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

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Andreev Billiards 153 P (x) ≈ 1 8π|x| exp � − 4 3 |x|3/2� , x ≪−1 . (69) The mesoscopic gap fluctuations induce a tail in the ensemble averaged density of states 〈ρ(E)〉 for E
154 C.W.J. Beenakker P(x) 0.4 0.3 0.2 0.1 0 0 1 2 E/E T 2 1 0 –6 –4 –2 0 2 4 6 x Fig. 12. Main plot: Gap distribution for the Andreev kicked rotator with parameters M =2π/δ = 8192, kicking strength K = 45, and M/N = τdwell =10(⋄), 20 (•), 40 (+), and 50 (×). There is no magnetic field. The solid line is the RMT prediction (62). Inset: Average density of states for the same system. The solid line is the RMT prediction (49). (Deviations from perturbation theory are not visible on the scale of the inset.) Adapted from [27] 6.7 Coulomb Blockade Coulomb interactions between electron and hole quasiparticles break the charge-conjugation invariance (37) of the Hamiltonian. Since Andreev reflection changes the charge on the billiard by 2e, this scattering process becomes energetically unfavorable if the charging energy EC exceeds the superconducting condensation energy (Josephson energy) EJ. ForEC > ∼ EJ one obtains the Coulomb blockade of the proximity effect studied by Ostrovsky, Skvortsov, and Feigelman [55]. The charging energy EC = e 2 /2C is determined by the capacitance C of the billiard. The Josephson energy is determined by the change in free energy of the billiard resulting from the coupling to the superconductor, � ∞ EJ = − [ρ(E) − 2/δ] EdE . (71) 0 The discrete spectrum E < Egap contributes an amount of order E2 gap/δ to EJ. In the continuous spectrum E > Egap the density of states ρ(E), calculated by RMT, decays ∝ 1/E2 to its asymptotic value 2/δ. This leads to a logarithmic divergence of the Josephson energy [37, 56], with a cutoff set by min(∆, �/τerg): EJ = E2 gap δ � � min(∆, �/τerg) ln . (72) Egap
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Lecture Notes in Physics Editorial
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W. Dieter Heiss (Ed.) Quantum Dots:
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Preface Nanoscale physics, nowadays
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Contents A Guide for the Reader ...
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A Guide for the Reader Quantum dots
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The Renormalization Group Approach
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RG for Interacting Fermions 5 where
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where � is a shorthand: � ≡ 3
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RG for Interacting Fermions 9 These
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RG for Interacting Fermions 11 is i
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RG for Interacting Fermions 13 the
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RG for Interacting Fermions 15 this
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RG for Interacting Fermions 17 equa
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� p � dθp = g 2π RG for Inter
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RG for Interacting Fermions 21 the
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References RG for Interacting Fermi
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Semiconductor Few-Electron Quantum
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1.2 Implementations Semiconductor F
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GaAs n-AlGaAs AlGaAs GaAs Semicondu
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ε1 ε0 e Semiconductor Few-Electro
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250 Ω twisted pair 20 MΩ powder
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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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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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98 M. Pustilnik and L.I. Glazman Co
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Page 155 and 156: 146 C.W.J. Beenakker Fig. 6. Ensemb
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Page 161: 152 C.W.J. Beenakker P 0.5 0.4 0.3
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Page 167 and 168: 158 C.W.J. Beenakker its momentum).
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Page 171 and 172: 162 C.W.J. Beenakker 〈ρ(E)〉 δ
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