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

N. R. Cooper, B. I. Halperin, Chin-Kun Hu, and I. M. Ruzin
Phys. Rev. B 55, 4551 – Published 15 February 1997
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Abstract

A recent theory has provided a possible explanation for the ``nonuniversal 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 that show this behavior contain density inhomogeneities. Theory then relates the nonuniversal 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 disk samples characterized by random density fluctuations that 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 nonuniversal conductance peak heights, and we compare these results with recent experimental measurements.

    DOI:https://doi.org/10.1103/PhysRevB.55.4551

    ©1997 American Physical Society

    Authors & Affiliations

    N. R. Cooper

    • Institut Laue-Langevin, Boite Postale 156, 38042 Grenoble, Cedex 9, France

    B. I. Halperin

    • Department of Physics, Harvard University, Cambridge, Massachusetts 02138

    Chin-Kun Hu

    • Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan

    I. M. Ruzin

    • Department of Molecular and Microbiology, Tufts University, Boston, Massachusetts 02111

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    Issue

    Vol. 55, Iss. 7 — 15 February 1997

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