Spin-orbit coupling and electron-phonon scattering - Fachbereich ...

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48 Rashba spin-orbit coupling in quantum wires
Chapter 3 Rashba spin-orbit coupling in quantum dots In the previous chapter we have derived an analogy between parabolically confined spin-orbit (SO) interacting quantum wires and quantum optics. This analogy amounts to the exact correspondence between the two-dimensional (2D) SOcoupled system and the Jaynes-Cummings model (JCM) that was introduced in Sec. 1.3. Apart from being integrable, this model is known to exhibit a number of striking quantum optical phenomena like Rabi oscillations and the collapse and revival of wavefunctions [33]. The origin of these effects is the periodic flux of excitation energy between atom and light field. With this analogy in mind, one could ask whether it is possible to observe similar phenomena in a SO-coupled system? Clearly, it is not feasible to coherently manipulate the vast number of electrons in a 2D system to exhibit synchronous Rabi oscillations. This is in contrast to quantum optics where stimulated emission in active media can lead to collective effects by coupling to the same light field (laser). In the solid-state counterpart, the electrons do not share a common boson field. Therefore, the number of carriers has to be reduced drastically, e.g. by using quantum dots. In these quasi-zero-dimensional systems the number of electrons can be reduced to the single particle limit – making it the optimal object to study SO-induced effects on the single-electron spectra and dynamics. It is the purpose of this chapter to elucidate the effects of SO coupling on fewelectron quantum dots. Motivated by the quest for SO-driven Rabi oscillations we show that for weak SO coupling the dot can effectively be described by the JCM with the roles of atomic pseudo-spin and light field played by the spin and orbital angular momentum of the electron, respectively. This effective model leads to characteristic anticrossings in the single-particle spectra, any of which can be interpreted as a two-level system (TLS) which describes the periodic exchange of energy between spin and orbital degree of freedom, thus forming a novel compos- 49
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Interaction and confinement in nano
Page 3 and 4: Abstract iii Abstract It is the pur
Page 5: Publications v Publications Some of
Page 8 and 9: 2 Table of Contents 3 Rashba spin-o
Page 10 and 11: 4 Introduction (phonons). Therefore
Page 12 and 13: 6 Introduction Figure 1: Scanning e
Page 15 and 16: Chapter 1 The Rashba effect Effects
Page 17 and 18: 1.2 The model 11 the position-depen
Page 19 and 20: 1.3 Rashba effect in a perpendicula
Page 21 and 22: Chapter 2 Rashba spin-orbit couplin
Page 23 and 24: 2.1 Rashba effect and magnetic fiel
Page 31 and 32: PSfrag replacements 2.1 Rashba effe
Page 33 and 34: 2.2 Spectral properties, various li
Page 39 and 40: 2.3 Electron transport in one-dimen
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Page 47 and 48: PSfrag replacements 2.3 Electron tr
Page 51 and 52: 2.4 Summary 45 For weak SO coupling
Page 53: 2.4 Summary 47 splitting can become
Page 57 and 58: 3.1 Spin-orbit driven coherent osci
Page 59 and 60: 3.1 Spin-orbit driven coherent osci
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Page 63 and 64: 0 0.5 1.5 3.1 Spin-orbit driven coh
Page 65 and 66: 3.2 Introduction to quantum dots an
Page 75 and 76: PSfrag replacements 3.2 Introductio
Page 77 and 78: 3.3 Effects of relaxation 71 page 5
Page 79 and 80: 3.3 Effects of relaxation 73 The re
Page 81 and 82: 3.3 Effects of relaxation 75 with q
Page 83 and 84: 3.3 Effects of relaxation 77 eh 14
Page 85 and 86: Chapter 4 Conclusion In this part o
Page 87 and 88: Tuneable quantum dots connected to
Page 89: Part II Phonon confinement in nanos
Page 92 and 93: 86 Introduction to electron-phonon
Page 94 and 95: 88 Introduction to electron-phonon
Page 96 and 97: 90 Coupled quantum dots in a phonon
Page 102 and 103: ) ) ) ) 3 4 + ) * - 96 Coupled quan
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98 Coupled quantum dots in a phonon
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100 Coupled quantum dots in a phono
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PSfrag replacements 1042 Coupled qu
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110 Conclusion due to phonon van-Ho
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Appendix A Jaynes-Cummings model Th
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Appendix B Fock-Darwin representati
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Appendix C Evaluation of the phonon
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Appendix D Matrix elements of dot e
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121 with λ ± l (q ‖) = F n B pz
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Bibliography [1] G. Bergmann, Phys.
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Bibliography 125 [31] M. Pletyukhov
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Bibliography 127 [72] T. Schäpers,
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Bibliography 129 [109] U. Merkt, J.
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Bibliography 131 [144] B. Auld, Aco
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Bibliography 133 [182] A. A. Kisele
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Acknowledgements Finally, I would l
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