Dynamical scaling analysis of the optical Hall conductivity in the quantum Hall regime

TL;DR

This paper performs a dynamical scaling analysis of the optical Hall conductivity in quantum Hall systems, revealing a crossover from dc to ac behavior and predicting observable plateau structures in the THz frequency range.

Contribution

It introduces a dynamical scaling framework for ac Hall conductivity in quantum Hall systems, with fitted critical exponents and predictions for THz regime observability.

Findings

Dynamical scaling of $\sigma_{xy}(\varepsilon_F,\omega)$ confirmed in 2D electron gas and graphene.

Identified crossover from dc-like to ac behavior in Hall conductivity.

Predicted robust Hall plateaux in the THz frequency range.

Abstract

Dynamical scaling analysis is theoretically performed for the ac (optical) Hall conductivity $\sigma_{xy}(\varepsilon_F,\omega)$ as a function of Fermi energy $\varepsilon_F$ and frequency $\omega$ for the two-dimensional electron gas and for graphene. In both systems, results based on exact diagonalization show that $\sigma_{xy}(\varepsilon_F,\omega)$ displays a well-defined dynamical scaling, for which the dynamical critical exponent as well as the localization exponent are fitted and plugged in. A crossover from the dc-like bahavior to the ac regime is identified. The dynamical scaling analysis has enabled us to quantify the plateau in the ac Hall conductivity previously obtained, and to predict that the plateaux structure in ac is robust enough to be observed in the THz regime.