Optical Hall Conductivity in Ordinary and Graphene Quantum Hall Systems

We reveal from numerical study that the optical Hall conductivity sigma(xy)(omega) has a characteristic feature even in the ac ( approximately THz) regime in that the Hall plateaus are retained both in the ordinary two-dimensional electron gas and in graphene in the quantum Hall 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 unexpectantly robust against the 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.