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On the Applicability of the Ergodicity Hypothesis to Mesoscopic Fluctuations

O. Tsyplyatyev·I. L. Aleiner·Vladimir I. Fal'ko·Igor V. Lerner
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Abstract

We evaluate a typical value of higher order cumulants (irreducible moments) of conductance fluctuations that could be extracted from magneto-conductance measurements in a single sample when an external magnetic field is swept over an interval $B_0$. We find that the n-th cumulant has a sample-dependent random part $\pm \gN 2^{n/2}\sqrt{a_{n}B_{c}/B_{0}}$, where $\gN 2$ is the variance of conductance fluctuations, $B_{c}$ is a correlation field, and $a_{n}\sim n!$. This means that an apparent deviation of the conductance distribution from a Gaussian shape, manifested by non-vanishing higher cumulants, can be a spurious result of correlations of conductances at different values of the magnetic field.

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O. Tsyplyatyev, I. L. Aleiner, Vladimir I. Fal'ko, Igor V. Lerner. 2003-06-24. On the Applicability of the Ergodicity Hypothesis to Mesoscopic Fluctuations. https://doi.org/10.1103/physrevb.68.121301

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