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

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PSfrag replacements 46 Rashba spin-orbit coupling in quantum wires (a) 1 (b) 0.0001 T++, T−− T++, T−− 0.9998(c) 0.0002 0.985 0.015 0.9999 0 1 0.995 0.99 T+−, T−+ T+−, T−+ 0.5 1 0 0 0.5 1 ak SO /π ak SO /π (d) 0.01 0.005 0 0.1 0.2 0.3 0.4 0.1 0.2 0.3 0.4 ak SO /π ak SO /π Figure 2.13: Transmission coefficients for a sinusoidal magnetic barrier [(a)+(b)] and 10 barriers in series [(c)+(d)] for weak spin-orbit coupling as a function of the barrier width a. System parameters: E F = 48meV, B 0 = 25 mT, α = 1.6 × 10 −11 eVm, g = −15, m = 0.042m 0 . field has been investigated. In general, SO interaction couples the spin of an electron to its orbital motion. Thus, confinement induced quantisation of motion is expected to influence the spin properties. A magnetic field which is perpendicular to the plane of motion is a further quantity, affecting both orbitals and spin. In Sec. 2.1 and 2.2, we have presented a detailed analysis of the one-electron spectral and spin properties of the QWR for various regimes in the interplay of confinement, SO coupling and magnetic field. Spectra and spin densities show features which are governed by a compound spin orbital-parity symmetry of the QWR. Without magnetic field, this spin parity – which is a characteristic property of any symmetrically confined quasi-1D system with Rashba effect – is shown to replace the quantum number of spin. It is also responsible for the well-known degeneracy at k = 0 in symmetrically confined systems with Rashba effect. A non-vanishing magnetic field breaks the spin-parity symmetry, thus lifting the corresponding degeneracy at k = 0. We show that this magnetic field induced energy
2.4 Summary 47 splitting can become much larger than the Zeeman splitting and should be accessible experimentally by means of optical or transport measurements. In addition, hybridisation effects of the spin density go along with the symmetry breaking. The one-electron spectrum is shown to be very sensitive to weak magnetic fields. SO-induced modifications of the subband structure of the QWR are strongly altered when the magnetic length becomes comparable to the confinement. This might imply consequences for spin transistor designs which depend on spin injection from ferromagnetic contacts because of magnetic stray fields. In Sec. 2.3 we have outlined the method of mode matching analysis for the evaluation of transport properties in quasi-1D system with SO coupling. In this context we have shown that the inclusion of evanescent modes is crucial to end up with reliable results. In SO-interacting quasi-1D systems, the determination of evanescent modes is complicated due to the structure of Hamiltonian. To our knowledge, a detailed treatment of this problem is still lacking despite its importance for assessing the approximations which are usually employed. In Sec. 2.3.2 we analysed the spin-dependent transmission properties of a strict-1D QWR with a single transverse subband in the interplay of SO coupling and external magnetic modulation. A commensurability effect is found when the period of modulation is comparable to the SO-induced spin precession. For the example of the QWR we have demonstrated that in the case of parabolic confinement it is useful to map the underlying one-electron model onto a bosonic representation, which highlights the effects of SO coupling in confined systems. For large magnetic fields this representation shows many similarities to matterlight interaction in quantum optics. In the next chapter of this thesis a similar mapping will be applied to the model of a parabolically confined quantum dot.
Page 1 and 2: 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
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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: 2.4 Summary 45 For weak SO coupling
Page 55 and 56: Chapter 3 Rashba spin-orbit couplin
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
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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
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) ) ) ) 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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