shot noise in mesoscopic conductors - Low Temperature Laboratory

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136 Ya.M. Blanter, M. Bu( ttiker / Physics Reports 336 (2000) 1}166 barriers dominates, see below), and for high voltages is described by a Fano factor F"(R #R )/(R #R ) . (258) The result (258) is genuinely the double-barrier Fano factor (78), since R J¹. This high- voltage behavior was independently obtained by Hung and Wu [284] using the Green's function technique. Korotkov [281] also studied the frequency dependence of shot noise and found that it is a regular function, which for high frequencies (RC);;e/C, R"R #R, saturates at an interaction-dependent value. For the general case (Coulomb staircase regime), shot noise was (independently) analyzed by Hersh"eld et al. [283] using a master equation. In the plateau regimes, the transport is via the only state with a "xed number of electrons, and the shot noise is Poissonian (up to exponentially small corrections); in particular, for
Ya.M. Blanter, M. Bu( ttiker / Physics Reports 336 (2000) 1}166 137 Coulomb blockade regime; in particular, the Fano factor tends to zero for high frequencies. Though we cannot point out an explicit error in these papers, the results seem quite surprising to us. We believe that in the simple model of the Coulomb blockade, when the electrostatic energy is approximated by Q/2C, it is quite unlikely that the shot noise is suppressed below , which is the non-interacting suppression factor for the symmetric double-barrier structure. Clearly, to answer these questions, an analytic investigation, currently unavailable, is required. Experiments on shot noise in the Coulomb blockade regime were performed by Birk et al. [30]. They put a nanoparticle between the STM tip and metallic surface, and were able to change the capacitances C and C and resistances R and R .ForR "2R they found the `smootha Coulomb blockade I}< characteristics (no traces of the Coulomb staircase), with the noise crossing over from Poissonian to Eq. (258) with increasing voltage (Fig. 36, left). In contrast, for the very asymmetric case R ;R Birk et al. [30] observe the Coulomb staircase and periodic shot noise suppression below the Poisson value (Fig. 36, right). They compare their experimental data with the theory of Hersh"eld et al. [283] and "nd quantitative agreement. 7.1.3. Arrays of tunnel barriers Consider now a one-dimensional array of metallic grains separated by tunnel barriers. This array also shows Coulomb blockade features: The current is blocked below a certain threshold voltage < (typically higher than the threshold voltage for a single junction), determined by the parameters of the array. Just above < , the transport through the array is determined by a single junction (a bottleneck junction), and corresponds to the transfer of charge e. Thus, the shot noise close to the threshold is Poissonian, the Fano factor equals one. With increasing voltage more and more junctions are opened for transport, and eventually a collective state is established in the array [278]: An addition of an electron to the array causes the polarization of all the grains, such that the e!ective charge transferred throughout the array is e/N, with N
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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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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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arrier, situated in the region !w/2
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we include weak localization e!ects
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Edge channels in the quantum Hall e
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Fig. 19. (a) Geometry of a ring thr
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a manifestation of interference e!e
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Physically, this corresponds to ele
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Our starting point is Eq. (51), whi
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introducing the transmission coe$ci
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investigated experimentally. A self
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