1 Ferromagnetic III-V Semiconductors and Their
Heterostructures
Hideo Ohno ................................................... 1
1.1 Introduction ............................................ 1
1.2 Preparation of III-V Based Ferromagnetic
Semiconductors .......................................... 2
1.3 Magnetic Properties ..................................... 4
1.4 Transport Properties .................................... 6
1.4.1 The Hall Effect .................................. 6
1.4.2 Temperature and Magnetic Field Dependence of
Resistivity ...................................... 8
1.5 Carrier-Induced Ferromagnetism ......................... 12
1.6 Basic Properties of Ferromagnetic III-V Semiconductor
Heterostructures ....................................... 16
1.7 Spin-Dependent Scattering and Tunnel
Magnetoresistance in Trilayer Structures ............... 17
1.8 Ferromagnetic Emitter Resonant Tunneling Diodes ........ 19
1.9 Spin-Injection in Ferromagnetic Semiconductor
Heterostructures ....................................... 21
1.10 Electric-Field Control of Hole-Induced
Ferromagnetism ......................................... 23
1.11 Summary and Outlook .................................... 25
References .................................................. 26
2 Spin Injection and Transport in Micro- and Nanoscale
Devices
Hong X. Tang, F.G. Monzon, Friso J. Jedema, Andrei
T. Filip, Bart J. van Wees, and Michael L. Roukes ........... 31
2.1 Overview ............................................... 31
2.2 Background ............................................. 32
2.2.1 Spin Polarized Tunneling ........................ 32
2.2.2 Spin Injection in Clean Bulk Metals ............. 33
2.2.3 Conceptual Picture of Spin Injection ............ 36
2.2.4 Spin Injection in Impure Metal Films ............ 39
2.3 Toward a Semiconducting "Spin Transistor" .............. 40
2.3.1 Why a Spin Transistor? .......................... 40
2.3.2 Why Semiconductors? ............................. 40
2.3.3 Concept ......................................... 41
2.3.4 Prerequisites for Realizing a Spin Transistor ... 42
2.3.5 Spin Lifetime in the Conduction Channel ......... 43
2.3.6 Gate Control of the Spin Orbit Interaction
(Theory) ........................................ 43
2.3.7 Gate Control of the Spin Orbit Interaction
(Experiment) .................................... 44
2.4 Initial Experiments on Spin Injection in
Semiconductor Heterostructures ......................... 47
2.4.1 Motivation and Initial Data ..................... 47
2.4.2 Local Hall Effect ............................... 50
2.4.3 Results from Smaller, Optimized Devices ......... 51
2.5 Spin Injection in Diffusive Systems .................... 55
2.5.1 Basic Model for Spin Transport in Diffusive
Systems ......................................... 56
2.5.2 The F/N Interface ............................... 58
2.5.3 Spin Accumulation in Multiterminal Spin Valve
Structures ...................................... 59
2.5.4 Observation of Spin-Injection and Spin-
Accumulation in an All-Metal Spin Valve ......... 61
2.5.5 Comparison with the Johnson "Spin Transistor" ... 62
2.5.6 Future Prospects for Spin Accumulation and
Spin Transport in All Metal Devices ............. 63
2.5.7 Spin Injection in a Diffusive Semiconductor ..... 63
2.5.8 Conductivity Mismatch ........................... 63
2.5.9 Possible Solutions to Conductivity Mismatch ..... 66
2.6 Spin Transport in the Ballistic Regime ................. 66
2.6.1 Multiprobe Model for Ballistic Spin Polarized
Transport ....................................... 68
2.6.2 Results of Spin Resolved 4-Probe Model .......... 72
2.6.3 8-Probe Model: Junction, Bulk, and Boundary
Scattering ...................................... 75
2.6.4 The Spin Transistor: A Closer Look .............. 77
2.6.5 Other Theoretical Treatments .................... 78
2.7 Projections and Conclusions ............................ 79
2.7.1 Retrospective: The Spin Transistor .............. 79
2.7.2 Recent Advances in Spin Transport Across
Interfaces ...................................... 81
2.7.3 Recent Advances in Spin Injection Via
Semimagnetic Semiconductors ..................... 85
2.7.4 Recent Advances in Spin Propagation in
Semiconductors .................................. 85
2.7.5 Detection of Nonequilibrium Spin Polarization ... 86
References .................................................. 87
3 Electrical Spin Injection: Spin-Polarized Transport from
Magnetic into Non-Magnetic Semiconductors
Georg Schmidt and Laurens W. Molenkamp ...................... 93
3.1 Introduction ........................................... 93
3.2 Electrical Spin Injection .............................. 94
3.2.1 Diluted Magnetic Semiconductors ................. 94
3.2.2 The Optical Detection of Spin Injection ......... 95
3.2.3 The Spin Aligner LED ............................ 96
3.2.4 Experimental Results ............................ 97
3.2.5 Exclusion of Side Effects ....................... 99
3.2.6 Hole Injection ................................. 100
3.3 A Novel Magnetoresistance Effect ...................... 101
3.3.1 Theoretical Prediction ......................... 101
3.3.2 Device Layout .................................. 102
3.3.3 Results and Interpretation ..................... 103
3.4 Outlook ............................................... 104
References ................................................. 105
4 Spin Dynamics in Semiconductors
Michael E. Flatté, Jeff M. Byers, and Wayne H. Lau ......... 107
4.1 Introduction .......................................... 107
4.2 Fundamentals of Semiconductor Spin Coherence .......... 108
4.2.1 Coherent Ensembles of Spins .................... 109
4.2.2 Mobile Electron Decoherence Via the Spin-
Orbit Interaction .............................. 110
4.2.3 Sources of Inversion Asymmetry ................. 115
4.2.4 Comparison with Ultrafast Probes of Orbital
Coherence ...................................... 121
4.2.5 Concluding Remarks ............................. 123
4.3 Precessional Spin Coherence Times in Bulk and
Nanostructure Semiconductors .......................... 123
4.3.1 Magnitude of the Fluctuating Field ............. 125
4.3.2 Calculation of the Effective Time for Field
Reversal ....................................... 126
4.3.3 Spin Decoherence Times in Bulk III-V
Semiconductors ................................. 126
4.3.4 Spin Decoherence in III-V (001) Quantum
Wells .......................................... 127
4.4 Spin Transport ........................................ 131
4.4.1 Drift-Diffusion Equations ...................... 132
4.4.2 Low-Field Motion of Spin Packets in
Nonmagnetic Semiconductors ..................... 133
4.4.3 Diffusion and Mobility of Packets in GaAs ...... 135
4.4.4 Influence of Many-Body Effects on Low-Field
Spin Diffusion ................................. 137
4.4.5 Motion of Spin Packets in Spin-Polarized
Semiconductors ................................. 138
4.4.6 High-Field Spin Transport in the Diffusive
Regime ......................................... 139
4.5 Spin Transport in Inhomogeneous Structures ............ 139
4.5.1 Transport Across the Ferromagnet /
Semiconductor Boundary ......................... 140
4.6 Conclusion ............................................ 142
References ................................................. 143
5 Optical Manipulation, Transport and Storage of Spin
Coherence in Semiconductors
David D. Awschalom and Nitin Samarth ....................... 147
5.1 Introduction .......................................... 147
5.2 Experimental Techniques for Measuring Spin Coherence
in Semiconductors ..................................... 148
5.3 Electron Spin Coherence in Bulk Semiconductors ........ 153
5.4 Electron Spin Coherence in Semiconductor Quantum
Dots .................................................. 160
5.5 Coherent Spin Transport in Semiconductors ............. 162
5.5.1 Lateral Drag in GaAs ........................... 162
5.5.2 Transport Across Heterointerfaces in ZnSe/
GaAs ........................................... 166
5.6 Spin Coherence and Magnetic Resonance ................. 175
5.6.1 Electron Paramagnetic Resonance in II-VI
Magnetic Semiconductor Quantum Structures ...... 175
5.6.2 All-Optical Nuclear Magnetic Resonance in
Semiconductors ................................. 177
5.7 Coherent Manipulation of Spin in Semiconductors ....... 181
5.8 Spin Coherence in Hybrid Ferromagnet/Semiconductor
Heterostructures ...................................... 183
5.8.1 Ferromagnetic Imprinting of Nuclear Spins
in Semiconductors .............................. 184
5.8.2 Spontaneous Electron Spin Coherence in n-GaAs
Produced by Ferromagnetic Proximity
Polarization ................................... 188
5.9 Summary and Outlook ................................... 190
References ................................................. 192
6 Spin Condensates in Semiconductor Microcavities
Jeremy J. Baumberg ......................................... 195
6.1 Introduction .......................................... 195
6.2 Polariton Properties .................................. 196
6.2.1 Strongly Coupled Microcavity Dispersion ........ 196
6.2.2 Polariton Dynamics and Pair Scattering ......... 200
6.3 Experiments ........................................... 202
6.3.1 Experimental Geometry .......................... 202
6.3.2 Microcavity Sample ............................. 203
6.3.3 Parametric Scattering .......................... 205
6.4 Condensate Dynamics ................................... 211
6.4.1 Polariton Interferometry ....................... 211
6.4.2 Macroscopic Quantum States ..................... 214
6.4.3 Quantum-Correlated Pairs ....................... 216
6.4.4 Conclusions .................................... 217
References ................................................. 218
7 Spins for Quantum Information Processing
David P. DiVincenzo ........................................ 221
7.1 Introduction .......................................... 221
7.1.1 The Requirements ................................ 222
7.2 Timeline .............................................. 224
7.3 Final Thoughts ........................................ 226
References ................................................. 227
8 Electron Spins in Quantum Dots as Qubits for Quantum
Information Processing
Guido Burkard and Daniel Loss .............................. 229
8.1 Introduction .......................................... 229
8.1.1 Quantum Computing .............................. 230
8.1.2 Quantum Communication .......................... 231
8.1.3 Quantum Dots ................................... 231
8.2 Requirements for Quantum Computing .................... 232
8.2.1 Coherence ...................................... 232
8.2.2 Slow Spin Relaxation in GaAs Semiconductor
Quantum Dots ................................... 233
8.2.3 Scalability .................................... 236
8.2.4 Switching ...................................... 236
8.2.5 Quantum Error Correction ....................... 238
8.2.6 Gate Precision ................................. 239
8.2.7 Initialization ................................. 240
8.3 Coupled Quantum Dots as Quantum Gates ................. 240
8.3.1 Lateral Coupling ............................... 241
8.3.2 Vertical Coupling .............................. 244
8.3.3 Anisotropic Exchange ........................... 245
8.3.4 Superexchange .................................. 247
8.3.5 Accessing the Exchange Interaction J Between
the Spins in Coupled Quantum Dots Via the
Kondo Effect ................................... 248
8.4 Single-Spin Rotations ................................. 250
8.4.1 Local Magnetic Coupling ........................ 251
8.4.2 Local g-Factor Coupling ........................ 251
8.4.3 Quantum Computing with Exchange Interactions
Only ........................................... 251
8.5 Read-Out of a Single Spin ............................. 253
8.5.1 Spontaneous Magnetization ...................... 253
8.5.2 Measuring Spin Via Charge ...................... 253
8.5.3 Coupled Dots as Entangler ...................... 254
8.5.4 Spin Filter .................................... 254
8.5.5 Berry Phase Controlled Spin Filter ............. 255
8.5.6 Detection of Single-Spin Decoherence ........... 256
8.5.7 Rabi Oscillations and Pulsed ESR ............... 257
8.5.8 Spin Read-Out .................................. 258
8.5.9 Optical Measurements ........................... 259
8.6 Quantum Information Processing with Large-Spin
Systems ............................................... 259
8.7 Quantum Communication ................................. 260
8.7.1 Andreev Entangler .............................. 261
8.7.2 Andreev Entangler with Luttinger Liquid
Leads .......................................... 264
8.7.3 Entangled Electrons in a Fermi Sea ............. 265
8.7.4 Noise of Entangled Electrons ................... 266
8.7.5 Double-Dot with Normal Leads ................... 268
8.7.6 Double-Dot with Superconducting Leads .......... 269
8.7.7 Biexcitons in Coupled Quantum Dots as
a Source of Entangled Photons and Electrons .... 270
8.8 Conclusions ........................................... 272
9 Regulated Single Photons and Entangled Photons From
a Quantum Dot Microcavity
Yoshihisa Yamamoto, Matthew Pelton, Charles Santori,
Glenn S. Solomon, Oliver Benson, Jelena Vuckovic, and
Axel Scherer ............................................... 277
9.1 Introduction .......................................... 277
9.2 Single InAs/GaAs Quantum Dots ......................... 279
9.3 Generation of Single Photons .......................... 285
9.4 Coupling Single Quantum Dots to Micropost
Microcavities ......................................... 286
9.5 Theoretical Analysis of a Micropost DBR Cavity ........ 293
9.6 Entangled Photon-Pairs from a Single Quantum Dot ...... 298
9.7 Conclusions ........................................... 303
Index ......................................................... 307
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