Deviations from the Gaussian distribution of mesoscopic conductance fluctuations

TL;DR

This paper investigates how the conductance distribution in mesoscopic metallic systems deviates from Gaussian behavior by calculating the third cumulant, revealing dimension-dependent signs of deviation.

Contribution

It provides a diagrammatic calculation of the third cumulant, showing dimension-specific deviations from Gaussian conductance fluctuations.

Findings

Third cumulant vanishes in quasi-one dimension.

Negative third cumulant in quasi-two dimensions.

Positive third cumulant in three dimensions.

Abstract

The conductance distribution of metallic mesoscopic systems is considered. The variance of this distribution describes the universal conductance fluctuations, yielding a Gaussian distribution of the conductance. We calculate diagrammatically the third cumulant of this distribution, the leading deviation from the Gaussian. We confirm random matrix theory calculations that the leading contribution in quasi-one dimension vanishes. However, in quasi two dimensions the third cumulant is negative, whereas in three dimensions it is positive.