Critical Conductance and Its Fluctuations at Integer Hall Plateau Transitions

TL;DR

This paper calculates the universal conductance and its fluctuations at the critical point of integer quantum Hall transitions, providing precise values and finite size scaling corrections, with implications for experimental verification.

Contribution

It presents the first detailed calculation of universal conductance and fluctuation values at the integer quantum Hall plateau transition, including finite size effects.

Findings

Universal average conductance of 0.58 e^2/h.

Specific fluctuation values for different moments.

Finite size scaling corrections to conductance and fluctuations.

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.