Anomalous Frequency-Dependent Conductivity near the Quantum Hall Transition

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 ω and low temperature near the ν=1 filling factor Hall transition, with the observation of an unusual broadening and an overall increase of the longitudinal conductivity Re{σxx} as a function of ω. We find in our approach that, unlike for normal metals, the longitudinal conductivity increases as the frequency increases, while the width ΔB (or Δν) of the conductivity peak near the Hall transition increases. These findings are in reasonable quantitative agreement with recent experiments by Engel et al. [Phys. Rev. Lett. 71, 2638 (1993)], as well as with recent numerical work by Avishai and Luck (cond-mat/9609265).