Critical Conductance and Its Fluctuations at Integer Hall Plateau Transitions

Abstract

Under periodic boundary condition in the transverse direction, we calculate the averaged zero-temperature two-terminal conductance ($<G>$) and its statistical fluctuations ($<(\dg)^{2n}>$ for $n\le 4$) at the critical point of integer quantum Hall plateau transitions. We find {\it universal} values for $<G>=(0.58\pm0.03){e^2\over h}$, and $<(\dg)^{2n}>=({e^2\over h})^{2n}A_{2n}$, where $A_{2,4,6,8}=0.081\pm0.005$; $0.013\pm0.003$; $0.0026\pm0.005$; and $(8\pm2)\times10^{-4}$ respectively. We also determine the leading finite size scaling corrections to these observables. Comparisons with experiments will be made.