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

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