SPATIAL-DISTRIBUTION OF THE CURRENT-DENSITY AND ELECTRIC-FIELD IN MESOSCOPIC QUANTUM HALL CONDUCTORS

A microscopic treatment of the spatial distributions of the current de nsity and of the electric field in mesoscopic quantum Hall conductors is presented. It is shown that the spatial inhomogeneity of the electr ic field and the relevant nonlocality of voltage measurements depend s ubstantially on the smoothness of the confining potential, the sample geometry, and the temperature. This nonlocality is much stronger when both the n=0 and n=1 Landau levels are occupied than when only the n=0 Landau level is occupied. Nonelastic scattering is neglected assuming very low temperatures. For a certain geometry used in the experiments the nonlocality leads to a negative longitudinal resistance between t he top voltage probes and to a positive longitudinal resistance betwee n the bottom probes. The results agree qualitatively with those of the experiments.