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

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108 Coupled quantum dots in a phonon cavity The energy that limits the current spectrum is given by the source-drain voltage V SD since ε = E L −E R ≤ eV SD . For V SD = 140µV as in [146], 16 phonon subbands contribute to the current. Since every real experimental system is finite, we expect structures in the current which were derived for an infinitely extended system to be broadened due the finite area of the cavity A. This broadening should be on an energy scale c l /L, where A = L 2 . Thus, for a setup with c l /L ≈ 0.1ω b ≈ 1µeV (L ≈ 10b) the broadening is negligible. Finite temperatures yield a similar effect. Since Eq. (6.16) is strictly valid only at T = 0, structures in the I–V characteristic should be broadened on a scale of ω ≈ k B T ≈ 2µeV (at 20 mK). In addition, phonon absorption may become relevant at higher temperatures. Besides the transport that is mediated by the DP, there is also an influence of the PZ electron-phonon coupling. In a phonon cavity, the PZ effect couples all mode families, shear and Lamb waves, to the dot electrons. Moreover, the anisotropy of the piezo-electric tensor leads to a highly non-trivial q ‖ dependence of the matrix elements [176], and thus to anisotropic transport properties. However, this anisotropy is expected to be a minor correction since the PZ coupling yields only a small contribution to the inelastic scattering rate in small FSQWs. From the above arguments we conclude that there is no fundamental obstacle to measure the predicted features of phonon confinement in electron transport. Recently, the electron transport through a Coulomb blockaded quantum dot in a free-standing 130nm thick GaAs/AlGaAs membrane was measured [170]. At zero bias, a complete suppression of single-electron tunnelling was found. The authors attributed the associated energy gap in the transport spectrum to the excitation of a localised cavity phonon. The observed energy gap of ε 0 ≈ 100µeV matches reasonably well with the lowest dilatational (73µeV) or flexural (145µeV) van–Hove singularity in the DOS of a 130nm thick planar cavity. Although, a detailed microscopic explanation of the experimental findings is to our knowledge still missing, this experiment clearly highlights the feasibility to built artificial structures with well controlled electro-mechanical properties.
Chapter 7 Conclusion In this part we have investigated the non-linear electron transport through a double quantum dot which is placed in a phonon cavity. A free-standing quantum well is used as a model for a nano-size planar phonon cavity. Phonons are quantised lattice vibrations. Therefore, their properties are determined by the acoustomechanical characteristics of the elastic medium. Mechanical confinement is known to strongly affect the vibrational properties of the system. For instance, confinement leads to a splitting of the phonon spectrum in several subbands, and non-linearities in the dispersion may lead to van–Hove singularities in the phonon density of states by modes with zero phonon group velocity at a finite wavelength. We show that in the Coulomb–blockade regime, such features of mechanically confined phonons produce clear signatures in the I–V characteristics of the double quantum dot. Therefore, it is a useful tool to detect phonon quantum size effects in the electron-phonon interaction via electron transport measurements. We find that the coupling to the different phonon mode families of a freestanding quantum well (two families of shear and Lamb waves each) depends on the orientation of the dots with respect to the cavity. This is due to different symmetries of the phonon induced interaction potential and holds for both piezo-electric and deformation potential electron-phonon coupling. For certain orientations, the double dot decouples from all phonon mode families except one. Thus, one can tune the coupling between double dot and phonons by changing the orientation of the dots in the cavity. Since, at low temperatures, the inelastic transport is mediated by spontaneous emission of phonons, double quantum dots can be used as an energy-selective phonon emitter which orientation dependent emission characteristic. At low energies, which are determined by small splittings of the double quantum dot levels ∆, only the lowest phonon subbands contribute to inelastic scattering and hence to transport through the double dot. For particular values of ∆, deformation potential or piezo-electric scattering is either drastically enhanced 109
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Interaction and confinement in nano
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Abstract iii Abstract It is the pur
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Publications v Publications Some of
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2 Table of Contents 3 Rashba spin-o
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4 Introduction (phonons). Therefore
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6 Introduction Figure 1: Scanning e
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Chapter 1 The Rashba effect Effects
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1.2 The model 11 the position-depen
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1.3 Rashba effect in a perpendicula
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Chapter 2 Rashba spin-orbit couplin
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2.1 Rashba effect and magnetic fiel
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PSfrag replacements 2.1 Rashba effe
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2.2 Spectral properties, various li
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2.3 Electron transport in one-dimen
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PSfrag replacements 2.3 Electron tr
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2.4 Summary 45 For weak SO coupling
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2.4 Summary 47 splitting can become
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Chapter 3 Rashba spin-orbit couplin
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3.1 Spin-orbit driven coherent osci
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3.1 Spin-orbit driven coherent osci
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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
Page 102 and 103: ) ) ) ) 3 4 + ) * - 96 Coupled quan
Page 106 and 107: 100 Coupled quantum dots in a phono
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Page 116 and 117: 110 Conclusion due to phonon van-Ho
Page 119 and 120: Appendix A Jaynes-Cummings model Th
Page 121 and 122: Appendix B Fock-Darwin representati
Page 123 and 124: Appendix C Evaluation of the phonon
Page 125 and 126: Appendix D Matrix elements of dot e
Page 127 and 128: 121 with λ ± l (q ‖) = F n B pz
Page 129 and 130: Bibliography [1] G. Bergmann, Phys.
Page 131 and 132: Bibliography 125 [31] M. Pletyukhov
Page 133 and 134: Bibliography 127 [72] T. Schäpers,
Page 135 and 136: Bibliography 129 [109] U. Merkt, J.
Page 137 and 138: Bibliography 131 [144] B. Auld, Aco
Page 139 and 140: Bibliography 133 [182] A. A. Kisele
Page 141: Acknowledgements Finally, I would l
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