Preface ...................................................... XIII
1 Introduction ................................................. 1
1.1 Preliminary remarks ..................................... 1
1.2 Mesoscopic transport .................................... 2
1.2.1 Ballistic Transport .............................. 3
1.2.2 The Quantum Hall Effect and Shubnikov-de Haas
Oscillations ..................................... 5
1.2.3 Size Quantization ................................ 7
1.2.4 Phase Coherence .................................. 8
1.2.5 Single-Electron Tunneling and Quantum Dots ....... 9
1.2.6 Superlattices ................................... 10
1.2.7 Spintronics ..................................... 11
1.2.8 Samples, Experimental Techniques, and
Technological Relevance ......................... 11
1.2.9 Modeling ........................................ 15
1.2.10 What is not in this book ........................ 15
2 An update of solid state physics ............................ 17
2.1 Crystal structures ..................................... 18
2.2 Electronic energy bands ................................ 20
2.3 Occupation of energy bands ............................. 34
2.3.1 The electronic density of states ................ 34
2.3.2 Occupation probability and chemical potential ... 36
2.3.3 Transition between dimensions: quasi-n-
dimensional systems ............................. 37
2.3.4 Intrinsic carrier concentration ................. 39
2.3.5 Bloch waves and localized electrons ............. 40
2.4 Envelope wave functions ................................ 41
2.5 Doping ................................................. 44
2.6 Diffusive transport and the Boltzmann equation ......... 49
2.6.1 The Boltzmann equation .......................... 50
2.6.2 The conductance predicted by the simplified
Boltzmann equation .............................. 53
2.6.3 The magneto-resistivity tensor .................. 54
2.6.4 Diffusion currents .............................. 58
2.7 Scattering mechanisms .................................. 59
2.8 Screening .............................................. 62
3 Surfaces, interfaces, and layered devices ................... 69
3.1 Electronic surface states .............................. 71
3.1.1 Surface States in One Dimension ................. 71
3.1.2 Surfaces of Three-Dimensional Crystals .......... 77
3.1.3 Band Bending and Fermi Level Pinning ............ 79
3.2 Semiconductor-metal interfaces ......................... 80
3.2.1 Band Alignment and Schottky Barriers ............ 81
3.2.1.1 The Schottky model ..................... 83
3.2.1.2 The Schottky diode ..................... 84
3.2.2 Ohmic contacts .................................. 85
3.3 Semiconductor heterointerfaces ......................... 86
3.4 Field effect transistors and quantum wells ............. 88
3.4.1 The Silicon Metal-Oxide-Semiconductor Field
Effect Transistor
3.4.1.1 The MOSFET and digital electronics ..... 92
3.4.2 The Ga[Al]As High Electron Mobility
Transistor ...................................... 95
3.4.3 Other Types of Layered Devices .................. 97
3.4.3.1 The AlSb-InAs-AlSb quantum well ........ 99
3.4.3.2 Hole gas in Si-Si1-xGex-Si quantum
wells ................................. 100
3.4.3.3 Hole gases in in Ga[Al]As quantum
wells ................................. 100
3.4.3.4 Organic FETs .......................... 107
3.4.4 Quantum Confined Carriers in Comparison to
Bulk Carriers .................................. 102
4 Experimental techniques .................................... 107
4.1 Sample preparation .................................... 107
4.1.1 Single Crystal Growth .......................... 108
4.1.2 Growth of Layered Structures ................... 110
4.1.2.1 Metal organic chemical vapor
deposition (MOCVD) .................... 111
4.1.2.2 Molecular beam epitaxy (MBE) .......... 111
4.1.3 Lateral Patterning ............................. 116
4.1.3.1 Defining patterns in resists .......... 117
4.1.3.2 Direct writing methods ................ 120
4.1.3.3 Etching ............................... 127
4.1.4 Metallization .................................. 122
4.1.5 Bonding ........................................ 124
4.2 Elements of cryogenics ................................ 125
4.2.1 Properties of Liquid Helium .................... 126
4.2.1.1 Some properties of pure 4He ........... 126
4.2.1.2 Some properties of pure 3He ........... 129
4.2.1.3 The 3He/4He mixture ................... 130
4.2.2 Helium Cryostats ............................... 132
4.2.2.1 4He cryostats ......................... 132
4.2.2.2 3He cryostats ......................... 133
4.2.2.3 3He/4He dilution refrigerators ........ 134
4.3 Electronic measurements on nanostructures ............. 136
4.3.1 Sample Holders ................................. 136
4.3.2 Application and Detection of Electronic
Signals ........................................ 137
4.3.2.1 General considerations ................ 137
4.3.2.2 Voltage and current sources ........... 138
4.3.2.3 Signal detectors ...................... 139
4.3.2.4 Some important measurement setups ..... 142
5 Important quantities in mesoscopic transport ............... 147
5.1 Fermi wavelength ...................................... 147
5.2 Elastic scattering times and lengths .................. 147
5.3 Diffusion constant .................................... 148
5.4 Dephasing time and phase coherence length ............. 152
5.5 Electron-electron scattering time ..................... 152
5.6 Thermal length ........................................ 152
5.7 Localization length ................................... 153
5.8 Interaction parameter (or gas parameter) .............. 153
5.9 Magnetic length and magnetic time ..................... 153
6 Magneto-transport properties of quantum films .............. 155
6.1 Landau quantization ................................... 156
6.1.1 Two-dimensional electron gases in
perpendicular magnetic fields .................. 156
6.1.2 The chemical potential in strong magnetic
fields ......................................... 159
6.2 The quantum Hall effect ............................... 162
6.2.1 Phenomenology of the QHE ....................... 162
6.2.2 Toward an explanation of the integer quantum
Hall effect .................................... 164
6.2.3 The quantum Hall effect and three dimensions ... 168
6.3 Elementary analysis of Shubnikov-de Haas
oscillations .......................................... 170
6.4 Some examples of magneto-transport experiments ........ 172
6.4.1 Quasi-two-dimensional electron gases ........... 173
6.4.2 Mapping of the probability density ............. 175
6.4.3 Displacement of the quantum Hall plateaux ...... 176
6.4.4 In-plane magnetic fields ....................... 177
6.5 The QHE in graphene ................................... 182
7 Quantum wires and ballistic transport ...................... 187
7.1 Diffusive quantum wires ............................... 189
7.1.1 Basic Properties ............................... 189
7.1.2 Boundary Scattering ............................ 192
7.2 Ballistic quantum wires ............................... 193
7.2.1 Phenomenology .................................. 193
7.2.2 Conductance Quantization in QPCs ............... 194
7.2.3 Magnetic Field Effects ......................... 202
7.2.4 The "0.7 Structure" ............................ 205
7.2.5 Four-Probe Measurements on Ballistic Quantum
Wires .......................................... 205
7.3 The Landauer-Büttiker formalism ....................... 207
7.3.1 Edge States .................................... 208
7.3.2 Edge Channels .................................. 272
7.4 Further examples of quantum wires ..................... 274
7.4.1 Conductance Quantization in Conventional
Metals ......................................... 274
7.4.2 Molecular Wires ................................ 276
7.4.2.1 Carbon nanotubes ...................... 276
7.5 Quantum point contact circuits ........................ 279
7.5.1 Non-Ohmic Behavior of QPCs in Series ........... 279
7.5.2 QPCs in Parallel ............................... 222
7.6 Semiclassical limit: conductance of ballistic 2D
systems ............................................... 223
7.7 Concluding remarks .................................... 228
8 Modeling of Ballistic Transport in Mesoscopic Structures ... 233
Igor Zozoulenko
8.1 Scattering problem in one dimension ................... 234
8.1.1 Formulation of the scattering problem .......... 234
8.1.2 Transfer matrix technique ...................... 236
8.1.3 Scattering matrix technique .................... 238
8.1.4 Greens function technique ...................... 239
8.1.4.1 Tight-binding Hamiltonian ............. 239
8.1.4.2 Concept of the Green's function ....... 243
8.1.4.3 Dyson equation ........................ 247
8.1.4.4 Recursive Green's function
technique ............................. 247
8.1.4.5 Green's function and the scattering
matrix ................................ 254
8.2 Scattering problem in two dimensions .................. 257
8.2.1 Formulation of the scattering problem .......... 257
8.2.2 The unitary scattering matrix and its
properties ..................................... 259
8.2.3 Calculations of the conductance of mesoscopic
structures in two dimensions ................... 264
9 Electronic phase coherence ................................. 269
9.1 The Aharonov-Bohm effect in mesoscopic conductors ..... 269
9.2 Weak localization ..................................... 273
9.3 Universal conductance fluctuations .................... 275
9.4 Phase coherence in ballistic 2DEGs .................... 280
9.5 Resonant tunneling .................................... 282
10 Single-electron tunneling .................................. 293
10.1 The principle of Coulomb blockade ..................... 293
10.2 Basic single-electron tunneling circuits .............. 296
10.2.1 Coulomb Blockade at the Double Barrier ......... 298
10.2.2 Current-Voltage Characteristics: the Coulomb
Staircase ...................................... 302
10.2.3 The SET Transistor ............................. 306
10.3 SET circuits with many islands: the single-electron
pump .................................................. 311
11 Quantum dots ............................................... 319
11.1 Phenomenology of quantum dots ......................... 320
11.2 The constant interaction model ........................ 324
11.2.1 Quantum Dots in Intermediate Magnetic Fields ... 329
11.2.2 Quantum Rings .................................. 331
11.3 Beyond the constant interaction model ................. 332
11.3.1 Hund's Rules in Quantum Dots ................... 333
11.3.2 Quantum Dots in Strong Magnetic Fields ......... 334
11.3.3 The Distribution of Nearest-Neighbor
Spacings ....................................... 336
11.4 Shape of conductance resonances and I-V
characteristics ....................................... 340
11.5 Other types of quantum dots ........................... 342
11.5.1 Metal Grains ................................... 343
11.5.2 Molecular Quantum Dots ......................... 344
11.6 Quantum dots and quantum computation .................. 346
12 Mesoscopic superlattices ................................... 353
12.1 One-dimensional superlattices ......................... 354
12.2 Two-dimensional superlattices ......................... 356
12.2.1 Semiclassical Effects .......................... 356
12.2.2 Quantum Effects ................................ 362
13 Spintronics ................................................ 365
13.1 Spintronics ........................................... 365
Ferromagnetic sandwich structures ..................... 366
13.1.1 Tunneling Magneto-Resistance (TMR) and Giant
Magneto-Resistance (GMR) ....................... 366
13.1.2 Spin Injection Into a Non-Magnetic Conductor ... 369
13.2 The Datta-Das spin field effect transistor ............ 373
13.2.1 Concept of the Datta-Das Transistor ............ 373
13.2.2 Spin Injection in Semiconductors ............... 374
13.2.2.1 Interface tunnel barriers ............. 374
13.2.2.2 Ferromagnetic semiconductors .......... 376
13.2.3 Gate-Induced Spin Rotation: the Rashba
Effect ......................................... 378
13.2.4 Spin Relaxation and Spin Dephasing ............. 380
A SI and cgs units ........................................... 383
В Correlation and convolution ................................ 385
B.l Fourier transformation ................................ 385
B.2 Convolutions .......................................... 385
B.3 Correlation functions ................................. 386
С Capacitance matrix and electrostatic energy ................ 389
D The transfer Hamiltonian ................................... 393
E Solutions to selected exercises ............................ 395
References .................................................... 425
Index ......................................................... 435
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