Magnetism in Topological Insulators (eBook)

Preface 6
Contents 7
Chapter 1: Energy Bands in Topological Insulators 10
1.1 Spin-Orbit Interaction in Bismuth Chalcogenides 10
1.2 Electron Spectrum and Band Inversion 12
1.3 Surface States 14
1.4 Thin Film 16
1.4.1 Wave Functions 16
1.4.2 Effective Surface Hamiltonian 20
1.5 Spin-Momentum Locked Fermions 23
1.6 Top-Bottom Representation 26
1.7 Lateral Transport of Dirac Fermions. Inverse Spin-Galvanic Effect 29
References 32
Chapter 2: Hall Effects and Berry Phase 34
2.1 Hall Effects 35
2.2 Berry Phase 38
2.3 Spin in a Magnetic Field: Magnetic Monopole 41
2.4 Crystalline Solids: Berry and Zak Phases 45
2.5 Hall Conductivity and Berry Phase 46
2.6 Quantized Hall Effects 49
2.6.1 Integer Quantum Hall Effect 50
2.6.2 Quantum Anomalous Hall Effect 52
2.6.3 Quantum Spin Hall Effect: Z2 Topological Index 53
References 60
Chapter 3: Magnetic Field and Ferromagnetic Proximity Effects 63
3.1 Magnetic Energy Gap 64
3.1.1 Independent Surfaces 64
3.2 Proximity-Induced Topological Phase Transition 65
3.3 Quantum Anomalous Hall Effect 68
3.4 Berry Curvature and Kubo Hall Conductivity 70
3.4.1 Generic Two-Band Model and Skyrmion Topology 72
3.5 Quantum Phase Transition Driven by a Parallel Magnetic Field 73
3.6 Thin Film in a Perpendicular Magnetic Field. Parity Anomaly 75
3.7 Anisotropic Ferromagnetic Proximity 78
3.8 Spiral Proximity Field 80
3.9 Lateral Heterostructures and Domain Walls 81
3.10 Proximity Coupling and Torque 83
References 84
Chapter 4: Topological Magnetoelectric Effect 86
4.1 Axion Electrodynamics 88
4.2 Axion Field and Topological Polarization 90
4.3 Axion Field and Quantized Magnetization 92
4.4 TME Experimental Settings 93
References 94
Chapter 5: Rashba Effect in Topological Quantum Wells 95
5.1 Rashba Interaction in Normal Semiconductors 95
5.2 Microscopic Theory of Rashba Spin-Splitting 101
5.2.1 Zinc-Blende III-V Quantum Wells 102
5.2.2 Rashba Coefficient in III-Nitrides 102
5.3 Spin-Splitting in Topological Quantum Wells 105
5.3.1 Hamiltonian 106
5.3.2 Zero Field Spin-Splitting in an Inverted Band Quantum Well 108
References 110
Chapter 6: Spin-Electron (s-d) Interaction in TI Thin Films 113
6.1 Contact s-d Interaction in Metals 114
6.2 Contact s-d Interaction in TI Films 115
6.3 Real Fermions Interacting with Magnetic Impurity 119
References 121
Chapter 7: Indirect Exchange Interaction Mediated by Dirac Fermions 122
7.1 Generic Indirect Exchange via Conduction Electrons 122
7.2 Three-Dimensional Metal: RKKY Model 125
7.3 Exchange Interaction in Semiconductors 127
7.4 Exchange Interaction via Surface Fermions 128
7.5 RKKY Range Function in Inversion Asymmetric TI Films 133
7.5.1 Voltage-Controlled Magnetic Ordering 134
7.6 Oscillating Bloembergen-Rowland Interaction Mediated by Gapped Fermions 135
Appendix 1. Spin Texture 141
Appendix 2. Calculation of the RKKY in a Vertically Biased Topological Insulator 142
Appendix 3. Calculation of Bloembergen-Rowland Coupling 144
References 147
Chapter 8: Device Applications 148
8.1 Contacts and Gating 148
8.2 Heterojunctions 149
8.3 Photodetectors 153
8.4 Field-Effect Transistors 154
8.5 Magnetic Devices 155
8.6 Optoelectronics 157
References 157
Index 160