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

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66 Chapter 3: WL/WAL Crossover and Spin Relaxation in Confined Systems correction than the bulk modes do, since they relax more slowly. This also results in a shift in the minimum of the conductivity towards smaller magnetic fields in comparison to the 0-mode approximation. The reduction of spin relaxation has recently been observed in optical measurements of n-doped InGaAs quantum wires[HSM + 06] and in transport measurements.[DLS + 05, LSK + 07, SGP + 06, WGZ + 06, Mei05] Recently in Ref.[KKN09], the enhancement of spin lifetime due to dimensional confinement in gated InGaAs wires with gate controlled SO coupling was reported. Reference [HSM + 06] reports saturation of spinrelaxation innarrowwires, W ≪ L SO , attributed tocubicDresselhaus coupling.[Ket07] The contribution of the linear and cubic Dresselhaus SO interaction to the spin relaxation turns out to depend strongly on growth direction and will be studied in more detail in Chapter4. Including both the linear Rashba and Dresselhaus SO coupling we have shown that there exist two long persisting spin helix solutions in narrow wires even for arbitrary strength of both SO coupling effects. This is in contrast to the 2D case, where the condition α 1 = α 2 , respectively in the case where the cubic Dresselhaus term cannot be neglected, α 1 −m e γ g E F /2 = α 2 , is required to find persistent spin helices [BOZ06, LCCC06] as it was measured recently (Ref. [KWO + 09]). Regarding the type of boundary, we found that the injection of polarized spins into nonmagnetic material is favorable for wires with a smooth confinement, λ F ∂ y V < ∆ α = 2k F α 2 . With such adiabatic boundary conditions, states which are polarized in z direction relax with a finite rate for wires with widths Q SO W ≪ 1, while the spin relaxation rate of all other states diverges in that limit. In tubular wires with periodic boundary conditions, the spin relaxation is found to remain constant as the wire circumference is reduced. Finally, by including the Zeeman coupling to the perpendicular magnetic field, we have shown that for spin-conserving boundary condition the critical wire width, W c , where the crossover from negative to positive magnetoconductivity occurs, depends not only on the dephasing rate but also depends on the g factor of the material.
Chapter 4 Direction Dependence of Spin Relaxation and Diffusive-Ballistic Crossover 4.1 Introduction In Chapter3 it was shown how the spin relaxes in a quasi 1D electron system in a quantum well grown in the [001] direction, depending on the width of the wire, where the normal of the boundary was pointing in the [010] direction. In a system with only Rashba SOC or linear Dresselhaus SOC in a (111) quantum well it is clear from the vector fields plotted in Fig.2.2 that a rotation in the plain should not effect the physics, i.e. the minimal spin relaxation rate will not reduce. The linear Rashba SOC does not depend on the growth direction at all. It is already known that on the other hand in a (001) 2D system with both BIA[Dre55] and SIA[BR84] we get an anisotropic spinrelaxation.[KRW03, CWd07, WJW10] This has also been studied numerically in quasi-1D GaAs wires[LLK + 10]. In this Chapter, Sec.4.2, we present analytical results concerning this anisotropy for the 2D case as well as the case of quantum wire with spin and charge conserving boundaries. As in the previous chapter, also here we focus on materials where the dominant mechanism for spin relaxation is governed by the DP spin relaxation. Furthermore we extend our analysis to other growth directions, Sec.4.3: Searching for long spin decoherence times at room temperature, the (110) quantum wire attracted attention. 67
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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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Page 25 and 26: Chapter 2: Spin Dynamics: Overview
Page 35 and 36: Chapter 3 WL/WAL Crossover and Spin
Page 37 and 38: Chapter 3: WL/WAL Crossover and Spi
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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 and 118: Chapter 6: Critical Discussion and
Page 119 and 120: 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
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Bibliography 117 [BB04] [BBF + 88]
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Bibliography 119 [DP71b] [DP71c] [D
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Bibliography 121 [HSM + 06] [HSM +
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Bibliography 123 [MACR06] T. Mickli
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Bibliography 125 [PMT88] [PP95] [PT
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Bibliography 127 [Tor56] H. C. Torr
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Appendix A SOC Strength in the Expe
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Appendix A: SOC Strength in the Exp
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Appendix B: Linear Response 133 in
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Appendix B: Linear Response 135 Pro
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Appendix C Cooperon and Spin Relaxa
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Appendix C: Cooperon and Spin Relax
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Appendix D: Hamiltonian in [110] gr
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Appendix E: Summation over the Ferm
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Appendix F: KPM 151 integer running
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