Statistical properties of the low-temperature conductance peak heights for Corbino disks in the quantum Hall regime
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.
Physical Review B
- Pub Date:
- February 1997
- Condensed Matter - Mesoscopic Systems and Quantum Hall Effect
- 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