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

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52 J.M. Elzerman et al. 2.3 Quantum Point Contact as Charge Detector As an alternative to measuring the current through the quantum dot, we can also measure the charge on the dot using one of the QPCs [44, 45]. To demonstrate this functionality, we first define only the left dot (by grounding gates R and PR), and use the left QPC as a charge detector. The QPC is formed by applying negative voltages to Q − L and L. This creates a narrow constriction in the 2DEG, with a conductance, G, that is quantized when sweeping the gate voltage VQ−L. The last plateau (at G =2e 2 /h) and the transition to complete pinch-off (i.e. G =0)areshowninFig.16b. We tune the QPC to the steepest point (G ≈ e 2 /h), where the QPC-conductance has a maximum sensitivity to changes in the electrostatic environment, including changes in the charge of the nearby quantum dot. To change the number of electrons in the left dot, we make gate voltage VM more negative (see Fig. 16c). This reduces the QPC current, due to the capacitive coupling from gate M to the QPC constriction. In addition, the changing gate voltage periodically pushes an electron out of the dot. The associated sudden change in charge lifts the electrostatic potential at the QPC constriction, resulting in a step-like feature in IQP C (see the expansion in Fig. 16c, where the linear background is subtracted). This step indicates a change in the electron number. So, even without passing current through the dot, IQP C provides information about the charge on the dot. To enhance the charge sensitivity we apply a small modulation (0.3 mV at 17.7 Hz) to VM and use lock-in detection to measure dIQP C/dVM [45]. The steps in IQP C now appear as dips in dIQP C/dVM . Figure 16d shows the resulting dips, as well as the corresponding Coulomb peaks measured in the current through the dot. The coincidence of the Coulomb peaks and dips demonstrates that the QPC indeed functions as a charge detector. From the height of the step in Fig. 16c (∼50 pA, typically 1–2% of the total current) compared to the noise (∼5 pA for a measurement time of 100 ms), we estimate the sensitivity of the charge detector to be about 0.1e, with e being the single electron charge. The unique advantage of QPC charge detection is that it provides a signal even when the tunnel barriers of the dot are so opaque that IDOT is too small to be measured [44, 45]. This allows us to study quantum dots even when they are virtually isolated from the reservoirs. 2.4 Double Dot Charge Stability Diagram The QPC can also detect changes in the charge configuration of the double dot. To demonstrate this, we use the QPC on the right to measure dIQP C/dVL versus VL and VPR (Fig. 17a), where VL controls (mainly) the number of electrons on the left dot, and VPR (mainly) that on the right. Dark lines in the figure signify a dip in dIQP C/dVL, corresponding to a change in the total number of electrons on the double dot. Together these lines form the so-called “honeycomb diagram” [46, 47]. The almost-horizontal lines correspond to a
G ( e / h) 2 2 1 0 Semiconductor Few-Electron Quantum Dots as Spin Qubits 53 a drain1 T source2 Q-L source1 b I DOT I QPC L M R P L -0.50 -0.55 -0.60 -0.65 V Q-L (V) P R I QPC 200 nm Q-R drain2 I QPC (nA) I DOT (pA) QPC M dI / dV (arb. units) 5 4 3 -1.25 -1.30 -1.35 -1.40 30 0 c d V M (V) transport QPC -1.25 -1.30 -1.35 -1.40 V M (V) Fig. 16. Operating the QPC as a charge detector of a single dot. (a) Scanning electron microscope image of the device, showing metallic surface gates (light gray) on top of a GaAs/AlGaAs heterostructure (dark gray). The device contains a 2DEG 90 nm below the surface, with an electron density of 2.9 × 10 11 cm −2 . White dotted circles indicate the two quantum dots, white arrows show the possible current paths. A bias voltage, VDOT , can be applied between source 2 and drain 1, leading to current through the dot(s), IDOT .Abiasvoltage,VSD1 (VSD2), between source 1 (source 2) and drain 1 (drain 2), yields a current, IQP C through the left (right) QPC. (b) Conductance, G, of the left QPC versus gate voltage, VQ−L, showing the last quantized plateau (at G =2e 2 /h) and the transition to complete pinch-off (G = 0). The QPC is set to the point of highest charge sensitivity, at G ≈ e 2 /h (indicated by the dashed cross). (c) Current through the left QPC, IQP C, versus left-dot gate voltage, VM , with VSD1 = 250µV and VSD2 = VDOT = 0. Steps indicated by arrows correspond to changes in the number of electrons on the left dot. Encircled inset: the last step (∼50 pA high), with the linear background subtracted. (d) Upper panel: Coulomb peaks measured in transport current through the left dot, with VDOT = 100 µV andVSD1 = VSD2 =0.Lower panel: changes in the number of electrons on the left dot measured with the left QPC, with VSD1 =250µV and VSD2 = VDOT =0)
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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 ...
Page 11 and 12: 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
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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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Page 53 and 54: 250 Ω twisted pair 20 MΩ powder
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158 C.W.J. Beenakker its momentum).
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