Optical Hall conductivity in ordinary and graphene QHE systems

TL;DR

This study numerically demonstrates that the optical Hall conductivity retains Hall plateaus in the ac regime for both ordinary 2D electron gases and graphene, with robustness against disorder and potential for experimental detection via Faraday rotation.

Contribution

It reveals the persistence of Hall plateaus in optical frequencies and links the behavior to Landau level structure and localization effects, extending understanding of quantum Hall systems.

Findings

Hall plateaus persist in ac regime in both systems

Plateau height is not quantized in ac

Robustness against disorder due to localization

Abstract

We have revealed from a numerical study that the optical Hall conductivity $\sigma_{xy}(\omega)$ has a characteristic feature even in the ac ($\sim$ THz) regime in that the Hall plateaus are retained both in the ordinary two-dimensional electron gas and in graphene in the quantum Hall (QHE) regime, although the plateau height is no longer quantized in ac. In graphene $\sigma_{xy}(\omega)$ reflects the unusual Landau level structure. The effect remains unexpectedly robust against a significant strength of disorder, which we attribute to an effect of localization. We predict the ac quantum Hall measurements are feasible through the Faraday rotation characterized by the fine-structure constant $\alpha$.