shot noise in mesoscopic conductors - Low Temperature Laboratory

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40 Ya.M. Blanter, M. Bu( ttiker / Physics Reports 336 (2000) 1}166 where N is the number of transverse channels, and we have taken into account ¹ ;1, ¹ ;1. The same calculation for the shot noise yields [56,1] S" e
arrier, situated in the region !w/2(z(w/2. We assume that there are resonant states which are randomly distributed inside the barrier and strongly localized. Applying the model suggested for this situation by Larkin and Matveev [62], we assume that these resonant states are provided by impurities inside the barrier; the localization radius of each state is denoted by , ;w. Transition rates are exponentially sensitive to the position of these impurities inside the barrier. In the regime of low impurity concentration, only those situated close to the center of the barrier contribute to the transport properties. Thus, the problem is e!ectively mapped onto a doublebarrier problem, where the impurity region near the center of the barrier serves as a potential well, and is separated by two `barriersa from the left and right reservoirs. The tunneling rates through these `barriersa to a resonant state depend on the position z of the impurity which provides this resonant state. We have [62] (z)" exp[$z/], z(w/2 . We have assumed that this amplitude is energy independent, and that impurities are uniformly distributed in energy and space. Thus, our expressions (76) and (77) hold, and must be averaged over impurity con"gurations. We write and I" e n dz 2 cosh(z/) S" 2e n dz cosh(2z/) 4 cosh(z/) , where n is the spatial concentration of impurities. By extending the integration to in"nity, we have taken into account ;w. Performing the average and calculating the Fano factor, we "nd [61] F" , Ya.M. Blanter, M. Bu( ttiker / Physics Reports 336 (2000) 1}166 41 which is markedly di!erent form the usual double-barrier suppression F" . The model can be generalized to include Coulomb correlations [63]. Imagine that each resonant center has two degenerate electron states available for tunneling, corresponding to two di!erent spin states. However, if one of the states is "lled, the other one is shifted up by the Coulomb energy ;. We assume that the Coulomb energy is very large, so that once one electron has tunneled, the tunneling of the second one is suppressed. Then the e!ective tunneling rate through the `lefta barrier is 2 (we assume that voltage is applied from left to the right), and instead of Eqs. (76) and (77) we write for the current [63] and shot noise power per spin [61] I" eN , S" 2 # 2eN (4#) . (2 # ) Averaging over impurity con"gurations and calculating the Fano factor, we "nd again F" [61]. This example concerns interacting systems, and is included in this section only as an exception.
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Ya.M. Blanter, M. Bu( ttiker / Phys
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with D ,¹ (2!¹ ). Performing t
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For completeness, we mention that i
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We note here, however, that there i
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The noise power (201) is strongly v
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Fig. 32. Experimental results of Ku
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where Ya.M. Blanter, M. Bu( ttiker
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where the quantity is expressed th
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6.3. Interaction ewects Ya.M. Blant
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one "rst goes from the non-interact
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non-thermalized electrons, the high
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Fig. 34. Geometry of the chaotic ca
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which describes strictly ballistic
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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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