Statistical properties of the low-temperature conductance peak-heights for Corbino discs in the quantum Hall regime

TL;DR

This paper analyzes the statistical properties of low-temperature conductance peak-heights in Corbino discs within the quantum Hall regime, linking inhomogeneities and percolation theory to experimental observations.

Contribution

It introduces a statistical framework based on percolation theory to explain non-universal conductance peak-heights in quantum Hall systems with density inhomogeneities.

Findings

Provides a lower bound on conductance peak-heights

Connects critical percolation properties to experimental data

Highlights the role of density fluctuations in conductance behavior

Abstract

A recent theory has provided a possible explanation for the ``non-universal scaling'' of the low-temperature conductance (and conductivity) peak-heights of two-dimensional electron systems in the integer and fractional quantum Hall regimes. This explanation is based on the hypothesis that samples which show this behavior contain density inhomogeneities. Theory then relates the non-universal conductance peak-heights to the ``number of alternating percolation clusters'' of a continuum percolation model defined on the spatially-varying local carrier density. We discuss the statistical properties of the number of alternating percolation clusters for Corbino disc samples characterized by random density fluctuations which have a correlation length small compared to the sample size. This allows a determination of the statistical properties of the low-temperature conductance peak-heights of such samples. We focus on a range of filling fraction at the center of the plateau transition for which the percolation model may be considered to be critical. We appeal to conformal invariance of critical percolation and argue that the properties of interest are directly related to the corresponding quantities calculated numerically for bond-percolation on a cylinder. Our results allow a lower bound to be placed on the non-universal conductance peak-heights, and we compare these results with recent experimental measurements.