Conductance distribution between Hall plateaus

TL;DR

This paper investigates mesoscopic conductance fluctuations in a 2D electron gas under magnetic fields, revealing characteristic distributions that align with recent experimental observations.

Contribution

It provides a detailed analysis of conductance and resistance distributions between Hall plateaus using a realistic model, highlighting their shapes and peaks.

Findings

Conductance distribution $P(g)$ is concave between 0 and 1.

Distribution peaks sharply near $g=0$ and $g=1$.

Resistance distributions have a central peak with large width.

Abstract

Mesoscopic fluctuations of two-port conductance and four-port resistance between Hall plateaus are studied within a realistic model for a two-dimensional electron gas in a perpendicular magnetic field and a smooth disordered potential. The two-port conductance distribution $P(g)$ is concave between $g=0$ and $g=1$ and is nearly flat between $g=0.2$ and $g=0.8$. These characteristics are consistent with recent observations. The distribution is found to be sharply peaked near the end-points $g=0$ and $g=1$. The distribution functions for the three independent resistances in a four-port Hall bar geometry are, on the other hand, characterized by a central peak and a relatively large width.