Scaling Properties of Conductance at Integer Quantum Hall Plateau Transitions

TL;DR

This paper studies the scaling behavior of conductance at integer quantum Hall transitions, confirming a universal critical exponent and average conductance consistent with theoretical predictions.

Contribution

It provides numerical evidence for the universal scaling properties and conductance distribution at quantum Hall plateau transitions in a tight-binding model.

Findings

Critical exponent nu = 7/3 for conductance scaling

Average conductance at critical point <G>_c = 0.506 e^2/h

Conductance distribution is broad with a dip at small G

Abstract

We investigate the scaling properties of zero temperature conductances at integer quantum Hall plateau transitions in the lowest Landau band of a two-dimensional tight-binding model. Scaling is obeyed for all energy and system sizes with critical exponent nu =7/3 . The arithmetic average of the conductance at the localization-delocalization critical point is found to be <G>_c = 0.506 e^2 / h, in agreement with the universal longitudinal conductance predicted by an analytical theory. The probability distribution of the conductance at the critical point is broad with a dip at small G.