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

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68 J.M. Elzerman et al. home-built as well. The IV-convertor is based on a dual low-noise JFET (Interfet 3602). Finally, the signal is AC-coupled to an 8th-order elliptic low-pass filter (SRS650), and the current fluctuations, ∆I, are digitized at 2.2 × 10 6 14-bit samples per second (ADwin Gold). The measurement bandwidth is limited by the low-pass filter formed by the capacitance of the line and Cu-powder filters, CL ≈ 1.5 nF, and the input impedance of the IV-convertor, Ri = RFB/A. Thermal noise considerations (below) impose RFB = 10 MΩ. We choose the amplifier gain A = 10000, such that 1/(2πRiCL) ≈ 100 kHz. The bandwidth of the amplifier inside the IVconvertor is 500 kHz, and the output ISO-amp bandwidth is 300 kHz. However, we shall see that the true limitation to measurement speed is not the bandwidth but the signal-to-noise ratio. 4.3 Sensitivity and Speed The measured signal corresponding to a single electron charge on the dot amounts to ∆I ≈ 0.3 nA with the QPC biased at Vi = 1 mV, a 1% change in the overall current I (I ≈ 30 nA, consistent with the series resistance of RQ, Ri = 1 kΩ and the resistance of the Ohmic contacts of about 2 kΩ). Naturally, the signal strength is proportional to Vi, but we found that for Vi ≥ 1mV,the dot occupation was affected, possibly due to heating. We therefore proceed with the analysis using I =30nAand∆I =0.3nA. The most relevant noise sources [62] are indicated in the schematic of Fig. 25b. In Table 1, we give an expression and value for each noise contribution in terms of rms current at the IV-convertor input, so it can be compared directly to the signal, ∆I. We also give the corresponding value for the rms charge noise on the quantum dot. Shot noise, ISN, is intrinsic to the QPC and therefore unavoidable. Both ISN and ∆I are zero at QPC transmission T =0orT = 1, and maximal at T =1/2; here we use T ≤ 1/2. The effect of thermal noise, VT , can be kept small compared to other noise sources by Table 1. Contributions to the noise current at the IV-convertor input. By dividing the noise current by 300 pA (the signal corresponding to one electron charge leaving the dot), we obtain the rms charge noise on the dot RMS Noise Current Noise Source Expression A/ RMS Charge Noise √ Hz e/ √ Hz ISN � T (1 − T )2eI −15 49 × 10 1.6 × 10 −4 � 4kBT/RFB −15 41 × 10 1.4 × 10 −4 VT VA 1+j2πfRQCL VA RQ VA, lowf VA/RFB 32 × 10 −15 1.1 × 10 −4 VA, highf VA2πfCL 7.5 × 10 −18 f 2.5 × 10 −8 f IA IA – –
Semiconductor Few-Electron Quantum Dots as Spin Qubits 69 choosing RFB sufficiently large; here RFB = 10 MΩ. The JFET input voltage noise is measured to be VA =0.8 nV/ √ Hz. As a result of VA, itisasifanoise current flows from the IV-convertor input leg to ground, through the QPC in parallel with the line capacitance. Due to the capacitance, CL, the rms noise current resulting from VA increases with frequency; it equals ∆I at 120 kHz. There is no specification available for the JFET input current noise, IA, but usually IA is small in JFETs. We summarize the expected noise spectrum in Fig. 25c, and compare this with the measured noise spectrum in the same figure. For a 300 pF reference load, the noise level measured below a few kHz is 52 fA/ √ Hz, close to the noise current due to VT , as expected; at high frequencies, the measured noise level is significantly higher than would be caused by VA in combination with the 300 pF load, and appears to be dominated by IA. With the sample connected, we observe substantial 1/f 2 noise (1/f in the noise amplitude), presumably from spurious charge fluctuations near the QPC, as well as interference at various frequencies. Near 100 kHz, the spectrum starts to roll off because of the 100 kHz low-pass filter formed by CL =1.5nF and Ri = 1 kΩ (for the reference load, CL is only 300 pF so the filter cut-off is at 500 kHz). From the data, we see that the measured charge noise integrated from DC is comparable to e at 80 kHz, and 2.5 times smaller than e around 40 kHz. We set the cut-off frequency of the external low-pass filter at 40 kHz, so we should see clear steps in time traces of the QPC current, corresponding to single electrons tunnelling on or off the dot. 4.4 Real-Time Single Electron Tunnelling We test this experimentally, in the regime where the electrochemical potential in the dot is nearly lined up with the electrochemical potential in the reservoir. The electron can then spontaneously tunnel back and forth between the dot and the reservoir, and the QPC current should exhibit a random telegraph signal (RTS). This is indeed what we observe experimentally (Fig. 26). In order to ascertain that the RTS really originates from electron tunnel events between the dot and the reservoir, we verify that (1) the dot potential relative to the Fermi level determines the fraction of the time an electron resides in the dot (Fig. 26a) and (2) the dot-reservoir tunnel barrier sets the RTS frequency (Fig. 26b). The shortest steps that clearly reach above the noise level are about 8 µs long. This is consistent with the 40 kHz filter frequency, which permits a rise time of 8 µs. Next, we induce tunnel events by pulsing the dot potential, so N predictably changes from 0 to 1 and back to 0. The response of the QPC current to such a pulse contains two contributions (Fig. 27a). First, the shape of the pulse is reflected in ∆I, as the pulse gate couples capacitively to the QPC. Second, some time after the pulse is started, an electron tunnels into the dot and ∆I goes down by about 300 pA. Similarly, ∆I goes up by 300 pA when an electron leaves the dot, some time after the pulse ends. We observe that
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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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Page 29 and 30: � p � dθp = g 2π RG for Inter
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Page 33 and 34: References RG for Interacting Fermi
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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
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Page 63 and 64: 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
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Page 77: a RESERVOIR 200 nm Semiconductor Fe
Page 81 and 82: 4.5 QPC Versus SET Semiconductor Fe
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128 M. Pustilnik and L.I. Glazman 1
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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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