3.5 Dimensional Crossover 124

4.3.6 Topological Insulator Terraces and 1D Perfectly Conducting Helical Channel 125

4.4 Effects of Disorder 126 ...