Anomalous Frequency-Dependent Conductivity near the Quantum Hall Transition

TL;DR

This paper investigates the frequency-dependent conductivity near the quantum Hall transition using a Dirac fermion model, revealing unique increasing behavior with frequency and broadening of the conductivity peak, aligning with experimental and numerical results.

Contribution

It introduces a Dirac fermion approach to analyze dynamical transport near the quantum Hall transition, highlighting anomalous frequency dependence not seen in normal metals.

Findings

Longitudinal conductivity increases with frequency.

The width of the conductivity peak broadens near the transition.

Results agree with recent experiments and numerical studies.

Abstract

The dynamical transport properties near the integer quantum Hall transition are investigated at zero temperature by means of the Dirac fermion approach. These properties have been studied experimentally at low frequency omega and low temperature near the nu=1 filling factor Hall transition, with the observation of an anusual broadening and an overall increase of the longitudinal conductivity Re sigma_{xx} as a function of omega. We find in our approach that, unlike for normal metals, the longitudinal conductivity increases as the frequency increases, whilst the width Delta B (or Delta nu) of the conductivity peak near the Hall transition increases. These findings are in reasonable quantitative agreement with recent experiments by Engel et al. as well as with recent numerical work by Avishai and Luck.