Universal Statistics of Transport in Disordered Conductors

TL;DR

This paper analyzes the statistical distribution of charge transport in disordered conductors at low temperatures, revealing Gaussian peaks and non-Gaussian tails with significant sample-to-sample variations.

Contribution

It derives a universal expression for charge transmission distribution using random matrix theory, highlighting distinct behaviors in metallic regimes.

Findings

Gaussian peak in charge distribution with negligible sample variation

Non-Gaussian, non-Poisson tails with strong sample-to-sample variations

Universal statistical description applicable to disordered conductors

Abstract

In low temperature limit, we study electron counting statistics of a disordered conductor. We derive an expression for the distribution of charge transmitted over a finite time interval by using a result from the random matrix theory of quasi one dimensional disordered conductors. In the metallic regime, we find that the peak of the distribution is Gaussian and shows negligible sample to sample variations. We also find that the tails of the distribution are neither Gaussian nor Poisson and exhibit strong sample to sample variations.