| Abstract | 第5-7页 |
| 摘要 | 第8-22页 |
| Chapter 1 Introduction | 第22-50页 |
| 1.1 Topological Band Theory | 第25-31页 |
| 1.1.1 Berry phase and Chern number | 第26-27页 |
| 1.1.2 Z_2 topological invariant | 第27-31页 |
| 1.2 Disorder-Induced Effects in Topological Insulator | 第31-36页 |
| 1.2.1 Magnetic impurities in topological insulators | 第31-34页 |
| 1.2.2 Topological Anderson insulator | 第34-36页 |
| 1.3 Topological Superconductor and Majorana Fermion | 第36-48页 |
| 1.3.1 Majorana fermions in spinless superconductors and non-Abelian statistics | 第37-42页 |
| 1.3.2 Proximity-induced topological superconductor | 第42-45页 |
| 1.3.3 Time-reversal invariant topological superconductor | 第45-48页 |
| 1.4 Classifications of topological insulators and superconductors | 第48-50页 |
| Chapter 2 The Effects of Magnetic Impurities at the Interface ofTI/SC Heterostructure | 第50-70页 |
| 2.1 Introduction | 第50-51页 |
| 2.2 Theoretical Model | 第51-52页 |
| 2.3 Magnetic Impurity-induced Phenomena | 第52-58页 |
| 2.3.1 Local density of states around a single magnetic impurity | 第52-55页 |
| 2.3.2 Yu-Shiba states | 第55-56页 |
| 2.3.3 The robustness of superconductivity | 第56-58页 |
| 2.4 Collective Behaviors of Multiple Magnetic Impurities | 第58-63页 |
| 2.4.1 RKKY interaction mediated by BCS quasiparticles | 第58-62页 |
| 2.4.2 Ferromagnetism of randomly distributed magnetic impurities | 第62-63页 |
| 2.5 Chiral Topological Superconductivity at TI/SC Interface | 第63-67页 |
| 2.5.1 Temperature dependence of the effective exchange field | 第63-64页 |
| 2.5.2 Majorana edge states | 第64-66页 |
| 2.5.3 Topological phase transition | 第66-67页 |
| 2.6 Discussion and Conclusion | 第67-70页 |
| Chapter 3 Disorder-Induced Topological Phase Transitions in 2DSOC Superconductors | 第70-86页 |
| 3.1 Introduction | 第70-72页 |
| 3.2 Theoretical Modeling | 第72-76页 |
| 3.2.1 The clean-limit properties | 第73-74页 |
| 3.2.2 General analytical formalism of the disorder effect | 第74-76页 |
| 3.3 Disorder-Induced Topological Phase Transition | 第76-79页 |
| 3.3.1 Magnetic disorder-induced topological phase transition | 第77-78页 |
| 3.3.2 Anderson disorder-induced topological phase transition | 第78-79页 |
| 3.4 Numerical Study of the Disorder-Induced Topological Phase Transition | 第79-83页 |
| 3.4.1 Numerical modeling | 第79-81页 |
| 3.4.2 Simulations of magnetic disorder | 第81-83页 |
| 3.4.3 Simulations of magnetic disorder | 第83页 |
| 3.5 Discussion and Conclusion | 第83-86页 |
| Chapter 4 Potential Topological Superconductivity in Monolayer Pb_3BiGrown on Ge(111) | 第86-102页 |
| 4.1 Introduction | 第86-87页 |
| 4.2 Theoretically Methodology | 第87-90页 |
| 4.2.1 Wilsonian Renormalization Group | 第87-89页 |
| 4.2.2 Functional renormalization group | 第89-90页 |
| 4.3 Band Structures of Pb_3Bi on Ge(111)Substrate | 第90-93页 |
| 4.4 Renormalization Group Analysis | 第93-99页 |
| 4.4.1 General formula of RG flow equation for spinless fermions | 第93-94页 |
| 4.4.2 The effective model for Pb_3Bi and multichannel susceptibilities | 第94-96页 |
| 4.4.3 RG flow equations and superconductivity instability | 第96-98页 |
| 4.4.4 Superconducting pairing symmetry | 第98-99页 |
| 4.5 Discussion and Conclusion | 第99-102页 |
| Chapter 5 Conclusion and outlook | 第102-104页 |
| Bibliography | 第104-120页 |
| 致谢 | 第120-122页 |
| Publications and Talks | 第122-123页 |
