Universal Conductance and Conductivity at Critical Points in Integer Quantum Hall Systems

TL;DR

This paper calculates the universal conductance and conductivity at quantum critical points in integer quantum Hall systems, revealing values around 0.6 e^2/h that challenge previous beliefs of 0.5 e^2/h, and linking these to wavefunction multifractality.

Contribution

It provides numerical evidence for the universality of conductance at quantum Hall critical points and highlights the role of wavefunction multifractality in determining these values.

Findings

Conductance and conductivity are approximately 0.6 e^2/h at critical points.

These values differ from the traditionally assumed 0.5 e^2/h.

Multifractal wavefunctions influence the critical conductance values.

Abstract

The sample averaged longitudinal two-terminal conductance and the respective Kubo-conductivity are calculated at quantum critical points in the integer quantum Hall regime. In the limit of large system size, both transport quantities are found to be the same within numerical uncertainty in the lowest Landau band, $0.60\pm 0.02 e^2/h$ and $0.58\pm 0.03 e^2/h$, respectively. In the 2nd lowest Landau band, a critical conductance $0.61\pm 0.03 e^2/h$ is obtained which indeed supports the notion of universality. However, these numbers are significantly at variance with the hitherto commonly believed value $1/2 e^2/h$. We argue that this difference is due to the multifractal structure of critical wavefunctions, a property that should generically show up in the conductance at quantum critical points.