Frequency dependent conductivity in the integer quantum Hall effect

TL;DR

This paper investigates how the ac-conductivity of a disordered two-dimensional electron system in a strong magnetic field varies with frequency, revealing linear imaginary part behavior and complex real part dependence, with implications for understanding quantum Hall transport.

Contribution

It provides numerical analysis of frequency-dependent conductivity in the integer quantum Hall regime, confirming analytical predictions and uncovering scaling relations for peak broadening.

Findings

Linear frequency dependence of the imaginary part of conductivity in the Landau tail.

Complex frequency dependence of the real part not fitting simple power laws.

Scaling relation for the broadening of the conductivity peak.

Abstract

Frequency dependent electronic transport is investigated for a two-dimensional disordered system in the presence of a strong perpendicular static magnetic field. The ac-conductivity is calculated numerically from Kubo's linear response theory using a recursive Green's function technique. In the tail of the lowest Landau band, we find a linear frequency dependence for the imaginary part of $\sigma_{xx}(\omega)$ which agrees well with earlier analytical calculations. On the other hand, the frequency dependence of the real part can not be expressed by a simple power law. The broadening of the $\sigma_{xx}$-peak with frequency in the lowest Landau band is found to exhibit a scaling relation from which the critical exponent can be extracted.