Low-frequency impedance of quantized Hall conductors

Abstract

The longitudinal and the Hall impedances have been measured as a function of the frequency in a two-dimensional electron gas at low temperatures. The frequency dependence of the longitudinal impedance can be explained in terms of an equivalent parallel $\mathrm{LCR}$ circuit. An effective inductance term arises due to the capacitive coupling between edge states and is shown to scale as $1/{\ensuremath{\nu}}^{2}$ for different filling factors. In the low-frequency range the relative difference between the ac and dc values of the Hall impedance is found to depend quadratically on the frequency and to scale as $1/{\ensuremath{\nu}}^{3}.$ These results are shown to be consistent with the existing theoretical model based on the edge-state picture. Finally, the observed symmetry relations when exchanging current contacts or reversing magnetic field are discussed.