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1 High order moments of shot noise in mesoscopic systems Michael Reznikov, Technion Experiment: G. Gershon, Y. Bomze, D. Shovkun Theory: E. Sukhorukov Whether noise is noisence or signal may depend on whom you ask

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2 Classical Shot Noise f t ffff I S( )

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3 Noise in mesoscopic systems scattering approach Khlus (1987), Lesovik (1989), Yurke and Kochansky (1989)

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Magnetic Field (T) J. Smet, V. Umansky R xy (h/e 2 ) R xx (k ) Fractional Quantum Hall Effect - Experimental Results

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5 The QPC

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Expected Noise….. (intuitively) = 1/3 e/3 q = e ; whole electrons q = e/3 ; quasi particles quasi particles partition whole electrons partition e partitioning barrier Both, e or e /3 lead to the same conductance ! t t

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Quantum Shot Noise in QPC - Experimental Results - 0 2 4 6 0123 Current Noise, S i (10 -28 A 2 /Hz) T=57 mK =0.37 I Total Current (nA)

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n s =1.1x10 11 cm -2 ; B=13 T Current Noise Measurements at bulk preamp noise subtracted calibration at each point averaging time 4 s Lesovik’s formula, q=e/3 I=tVg 0 /3 See also : Saminadayar et. al. 1997 Current Noise, S [10 -29 A 2 /Hz] Back-scattered Current, I r [pA] I r =V(g 0 /3-g)

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Quantum Shot Noise at =2/5 - Weak Back Scattering - Current Noise, S [10 -30 A 2 /Hz] Conductance, g/g 0 Back-Scattered Current, I r [pA] B =2/5 t=0.86 T=85 mK e/3 e/5 =2/5 q=e/5 ! I r =V(2g 0 /5-g)

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10 High-order cumulants - motivation

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11 Photon counting statistics Glauber, 1963

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12 Is this what is really measured? At least not always S(ω)! Lesovik, Loosen (1997)

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13 Naïve calculations a b 1

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14 Naïve calculations For ~0 does not reproduce Poisson result q 3 =g 0 V =eI ! 1

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15 “Gentle” electron counting Spin 1/2 as a galvanometer Spin 1/2 as a galvanometer L.S. Levitov and G.B. Lesovik (1993) L.S. Levitov and H. Lee (1996)

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16 “Gentle” electron counting Spin 1/2 as a galvanometer Spin 1/2 as a galvanometer L.S. Levitov and G.B. Lesovik (1993) L.S. Levitov, H. Lee, G. Lesovik (1996) U=eV/T

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17 Gaussian vs. Poisson distributions n=20 In our measurements n~1000

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18 The PDF output voltage counts Typically 1000 electrons during 30 ns

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19 Intrinsic cumulants for a single channel conductor 0.5) Khlus (1987), Lesovik (1989), Yurke and Kochansky (1989) L.S. Levitov and G.B. Lesovik (1993) L.S. Levitov and H. Lee (1996)

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20 Experimental results from Yale B. Reulet, J. Senzier and D. E. Prober, 2002

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21 and in QPC Filling factor =4 T=4.2 K 0.3

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22 How to measure? Opening and closing of the barrier I. Klich, 2001 V0V0V0V0 Z sample V Rl Rl Rl Rl CV CV CV CV C st C st What is actually measured? 1

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23 Z s >>Z l – voltage bias V0V0V0V0 Z sample V Rl Rl Rl Rl CV CV CV CV C st C st K. Nagaev – cascade corrections Kindermann, Nazarov, Beenakker (2002)

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24 Z s <

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25 General case for a tunneling junction <<1, T<

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26 and in QPC Filling factor =4 T=4.2 K 0.3

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27 Experimental Setup I VgVg QPC N RlRl CvCv Low temperature C st CcCc Network analyzer A/D

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28 In the Tunneling Junction

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29 “Intrinsic” contribution tt3t3 t2t2 t1t1 J(t) A(t) “Intrinsic” (constant voltage) contribution

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30 Corrections, “environmental” and nonlinear t2t2 t1t1 t J(t) A(t)Z(t)

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31 Environmental correction is not small! If we ignore peculiarities of the circuit -mostly determined by the load thermal noise Not small even when R ! 0

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32 QPC characterization T=1.5K

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33 QPC ~0.3

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34 Two different amplifiers

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36 Calculation of the statistics T-ordering is to put q(0) to the right of q(t) Using e.g. wave packet approach one can get the statistics (Levitov, Lesovik, 1993)

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37 How to express it through the integral of the currents (Bachman, Graf, Lesovik, 2009) Consider a slightly different object Properties: Q 3 =0 if one of t i =0. Therefore it can be expressed as: Time ordering is crucial to ensure Q3=0 for t i =0 !!!

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38 “Contact” terms Differentiation ovet t 1 would generate 2 more -functions, provided [q,j] 0. So, there are additions to the term accounted for in naïve calculations: h j(t 1 ) j(t 2 ) j(t 3 ) i

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39 My favorable choice of j a 1 b L Compare with:

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40 Conclusions and questions Prediction for > in QPC is verified Effect of interactions on >. Charge statistics under FQHE? Charge statistics in HT C superconductors > in diffusive systems with interactions Frequency dependence of >.

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41 Setup in dilution fridge

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Markus Büttiker University of Geneva The Capri Spring School on Transport in Nanostructures April 3-7, 2006 Scattering Theory of Conductance and Shot Noise.

Markus Büttiker University of Geneva The Capri Spring School on Transport in Nanostructures April 3-7, 2006 Scattering Theory of Conductance and Shot Noise.

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