Table of Contents
Preface to the second edition vii
Preface to the first edition ix
1 Introduction 1
2 Low-dimensional semiconductor structures 6
2.1 Overview 6
2.2 Bulk semiconductors 7
2.2.1 Band structure 7
2.2.2 Effective mass 9
2.2.3 Density of states 11
2.2.4 Intrinsic semiconductors 13
2.3 Doped semiconductors 15
2.4 Transport 17
2.4.1 Classical diffusive transport 17
2.4.2 Einstein relation 18
2.4.3 Mobility 19
2.4.4 Characteristic length scales 20
2.5 Layer systems 23
2.5.1 Semiconductor heterostructures 23
2.5.2 Two-dimensional electron gases 25
2.6 Quantum wires and nanowires 27
2.6.1 Electron beam lithography 27
2.6.2 Semiconductor nanowires 29
2.6.3 Split-gate quantum point contacts 30
2.7 Zero-dimensional structures: quantum dots 34
2.7.1 Transport at small source-drain bias voltages 35
2.7.2 Transport as a function of source-drain bias voltage 38
2.8 Transport in a quantizing magnetic field 39
2.8.1 Landau quantization 40
2.8.2 Shubnikov-de Haas oscillations 43
2.8.3 Magnetic edge states 45
2.9 Summary 50
3 Magnetism in solids 52
3.1 Definitions and basics 52
3.1.1 Definitions 52
3.1.2 Magnetization 52
3.1.3 Magnetic moments of electrons in atomic orbitals 53
3.1.4 The electron spin 54
3.2 Classification 57
3.3 Paramagnetism 57
3.3.1 Paramagnetism of localized moments 57
3.3.2 Hund's rule 61
3.3.3 Pauli paramagnetism 62
3.4 Collective magnetism 63
3.4.1 Exchange interaction 63
3.4.2 Stoner model 67
3.5 Summary 71
4 Diluted magnetic semiconductors 73
4.1 Overview 73
4.2 II-VI diluted magnetic semiconductors 74
4.3 III-V diluted magnetic semiconductors 78
4.4 Transport properties of III-V diluted magnetic semiconductors 87
4.5 Summary 92
5 Magnetic electrodes 94
5.1 Overview 94
5.2 Formation of magnetic domains 95
5.2.1 Magnetic stray field 95
5.2.2 Crystal anisotropy 96
5.2.3 Form anisotropy contribution 97
5.2.4 Exchange energy contribution 98
5.3 Domain walls 98
5.4 Ferromagnetic electrodes 101
5.5 Local Hall effect measurements 105
5.6 Micromagnetic simulations 107
5.7 Domain wall motion 110
5.8 Summary 113
6 Spin injection 114
6.1 Overview 114
6.2 Resistor model 115
6.3 Local description of spin injection 119
6.4 Optical detection of spin-polarized carriers 126
6.5 Experiments on optical detection of spin polarization 130
6.6 Injection through a barrier 133
6.6.1 Free electron approximation 134
6.6.2 Diffusive transport regime 139
6.7 Experiments on spin injectors with interface barriers 142
6.8 Nonlocal spin injection 144
6.9 Optical spin generation 148
6.9.1 Optical absorption 148
6.9.2 Spin coherence and spin dephasing 149
6.9.3 Optical detection of magnetization 151
6.9.4 Pump-probe experiments 153
6.9.5 Resonant spin amplification 158
6.10 Summary 161
7 Spin transistor 162
7.1 Overview 162
7.2 InAs-based two-dimensional electron gases 162
7.3 The Rashba effect 164
7.4 Strength of the Rashba spin-orbit coupling 169
7.4.1 The k p method 169
7.4.2 Envelope function approach 171
7.5 Magnetoresistance measurements 175
7.5.1 Beating patterns due to the Rashba effect 176
7.5.2 Gate-control of the Rashba effect 178
7.6 Bulk inversion asymmetry 181
7.6.1 Time-reversal symmetry 181
7.6.2 Spatial inversion symmetry 182
7.6.3 Dresselhaus term 184
7.7 Rashba effect in quasi one-dimensional structures 187
7.7.1 Rashba effect in planar quasi one-dimensional structures 187
7.7.2 Helical energy gap 191
7.7.3 Rashba effect in tubular structures 194
7.8 Summary 199
8 Spin interference 202
8.1 Overview 202
8.2 Electron interference effects 202
8.2.1 Electron interference effects 203
8.2.2 Aharonov-Bohm effect 204
8.2.3 Altshuler-Aronov-Spivak oscillations 208
8.2.4 Weak localization 211
8.3 Spin interference effects 216
8.3.1 Weak antilocalization 216
8.3.2 Spin relaxation mechanisms 219
8.3.3 Weak antilocalization in two-dimensional electron gases 222
8.3.4 Weak antilocalization in wire structures 225
8.4 Spin interference effects in ring structures 231
8.4.1 Berry phase 231
8.4.2 Spin-interference in a ring with Rashba spin-orbit coupling 236
8.5 Summary 241
9 Spin Hall effect 244
9.1 Introductory remarks 244
9.2 Basic phenomena 245
9.3 Boltzmann equation and skew scattering 246
9.3.1 Boltzmann equation 246
9.3.2 Intrinsic spin Hall effect 249
9.3.3 Extrinsic spin Hall effect: skew scattering contribution 250
9.3.4 Skew scattering in a two-dimensional system 252
9.4 Experiments on spin Hall effect in semiconductor layers 254
9.5 Detection of the spin Hall effect by electroluminescence 257
9.6 Summary 260
10 Quantum spin Hall effect 262
10.1 Introductory remarks 262
10.2 Inverted quantum well in HgTe/CdTe 263
10.3 Band structure 267
10.4 Helical edge states 269
10.5 Conductance in a normal and inverted HgTe/CdTe quantum well 273
10.6 Edge channel transport 275
10.7 Spin-polarized transport 277
10.8 Summary 279
11 Topological insulators 282
11.1 Introductory remarks 282
11.2 Material system 283
11.3 Bulk band structure 283
11.3.1 Level evolution 285
11.3.2 Effective Hamiltonian 286
11.3.3 Ab-initio band structure calculations 287
11.4 Surface states 289
11.4.1 Surface states deduced from the effective Hamiltonian 289
11.4.2 Surface states obtained from ab initio calculations 290
11.4.3 Topological protection of surface states 291
11.5 Angle-resolved photo-emission spectroscopy 292
11.6 Transport experiments 295
11.6.1 Topologically protected surface states in nanowires 296
11.6.2 Flux-periodic oscillations in nanowire structures 300
11.6.3 Landau quantization in two-dimensional topological surface states 302
11.6.4 Shubnikov-de Haas oscillations in Dirac systems 304
11.7 Summary 306
12 Quantum computation with electron spins 309
12.1 Introductory remarks 309
12.2 Basic elements of a quantum computer 309
12.2.1 Quantum bit 309
12.2.2 Entangled states 311
12.3 Basic quantum gates 312
12.3.1 Single-qubit gate 312
12.3.2 Controlled-NOT gate 314
12.3.3 Realization of a quantum computer 315
12.4 Quantum algorithms 316
12.4.1 Deutsch-Josza quantum algorithm 316
12.5 Quantum dot spin qubits 320
12.5.1 General concept 320
12.5.2 Experimental realization of a quantum dot qubit 321
12.5.3 Initialization 323
12.5.4 Read-out 324
12.5.5 Electron spin resonance 326
12.5.6 Spin-control in a double dot system 329
12.5.7 Singlet-triplet qubit 335
12.5.8 Control of the S-T0 qubit 337
12.6 Summary 340
13 Majorana fermions 341
13.1 Overview 341
13.2 Majorana's version of the Dirac equation 341
13.3 Majorana modes in solid-state systems 343
13.3.1 Many-particle states 344
13.3.2 Bogoliubov-de Gennes equation 346
13.4 The Kitaev chain 349
13.5 Majorana zero modes in semiconductor nanowires 351
13.5.1 p-wave pairing in a proximitized semiconductor nanowire 351
13.5.2 Majorana zero modes 354
13.5.3 Experimental realization in nanowires 356
13.6 Topological quantum computing 358
13.6.1 Fermion parity and degenerate ground state 358
13.6.2 Braiding 359
13.6.3 Braiding with two pairs of Majoranas 362
13.6.4 Non-Abelian anyons 363
13.6.5 Majorana qubits 365
13.7 Summary 366
Solutions 369
Bibliography 395
Index 407
