Voltage and current distribution in a doubly connected two-dimensional quantum Hall system

Abstract

Numerical simulations are compared with experimental results for the so-called ``anti-Hall bar within a Hall bar'' configuration, which is a doubly connected, double-boundary electronic system that has been experimentally investigated by Mani. Here, we illustrate the application of a network model for magnetotransport, which allows the evaluation of the longitudinal and Hall voltages, and the current distribution, in this geometry. Thus, we rebuild the experimental configuration, including the sample geometry with the boundary conditions, and the two independent floating current sources, within our network. As in the reported experiment, we realize the Hall voltages and longitudinal voltages at both the inner and outer boundaries. In excellent agreement with Mani's experiments, we find that the Hall voltages at the inner (anti-Hall bar) and outer (Hall bar) boundaries depend just on the individual current injected via the corresponding boundary, while the longitudinal voltage depends exactly on the sum of the injected currents.