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

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64 J.M. Elzerman et al. lock-in signal (arb. units) b E F a c B // =10T -1.135 VM (V) -1.150 ES Γ GS b N =1 N =0 10 V P (mV) 1 f = 385 Hz -1.13 -1.15 c N =1 Γ eff V M (V) ∆E Z d N =0 Fig. 23. Excited-state spectroscopy in a one-electron dot. (a) Lock-in signal at f = 385 Hz versus VM ,withVP = 6 mV. The dip is half the maximum value (obtained at low f and small VP ) from which we conclude that Γ ≈ 2.4kHz. (b) Schematic electrochemical potential diagrams for the case that only the GS is pulsed across EF .(c) IdemwhenboththeGSandanESarepulsedacrossEF .(d) Derivative of the lock-in signal with respect to VM , plotted as a function of VM and VP (individual traces have been lined up to compensate for a fluctuating offset charge). The curve in (a) is taken at the dotted line. The Zeeman energy splitting between the one-electron GS (spin-up) and first ES (spin-down) is indicated by ∆EZ to determine independently the conversion factor between gate voltage and energy in this regime of a nearly closed quantum dot. Instead we take the measured Zeeman splitting from an earlier transport measurement [54] and deduce the conversion factor from gate voltage to energy, α = 105 meV/V. This value will be used below, to convert the two-electron data to energy. 3.4 Excited-State Spectroscopy for N =2 Figure 24a shows pulse spectroscopy data for the one-to-two electron transition, taken with the gate settings indicated by ⋄ in Fig. 22b. The rightmost vertical line corresponds to transitions between the one-electron GS (spinup) and the two-electron GS (spin singlet) only. As VP is increased above 5 mV, the two-electron ES (spin triplet) also becomes accessible, leading to an enhanced tunnel rate 2 . This gives rise to the left vertical line, and the distance between the two vertical lines corresponds to the singlet-triplet energy splitting ∆EST. Converted to energy, we obtain ∆EST =0.49 meV. 2 The expected Zeeman splitting of the triplet state is not resolved here.
Semiconductor Few-Electron Quantum Dots as Spin Qubits 65 10 ∆E ST V P (mV) c 1 E F N =2 N =1 N =2 N =1 f = 385 Hz -1.160 V -1.175 M (V) ↔S ↔S Γ a b f = 1.538 kHz -1.160 V -1.175 M (V) d Γ eff Fig. 24. Excited state spectroscopy in a two-electron dot. (a) Similar to Fig. 23d, but for the one-to-two electron transition. Again, f = 385 Hz. We clearly observe the singlet-triplet splitting ∆EST (individual traces in (a) and(b) have been lined up). (b) Same experiment but with f =1.538 kHz, which increases the contrast for excited states. An extra slanted line appears (arrow), corresponding to the N =1ES, spin-down. (c) Schematic electrochemical potential diagram for the case that only the spin-down electron can leave from the two-electron GS (spin singlet). This occurs to the left of the bright line indicated by the arrow in (b). (d) Idem when either the spin-up or the spin-down electron can leave from the spin singlet. This occurs to the right of the arrow in (b), and leads to a larger effective tunnel rate Excitations of the one-electron dot can be made visible at the one-totwo electron transition as well, by changing the pulse frequency to 1.538 kHz (Fig. 24b). This is too fast for electrons to tunnel if only the GS is accessible, so the rightmost line almost vanishes. However, a second slanted line becomes visible (indicated by the arrow in Fig. 24b), corresponding not to an increased tunnel rate into the dot (due to an N = 2 ES), but to an increased tunnel rate out of the dot (due to an N = 1 ES). Specifically, if the pulse amplitude is sufficiently large, either the spin-up or the spin-down electron can tunnel out of the two-electron dot. This is explained schematically in Fig. 24c and d. Similar experiments at the transition between two and three electrons, and for tunnel rates to the reservoir ranging from 12 Hz to 12 kHz, yield similar excitation spectra. The experiments described in this section demonstrate that an electrometer such as a QPC can reveal not only the charge state of a quantum dot, but also its tunnel coupling to the outside world and the energy level spectrum of
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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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Page 33 and 34: References RG for Interacting Fermi
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Page 63 and 64: G ( e / h) 2 2 1 0 Semiconductor Fe
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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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