Table of Contents
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
4.4.1 Model for Disordered STI/WTI 127
4.4.2 Phase Diagram of Disordered Topological Insulators 127
4.4.2.1 Phase Diagram: Isotropic Case 127
4.4.2.2 Phase Diagram: Anisotropic Case 130
4.5 Critical Properties of Topological Quantum Phase Transitions 130
4.5.1 Quantum Phase Transition in Random Systems 130
4.5.2 Critical Properties of Topological Insulator-Metal Transition 132
4.5.3 Topological Semimetal-Metal Transition: Evolution of Density of States 133
4.5.4 Effect of Disorder on Weyl/Dirac Semimetals 134
4.5.5 Density of State Scaling 134
4.5.6 Numerical Verification of Density of State Scaling 136
4.5.7 Relationships Derived from the Density of States Scaling 136
4.5.7.1 Conductivity 136
4.5.7.2 Specific Heat and Susceptibility 139
4.5.8 Future Problem for Semimetal-Metal Transition 140
4.6 Phase Diagrams Obtained from Machine Learning 142
4.6.1 Phase Diagram for Disordered Topological Insulators 144
4.6.2 Phase Diagram for Disordered Weyl Semimetal 146
4.6.3 Comparison of CNN Method and the Conventional Method 148
4.7 Summary and Concluding Remarks 149
References 149
5 Changing the Topology of Electronic Systems Through Interactions or Disorder 159
M.A.N. Araújo, E.V. Castro and P.D. Sacramento
5.1 Introduction 160
5.2 Change of an Insulator’s Topological Properties by a Hubbard Interaction 163
5.2.1 A Model for Spinless Fermions with Z Topological Number 163
5.2.2 A Spinful Model with Z Topological Number 169
5.2.3 Model with Z2 Topological Number 170
5.3 Effects of Disorder on Chern Insulators 172
5.3.1 Model and Methods 174
5.3.2 Disorder Equally Distributed in Both Sublattices 176
5.3.3 Disorder Selectively Distributed in Only One Sublattice and Anomalous Hall Metal 179
5.3.4 Wrapping Up the Effect of Disorder 182
5.4 Topological Superconductors 183
5.4.1 Magnetic Adatom Chains on a S-Wave Superconductor: Topological Modes and Quantum Phase Transitions 183
5.4.1.1 Model: S-Wave Superconductor with Magnetic Impurities 184
5.4.1.2 Energy Levels and Topological Invariant 185
5.4.1.3 Wave Functions: Cross-Over from YSR States to MZEM 186
5.4.2 Triplet Two-Dimensional Superconductor with Magnetic Chains 187
5.4.2.1 Pure Triplet Superconductor 187
5.4.2.2 Addition of Magnetic Impurities 188
5.4.3 Chern Number Analysis When Translational Invariance Is Broken 189
5.4.4 Magnetic Islands on a P-Wave Superconductor 190
5.5 Conclusions 191
5.6 Acknowledgements 195
References 196
6 Q-Switching Pulses Generation Using Topology Insulators as Saturable Absorber 207
Sulaiman Wadi Harun, Nurfarhanah Zulkipli, Ahmad Razif Muhammad and Anas Abdul Latiff
6.1 Introduction 208
6.2 Fiber Laser Technology 209
6.2.1 Working Principle of Erbium-Doped Fiber Laser (EDFL) 211
6.2.2 Q-Switching 212
6.3 Topology Insulator (TI) 215
6.4 Pulsed Laser Parameters 216
6.5 Bi2 Se3 Material as Saturable Absorber in Passively Q-Switched Fiber Laser 218
6.5.1 Preparation and Optical Characterization of Bi2 Se3 Based SA 219
6.5.2 Configuration of the Q-Switched Laser with Bi2 Se3 Based SA 221
6.5.3 Q-Switching Performances 222
6.6 Q-Switched EDFL with Bi2 Te3 Material as Saturable Absorber 226
6.6.1 Preparation and Optical Characterization of the SA 226
6.6.2 Experimental Setup 228
6.6.3 Q-Switched Laser Performances 229
6.7 Conclusion 233
References 234
7 Topological Phase Transitions: Criticality, Universality, and Renormalization Group Approach 239
Wei Chen and Manfred Sigrist
7.1 Generic Features Near Topological Phase Transitions 240
7.1.1 Topological Phase Transition in Lattice Models 240
7.1.2 Gap-Closing and Reopening 242
7.1.3 Divergence of the Curvature Function 243
7.1.4 Renormalization Group Approach 245
7.2 Topological Invariant in 1D Calculated from Berry Connection 249
7.2.1 Berry Connection and Theory of Charge Polarization 249
7.2.2 Su-Schrieffer-Heeger Model 251
7.2.3 Kitaev’s P-Wave Superconducting Chain 256
7.3 Topological Invariant in 2D Calculated from Berry Curvature 261
7.3.1 Berry Curvature and Theory of Orbital Magnetization 261
7.4 Universality Class of Higher Order Dirac Model 262
7.5 Topological Invariant in D-Dimension Calculated from Pfaffian 268
7.5.1 Pfaffian of the m-Matrix 268
7.5.2 Bernevig-Hughes-Zhang Model 272
7.6 Summary 277
References 277
8 Behaviour of Dielectric Materials Under Electron Irradiation in a SEM 281
Slim Fakhfakh, Khaled Raouadi and Omar Jbara
8.1 Introduction 282
8.2 Fundamental Aspects of Electron Irradiation of Solids 283
8.2.1 Volume of Interaction and Penetration Depth 283
8.2.2 Emissions and Spatial Resolutions Resulting from Electron Irradiation 284
8.3 Electron Emission of Solid Materials 285
8.3.1 Spectrum or Energy Distribution of the Electron Emission 285
8.3.2 Backscattered Electron Emission 286
8.3.3 Secondary Electron Emission 289
8.3.3.1 Mechanism of Secondary Electron Emission 289
8.3.3.2 Variation of the Electron Emission Rate as a Function of Primary Energy 292
8.3.4 Auger Electron Emission 293
8.3.5 Total Emission Yield 294
8.4 Electron Emission of Solid Materials 295
8.5 Trapping and Charge Transport in Insulators 296
8.5.1 Generalities 296
8.5.2 Defects and Impurities 297
8.5.3 Amorphous or Very Disordered Insulators: Disorder and Localized States in the Conduction Band 298
8.5.4 Injection, Localization and Transport of Charges 299
8.5.5 Space Charge 299
8.6 Application: Dynamic Trapping Properties of Dielectric Materials Under Electron Irradiation 300
8.6.1 Measurement of the Trapped Charge from Displacement Current and Conservation Law of the Current 301
8.6.1.1 Measurement of the Trapped Charge from the Displacement Current 301
8.6.1.2 Conservation Law of the Current and the Induced Charge 303
8.6.2 Device and Experimental Procedure 305
8.6.3 Typical Curves of Measured Currents and Influence Factor 307
8.6.4 Trapped Charge 309
8.6.4.1 Characteristic Parameters of the Charging Process 311
8.6.4.2 Characteristic Parameters of Discharging Process 311
8.6.5 Determination of the Total Electron Emission Yield 314
8.6.6 Flashover Phenomena and Determination of the Trapping Cross Section for Electrons 315
8.6.7 Determination of Effective Resistivity and Estimation of the Electric Field Strength Initiating Surface Discharge 319
8.6.8 Effect of Current Density 322
8.7 Conclusion 325
References 326
9 Photonic Crystal Fiber (PCF) is a New Paradigm for Realization of Topological Insulator 331
Gopinath Palai
9.1 Introduction 331
9.1.1 Electrical Topological Insulator 332
9.1.1.1 Hall Effect 332
9.1.2 Photonic Crystal Fiber 341
9.1.2.1 Solid-Core PCFs 343
9.1.2.2 Hollow-Core PCFs 344
9.1.3 Photonic Topological Insulator 345
9.2 Structure of Photonic Crystal Fiber 346
9.3 Result and Discussion 347
9.4 Conclusion 353
References 353
10 Patterned 2D Thin Films Topological Insulators for Potential Plasmonic Applications 361
G. Padmalaya, E. Manikandan, S. Radha, B.S. Sreeja and P. Senthil Kumar
10.1 Introduction 362
10.2 Fundamentals of Plasmons 363
10.2.1 Plasmons at Metals/Insulator Interfaces 363
10.2.1.1 Properties of Surface Plasmons 363
10.2.2 Plasmons-Based on Electromagnetic Fields 364
10.2.3 Plasmons at Planar Interfaces 366
10.2.3.1 Behaviors of Plasmons at Planar Surfaces 366
10.2.4 Plasmons at Surface Imaging 366
10.3 Plasmons at Structured Surfaces 370
10.3.1 Graphene-Based Structure 370
10.3.2 Metal Oxide-Based Structure 371
10.3.3 Dimensional Thin Films-Based Topological Insulators 371
10.3.3.1 Graphene-Based Topological Insulators 372
10.3.3.2 Graphene in Spintronics Applications 372
10.3.3.3 Graphene in Memory-Based Applications 373
10.3.3.4 Graphene-Based Topological Insulator for Thermoelectric Applications 374
10.3.3.5 Graphene in Sensing Applications Based Topological Line Defects 375
10.3.4 Piezotronics-Based Topological Insulators 377
10.3.4.1 Fundamental Physics of Piezotronics and Its Applications 377
10.3.5 Metamaterials-Based Topological Insulators 379
10.3.5.1 Operation Principle 379
10.3.5.2 Mapping of MM with TI 380
10.4 Nanostructured Thin Films and Its Applications 387
10.4.1 Plasmonic Applications 387
10.4.2 Biomedical Applications 387
10.5 Summary 388
References 389
Index 393
