shot noise in mesoscopic conductors - Low Temperature Laboratory

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84 Ya.M. Blanter, M. Bu( ttiker / Physics Reports 336 (2000) 1}166 where K,(C#eN #eN ) plays the role of an e!ective interaction which determines the change in the electrostatic potential inside the conductor in response to a variation of the charge inside the conductor. In the following, we are only interested in the #uctuations of the current through the gate. For this quantity, which vanishes for zero frequency, we obtain S "CK[S#S#S#S] . (147) We note that the sum of all the current #uctuation spectra in Eq. (147) is just the #uctuation spectrum of the total charge on the conductor: The continuity equation gives [98] IK ()"ieNK () where NK is the operator of the charge in the mesoscopic conductor. From the current operator, Eq. (43), we obtain NK (t)" e 2 dE dEea( (E)N (E, E)a( (E) , (148) with the non-diagonal density of states elements N N(E, E)" 1 2i(E!E) ! s (E)s (E) , (149) _ _ or in matrix notation N "(1/2i) A (, E, E#) with the current matrix A (, E, E) given by Eq. (44). Thus, instead of Eq. (147) we can also express the #uctuation spectrum of the current at the gate in terms of the charge #uctuation spectrum S "eCKS , (150) with S ()" e 2 dE N(E, E#)N(E#, E) f (E)[1!f (E#)]#[1!f (E)] f (E#) . (151) Eq. (151) is, in the absence of interactions, the general #uctuation spectrum of the charge on a mesoscopic conductor. In the zero-temperature limit, we obtain [98] R #R (e
and the non-equilibrium resistance is Ya.M. Blanter, M. Bu( ttiker / Physics Reports 336 (2000) 1}166 85 R " 2 e Tr(N N ) Tr N , (155) with the notation N " 1 2i Rs s RE . It can be checked easily that equilibrium noise, S "2CR , satis"es the #uctuation- dissipation theorem. The resistance R can be extracted from the ac conductance as well. However, non-equilibrium noise is described by another resistance, R , which is a new quantity. It probes directly the non-diagonal density of states elements N of the charge operator. The non-diagonal density of states elements which describe the charge #uctuations in a conductor in the presence of shot noise can be viewed as the density of states that is associated with a simultaneous current amplitude at contact and contact , regardless through which contact the carriers leave the sample. These density of states can be also viewed as blocks of the Wigner}Smith time delay matrix (2i)s ds/dE. For a saddle-point quantum point contact the resistances R and R are evaluated in Ref. [98]. In the presence of a magnetic "eld R has been calculated for a saddle-point model by one of the authors and Martin [166], and is shown in Fig. 26. For a chaotic cavity connected to two single channel leads both resistances are random quantities, for which the whole distribution function is known [98]. Thus, the resistance R (in units of 2/e) assumes values between and , with the average of (orthogonal symmetry) or (unitary symmetry). The resistance R lies in the interval between 0 and , and is on average and for orthogonal and unitary symmetry, respectively. Fig. 26. R (solid line, in units of 2/e) and the conductance G (dashed line, in units of e/2) as a function of E !< for a saddle point QPC with / "1 and / "4, is the cyclotron frequency. After Ref. [166]. Copyright 2000 by the American Physical Society.
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Ya.M. Blanter, M. BuK ttiker / Phys
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8. Concluding remarks, future prosp
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text; they are usually extensions o
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such reviews are not readily availa
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Ya.M. Blanter, M. Bu( ttiker / Phys
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The above considerations are, of co
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and the initial state of our two-pa
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2.3.3. Multi-terminal case We consi
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Note that in the absence of time-de
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equilibrium and shot noise. For low
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approximately e/C. Between the peak
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Boltzmann}Langevin approach (see Se
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thermal to shot noise. It is, howev
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Note added in proof Ya.M. Blanter,
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and Lee et al. [340] obtain in this
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