Heiss W.D. (ed.) Quantum dots.. a doorway to - tiera.ru

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X Contents 3 Thermally-Activated Conduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 4 Activationless Transport throughaBlockadedQuantumDot.............................109 5 Kondo Regime in Transport through a Quantum Dot . . . . . . . . . . . . . 113 6 Discussion...................................................124 7 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Andreev Billiards C.W.J. Beenakker ................................................131 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 2 Andreev Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 3 Minigap in NS Junctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 4 Scattering Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 5 StroboscopicModel...........................................139 6 Random-MatrixTheory.......................................141 7 QuasiclassicalTheory.........................................156 8 Quantum-To-ClassicalCrossover ...............................162 9 Conclusion ..................................................169 A Excitation Gap in Effective RMT and Relationship with Delay Times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
A Guide for the Reader Quantum dots, often denoted artificial atoms, are the exquisite tools by which quantum behavior can be probed on a scale appreciably larger than the atomic scale, that is, on the nanometer scale. In this way, the physics of the devices is closer to classical physics than that of atomic physics but they are still sufficiently small to clearly exhibit quantum phenomena. The present volume is devoted to some of these fascinating aspects. In the first contribution general theoretical aspects of Fermi liquids are addressed, in particular, the renormalization group approach. The choice of appropriate variables as a result of averaging over “unimportant” variables is presented. This is then aptly applied to large quantum dots. The all important scales, ballistic dots and chaotic motion are discussed. Nonperturbative methods and critical phenomena feature in this thorough treatise. The traditional phenomenological Landau parameters are given a more satisfactory theoretical underpinning. A completely different approach is encountered in the second contribution in that it is a thorough experimental expose of what can be done or expected in the study of small quantum dots. Here the emphasis lies on the electron spin to be used as a qubit. The experimental steps toward using a single electron spin – trapped in a semiconductor quantum dot – as a spin qubit are described. The introduction contains a resume of quantum computing with quantum dots. The following sections address experimental implementations, the use of different quantum dot architectures, measurements, noise, sensitivity and high-speed performance. The lectures are based on a collaborative effort of research groups in the Netherlands and in Japan. The last two contributions are again theoretical in nature and address particular aspects relating to quantum dots. In the third lecture series, mechanisms of low-temperature electronic transport through a quantum dot – weakly coupled to two conducting leads – are reviewed. In this case transport is dominated by electron–electron interaction. At moderately low temperatures (comparing with the charging energy) the linear conductance is suppressed by
Page 1 and 2: Lecture Notes in Physics Editorial
Page 3 and 4: W. Dieter Heiss (Ed.) Quantum Dots:
Page 5: Preface Nanoscale physics, nowadays
Page 9: Contents A Guide for the Reader ...
Page 13 and 14: The Renormalization Group Approach
Page 15 and 16: RG for Interacting Fermions 5 where
Page 17 and 18: where � is a shorthand: � ≡ 3
Page 19 and 20: RG for Interacting Fermions 9 These
Page 21 and 22: RG for Interacting Fermions 11 is i
Page 23 and 24: RG for Interacting Fermions 13 the
Page 25 and 26: RG for Interacting Fermions 15 this
Page 27 and 28: RG for Interacting Fermions 17 equa
Page 29 and 30: � p � dθp = g 2π RG for Inter
Page 31 and 32: RG for Interacting Fermions 21 the
Page 33 and 34: References RG for Interacting Fermi
Page 35 and 36: Semiconductor Few-Electron Quantum
Page 39 and 40: 1.2 Implementations Semiconductor F
Page 43 and 44: GaAs n-AlGaAs AlGaAs GaAs Semicondu
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10 5 0 -5 Semiconductor Few-Electro
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G ( e / h) 2 2 1 0 Semiconductor Fe
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Semiconductor Few-Electron Quantum
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V R (V) V R (V) Semiconductor Few-E
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V L (V) -1.084 -1.082 -1.080 -1.078
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B // Semiconductor Few-Electron Qua
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a RESERVOIR 200 nm Semiconductor Fe
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4.5 QPC Versus SET Semiconductor Fe
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a reservoir dot Semiconductor Few-E
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a b c V P (mV) 10 5 0 ∆I QPC E F
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Spin-down counts 200 100 a Semicond
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6.7 Unresolved Issues Semiconductor
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132 C.W.J. Beenakker e e N I N S Fi
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134 C.W.J. Beenakker 2 Andreev Refl
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136 C.W.J. Beenakker F E x 8d/hv ga
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138 C.W.J. Beenakker and we have de
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140 C.W.J. Beenakker A stroboscopic
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142 C.W.J. Beenakker largely indepe
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144 C.W.J. Beenakker The effective
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146 C.W.J. Beenakker Fig. 6. Ensemb
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148 C.W.J. Beenakker 1.4 1.2 1.0 0.
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150 C.W.J. Beenakker 〈ρ(E)〉 =
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152 C.W.J. Beenakker P 0.5 0.4 0.3
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154 C.W.J. Beenakker P(x) 0.4 0.3 0
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156 C.W.J. Beenakker tunnel/ Egap 4
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158 C.W.J. Beenakker its momentum).
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160 C.W.J. Beenakker E00 = π� =
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162 C.W.J. Beenakker 〈ρ(E)〉 δ
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164 C.W.J. Beenakker As described i
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166 C.W.J. Beenakker 0.30 � Egap
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168 C.W.J. Beenakker The τE-depend
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170 C.W.J. Beenakker that a fully m
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172 C.W.J. Beenakker (τ−,τ+), w
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174 C.W.J. Beenakker 61. P. G. Silv
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