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 ''nonunive rsal scaling'' of the low-temperature conductance (and conductivity) p eak heights of two-dimensional electron systems in the integer and fra ctional quantum Hall regimes. This explanation is based on the hypothe sis that samples that show this behavior contain density inhomogeneiti es. Theory then relates the nonuniversal conductance peak heights to t he ''number of alternating percolation clusters'' of a continuum perco lation model defined on the spatially varying local carrier density. W e discuss the statistical properties of the number of alternating perc olation clusters for Corbino disk samples characterized by random dens ity 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 f ocus on a range of filling fraction at the center of the plateau trans ition 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 correspond ing quantities calculated numerically for bond percolation on a cylind er. Our results allow a lower bound to be placed on the nonuniversal c onductance peak heights, and we compare these results with recent expe rimental measurements.