Crossover from diffusive to strongly localized regime in two-dimensional systems

TL;DR

This study investigates how the conductance distribution in two-dimensional disordered systems transitions from diffusive to localized behavior, revealing a critical point near conductance value one where the distribution shape changes abruptly.

Contribution

It provides the first detailed analysis of the conductance distribution crossover in 2D systems, confirming the single-parameter scaling hypothesis and identifying a sharp transition at a critical conductance.

Findings

Distribution is Gaussian for high conductance

Distribution becomes log-normal for low conductance

A critical point near conductance value one marks a sharp change

Abstract

We have studied the conductance distribution function of two-dimensional disordered noninteracting systems in the crossover regime between the diffusive and the localized phases. The distribution is entirely determined by the mean conductance, g, in agreement with the strong version of the single-parameter scaling hypothesis. The distribution seems to change drastically at a critical value very close to one. For conductances larger than this critical value, the distribution is roughly Gaussian while for smaller values it resembles a log-normal distribution. The two distributions match at the critical point with an often appreciable change in behavior. This matching implies a jump in the first derivative of the distribution which does not seem to disappear as system size increases. We have also studied 1/g corrections to the skewness to quantify the deviation of the distribution from a Gaussian function in the diffusive regime.