8. Simple Models for the Chern Insulator

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