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10. Z2 Invariants

  • B. Andrei Bernevig
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Topological Insulators and Topological Superconductors
This chapter is in the book Topological Insulators and Topological Superconductors
© 2016 Princeton University Press, Princeton

© 2016 Princeton University Press, Princeton

Chapters in this book

  1. Frontmatter i
  2. Contents v
  3. 1. Introduction 1
  4. 2. Berry Phase 6
  5. 3. Hall Conductance and Chern Numbers 15
  6. 4. Time-Reversal Symmetry 33
  7. 5. Magnetic Field on the Square Lattice 41
  8. 6. Hall Conductance and Edge Modes: The Bulk-Edge Correspondence 60
  9. 7. Graphene 70
  10. 8. Simple Models for the Chern Insulator 91
  11. 9. Time-Reversal-Invariant Topological Insulators 109
  12. 10. Z2 Invariants 123
  13. 11. Crossings in Different Dimensions 147
  14. 12. Time-Reversal Topological Insulators with Inversion Symmetry 158
  15. 13. Quantum Hall Effect and Chern Insulators in Higher Dimensions 164
  16. 14. Dimensional Reduction of 4-D Chern Insulators to 3-D Time-Reversal Insulators 177
  17. 15. Experimental Consequences of the Z2 Topological Invariant 186
  18. 16. Topological Superconductors in One and Two Dimensions 193
  19. 17. Time-Reversal-Invariant Topological Superconductors 214
  20. 18. Superconductivity and Magnetism in Proximity to Topological Insulator Surfaces 226
  21. APPENDIX
  22. 3-D Topological Insulator in a Magnetic Field 237
  23. References 241
  24. Index 245
https://doi.org/10.1515/9781400846733-010

Chapters in this book

  1. Frontmatter i
  2. Contents v
  3. 1. Introduction 1
  4. 2. Berry Phase 6
  5. 3. Hall Conductance and Chern Numbers 15
  6. 4. Time-Reversal Symmetry 33
  7. 5. Magnetic Field on the Square Lattice 41
  8. 6. Hall Conductance and Edge Modes: The Bulk-Edge Correspondence 60
  9. 7. Graphene 70
  10. 8. Simple Models for the Chern Insulator 91
  11. 9. Time-Reversal-Invariant Topological Insulators 109
  12. 10. Z2 Invariants 123
  13. 11. Crossings in Different Dimensions 147
  14. 12. Time-Reversal Topological Insulators with Inversion Symmetry 158
  15. 13. Quantum Hall Effect and Chern Insulators in Higher Dimensions 164
  16. 14. Dimensional Reduction of 4-D Chern Insulators to 3-D Time-Reversal Insulators 177
  17. 15. Experimental Consequences of the Z2 Topological Invariant 186
  18. 16. Topological Superconductors in One and Two Dimensions 193
  19. 17. Time-Reversal-Invariant Topological Superconductors 214
  20. 18. Superconductivity and Magnetism in Proximity to Topological Insulator Surfaces 226
  21. APPENDIX
  22. 3-D Topological Insulator in a Magnetic Field 237
  23. References 241
  24. Index 245
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