shot noise in mesoscopic conductors - Low Temperature Laboratory

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46 Ya.M. Blanter, M. Bu( ttiker / Physics Reports 336 (2000) 1}166 Fig. 11. Shot noise measurements by Henny et al. [81] on three di!erent samples. The lower solid line is the -suppression, the upper line is the hot-electron result F"3/4 (see Section 6). The samples (b) and (c) are short, and clearly display -suppression. The sample (a) is longer (has lower resistance), and the shot noise deviates from the non-interacting suppression value due to inelastic processes. Copyright 1999 by the American Physical Society. yields the Fano factor F" 1 4 ¸ # . (90) 3 45 N l The second terms represent weak localization corrections (¸;N l). These expressions are valid for the case of preserved time-reversal symmetry (orthogonal symmetry). In the case of broken time-reversal symmetry (unitary symmetry; technically, this means that a weak magnetic "eld is applied) weak localization corrections are absent and the Fano factor stays at . Thus, we see that weak localization e!ects suppress noise, but enhance the Fano factor, in agreement with the general expectation that it lies above in the localized regime. The crossover from the metallic to the localized regime for shot noise has not been investigated. De Jong and Beenakker [82], Mace( do [83], and Mace( do and Chalker [84] studied also mesoscopic #uctuations of shot noise, which are an analog of the universal conductance #uctuations. For the root mean square of the shot noise power, they found r.m.s. S" e< 46 2835 , where the parameter equals 1 and 2 for the orthogonal and unitary symmetry, respectively. These #uctuations are independent of the number of transverse channels, length of the wire, or degree of disorder, and may be called [82] `universal noise #uctuationsa. The picture which emerges is, therefore, that like the conductance, the ensemble-averaged shot noise is a classical quantity. Quantum e!ects in the shot noise manifest themselves only if This requires the knowledge of the joint distribution function of two transmission eigenvalues.
we include weak localization e!ects or if we ask about #uctuations away from the average. With these results it is thus no longer surprising that the noise suppression factor derived quantum mechanically and from a classical Boltzmann equation for the #uctuating distribution are in fact the same. The same picture holds of course not only for metallic di!usive wires but whenever we ensemble average. We have already discussed this for the resonant double barrier and below will learn this very same lesson again for chaotic cavities. Chiral symmetry. Mudry et al. [86,87] studied the transport properties of disordered wires with chiral symmetry (i.e. when the system consists of two or several sublattices, and only transitions between di!erent sublattices are allowed). Examples of these models include tight-binding hopping models with disorder or the random magnetic #ux problem. Chiral models exhibit properties usually di!erent from those of standard disordered wires, for instance, the conductance at the band center scales not exponentially with the length of the wire ¸, but rather as a power law [88]. Ref. [87], however, "nds that in the di!usive regime (l;¸;N l) the Fano factor equals precisely , like for ordinary symmetry. The only feature which appears due to the chiral symmetry is the absence of weak localization corrections in the zero order in N . Weak localization corrections, both for conductance and shot noise, scale as ¸/(lN ) and discriminate between chiral unitary and chiral orthogonal symmetries. Transition to the ballistic regime. In the zero-temperature limit, a perfect wire does not exhibit shot noise. For this reason, one should anticipate that in the ballistic regime, l'¸, shot noise is suppressed below . The crossover between metallic and ballistic regimes in disordered wires was studied by de Jong and Beenakker [82] (see their Eq. (A.10)), who found for the noise suppression factor F" 1 31! 1 . (91) (1#¸/l) It, indeed, interpolates between F" for l;¸ and F"0 for ¸
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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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