Phenomenological Model for Frequency-Related Dissipation in the Quantized Hall Resistance

Recently, ac measurements of the quantized Hall resistance have shown a linear relationship between the deviation of the Hall resistance from the perfectly quantized value DeltaR_H and the dissipation in the system represented by the longitudinal resistivity rho_xx ^ac. In this paper, we present a phenomenological model based on electrodynamic arguments that model this relation. The dissipation is due to the displacement current flowing in the system. All the microscopic features are included in a complex tensorial dielectric susceptibility which remains to be investigated if more physical insight in the ac transport properties of the 2-D electron gas is desired