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
10.4 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
Description 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.
About the Author 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).