Frequency Dependent Electrical Transport in the Integer Quantum Hall Effect

TL;DR

This paper reviews the theoretical developments in the ac quantum Hall effect, focusing on numerical calculations of frequency-dependent conductivities and their scaling behavior at critical points.

Contribution

It provides detailed numerical approaches for calculating frequency-dependent conductivities and analyzes their scaling at the critical point in the quantum Hall effect.

Findings

Frequency scaling at the critical point analyzed

Frequency-dependent deviation of Hall conductivity quantified

Numerical methods for non-interacting electrons developed

Abstract

The status of the ac quantum Hall effect is reviewed with emphasis on the theoretical development in recent years. In particular, the numerical approaches for the calculation of the frequency dependent Hall and longitudinal conductivities of non-interacting electrons are considered in detail. Results for the frequency scaling at the critical point and for the frequency dependent deviation of the Hall conductivity from the quantised plateau value are presented.