Itinerant Spin Dynamics in Structures of ... - Jacobs University

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List of Symbols SOC spin-orbit coupling.......................................................2 2DES 2D electron system ......................................................2 m e effective electron mass .................................................. 3 λ F Fermi wavelength .......................................................3 WL weak localization ........................................................4 WAL weak antilocalization ....................................................4 m e0 free electron mass .......................................................6 ∆ SO Pauli splitting .......................................................... 7 γ g gyromagnetic ratio ......................................................8 τ elastic scattering time ...................................................9 l e elastic mean free path ...................................................9 D e diffusion constant .......................................................9 v F Fermi velocity .......................................................... 9 d D diffusion dimension of the electron system ...............................9 ν density of states per spin at E F .........................................9 DOS density of states ........................................................ 9 L D diffusion length ........................................................10 a z thickness of the 2D electron system ....................................11 γ D Dresselhaus-spin-orbit coefficient .......................................11 α 1 linear Dresselhaus parameter ...........................................11 BIA bulk inversion asymmetry ..............................................11 SIA structural inversion asymmetryy .......................................13 α 2 linear Rashba parameter ...............................................13 L SO spin precession length ..................................................14 108
Chapter 6: Critical Discussion and Future Perspective 109 τ s spin relaxation time ....................................................16 L s spin relaxation length ..................................................19 DP D’yakonov-Perel’ .......................................................19 E F Fermi energy .......................................................... 20 W wire width .............................................................26 l ϕ phase coherence length .................................................27 Ĉ Cooperon propagator .................................................. 34 ˜α 1 reduced linear Dresselhaus parameter ..................................36 l B magnetic length ........................................................37 τ B magnetic phase-shifting rate ........................................... 37 Q SO spin precession wave vector equal to 2π/L SO ...........................38 H c Cooperon Hamiltonian .................................................38 H SD spin-diffusion Hamiltonian .............................................39 B ∗ effective external magnetic field ........................................45 H s spin relaxation field ....................................................45 ∆ α spin orbit splitting 2k F α 2 ..............................................53 LDES low dimensional electron systems .......................................83 SHE spin Hall effect .........................................................84 KPM Kernel Polynomial Method .............................................84 SHC spin Hall conductivity ................................................. 85 J z spin current ............................................................85 σxy z ≡ σ SH spin hall conductivity ..................................................88 ∆ B band width ............................................................98 MIT metal-insulator transition ..............................................98 g scaling parameter in scaling theory of localization ......................99 E Th Thouless energy ....................................................... 99 ∆ LS typical energy level spacing ............................................ 99
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Itinerant Spin Dynamics in Structur
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Itinerant Spin Dynamics in Structur
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Contents v 3.2.2 Weak Localization
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Citations to Previously Published W
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Dedicated to Linda, my parents and
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Chapter 1 Introduction Structure of
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Chapter 1: Introduction 3 the coupl
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Chapter 1: Introduction 5 Throughou
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Chapter 2: Spin Dynamics: Overview
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Chapter 3 WL/WAL Crossover and Spin
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Chapter 3: WL/WAL Crossover and Spi
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Page 67 and 68: Chapter 3: WL/WAL Crossover and Spi
Page 77 and 78: Chapter 4 Direction Dependence of S
Page 79 and 80: Chapter 4: Direction Dependence of
Page 93 and 94: Chapter 5 Spin Hall Effect 5.1 Intr
Page 95 and 96: Chapter 5: Spin Hall Effect 85 curr
Page 97 and 98: Chapter 5: Spin Hall Effect 87 with
Page 99 and 100: Chapter 5: Spin Hall Effect 89 1.0
Page 101 and 102: Chapter 5: Spin Hall Effect 91 as s
Page 103 and 104: Chapter 5: Spin Hall Effect 93 V⩵
Page 105 and 106: Chapter 5: Spin Hall Effect 95 0.4
Page 107 and 108: Chapter 5: Spin Hall Effect 97 oper
Page 109 and 110: Chapter 5: Spin Hall Effect 99 the
Page 111 and 112: Chapter 5: Spin Hall Effect 101 str
Page 113 and 114: Chapter 5: Spin Hall Effect 103 Com
Page 115 and 116: Chapter 5: Spin Hall Effect 105 Fin
Page 117: Chapter 6: Critical Discussion and
Page 121 and 122: List of Figures 111 3.3 Exemplifica
Page 123 and 124: List of Figures 113 4.2 The spin de
Page 125 and 126: List of Tables 3.1 Singlet and trip
Page 127 and 128: Bibliography 117 [BB04] [BBF + 88]
Page 129 and 130: Bibliography 119 [DP71b] [DP71c] [D
Page 131 and 132: Bibliography 121 [HSM + 06] [HSM +
Page 133 and 134: Bibliography 123 [MACR06] T. Mickli
Page 135 and 136: Bibliography 125 [PMT88] [PP95] [PT
Page 137 and 138: Bibliography 127 [Tor56] H. C. Torr
Page 139 and 140: Appendix A SOC Strength in the Expe
Page 141 and 142: Appendix A: SOC Strength in the Exp
Page 143 and 144: Appendix B: Linear Response 133 in
Page 145 and 146: Appendix B: Linear Response 135 Pro
Page 147 and 148: Appendix C Cooperon and Spin Relaxa
Page 149 and 150: Appendix C: Cooperon and Spin Relax
Page 157 and 158: Appendix D: Hamiltonian in [110] gr
Page 159 and 160: Appendix E: Summation over the Ferm
Page 161: Appendix F: KPM 151 integer running
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