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

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.

7 pages, 4 postscript figures included. Revtex with epsf.tex and multicol.sty. The revised version contains some additional discussion of the theory and slightly improved numerical results

References in corpus (4)

• Critical Percolation in Finite Geometries
• Universal relation between longitudinal and transverse conductivities in quantum Hall effect
• Non-Universal Behavior of Finite Quantum Hall Systems as a Result of Weak Macroscopic Inhomogeneities
• Peak Values of Conductivity in Integer and Fractional Quantum Hall Effect

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• Universal scaling functions for bond percolation on planar random and square lattices with multiple percolating clusters
• The longitudinal resistance of a quantum Hall system with a density gradient
• Shape Effects of Finite-Size Scaling Functions for Anisotropic Three-Dimensional Ising Models
• Real-space renormalization-group approach to the integer quantum Hall effect
• Cluster Analysis of the Ising Model and Universal Finite-Size Scaling
• Edge States on a Quantum Hall Liquid--Solid Interface