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

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54 J.M. Elzerman et al. V L (V) -1.1 -1.0 a b 00 -0.9 0.0 -0.2 -0.4 -0.6 V PR (V) -1.02 -1.00 -0.98 -0.96 12 22 01 11 21 00 10 -0.15 -0.20 -0.25 -0.30 V PR (V) Fig. 17. Using the QPC to measure the charge configuration of a double quantum dot in the few-electron regime. (a) dIQP C/dVL (in grayscale) versusVL and VPR,withVSD2 = 100 µV andVSD1 = VDOT = 0. A small modulation (0.3 mV at 17.77 Hz) is applied to VL, and the resulting modulation in IQP C is measured with a lock-in amplifier to give dIQP C/dVL directly. The label “00” indicates the region where the double dot is completely empty. In the bottom left corner the dark lines are poorly visible. Here the tunnel rates to the reservoirs are quite large, leading to smearing of the steps in the QPC current, and therefore to smaller dips in dIQP C/dVL. (b) Zoom-in of Fig. 17a, showing the “honeycomb” diagram for the first few electrons in the double dot. The black labels indicate the charge configuration, with “21” meaning 2 electrons in the left dot and 1 on the right change in the number of electrons on the left dot, whereas almost-vertical lines indicate a change in the electron number on the right. In the upper left region the “horizontal” lines are not present, even though the QPC can still detect changes in the charge, as demonstrated by the presence of the “vertical” lines. We conclude that in this region the left dot contains zero electrons. Similarly, a disappearance of the “vertical” lines occurs in the lower right region, showing that here the right dot is empty. In the upper right region, the absence of lines shows that here the double dot is completely empty. We are now able to identify the exact charge configuration of the double dot in every honeycomb cell, by simply counting the number of “horizontal” and “vertical” lines that separate it from the 00 region. In Fig. 17b the first few honeycomb cells are labelled according to their charge configuration, with e.g. the label “21” meaning 2 electrons in the left dot and 1 on the right. Besides the dark lines, also short bright lines are visible, signifying a peak in dIQP C/dVL. These bright lines correspond to an electron being transferred from one dot to the other, with the total electron number remaining the same. (The fact that some charge transitions result in a dip in dIQP C/dVL and others in a peak, derives from the fact that we use the QPC on the right and apply
Semiconductor Few-Electron Quantum Dots as Spin Qubits 55 the modulation to the gate on the left. When an electron is pushed out of the double dot by making VL more negative, the QPC opens up and dIQP C/dVL displays a dip. When VL pushes an electron from the left to the right dot, the QPC is closed slightly, resulting in a peak.) The visibility of all lines in the honeycomb pattern demonstrates that the QPC is sufficiently sensitive to detect even inter-dot transitions. 2.5 Tunable Tunnel Barriers in the Few-Electron Regime In measurements of transport through lateral double quantum dots, the fewelectron regime has never been reached [47]. The problem is that the gates that are used to deplete the dots also strongly influence the tunnel barriers. Reducing the electron number would therefore always lead to the Coulomb peaks becoming unmeasurably small, but not necessarily due to an empty double dot. The QPC detectors now permit us to compare charge and transport measurements. Figure 18a shows the current through the double dot in the same region as showninFig.17b. In the bottom left region the gates are not very negative, hence the tunnel barriers are quite open. Here the resonant current at the charge transition points is quite high (∼100 pA, dark gray), and lines due to cotunnelling are also visible [47]. Towards the top right corner the gate voltages become more negative, thereby closing off the barriers and reducing the current peaks (lighter gray). The last “triple points” [47] that are visible (
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Lecture Notes in Physics Editorial
Page 3 and 4:
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
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
Page 49 and 50: ε1 ε0 e Semiconductor Few-Electro
Page 53 and 54: 250 Ω twisted pair 20 MΩ powder
Page 61 and 62: 10 5 0 -5 Semiconductor Few-Electro
Page 63: G ( e / h) 2 2 1 0 Semiconductor Fe
Page 67 and 68: V R (V) V R (V) Semiconductor Few-E
Page 69 and 70: V L (V) -1.084 -1.082 -1.080 -1.078
Page 71 and 72: B // Semiconductor Few-Electron Qua
Page 77 and 78: a RESERVOIR 200 nm Semiconductor Fe
Page 81 and 82: 4.5 QPC Versus SET Semiconductor Fe
Page 83 and 84: a reservoir dot Semiconductor Few-E
Page 85 and 86: a b c V P (mV) 10 5 0 ∆I QPC E F
Page 91 and 92: Spin-down counts 200 100 a Semicond
Page 101 and 102: 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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