Magnetotransport in a doubly connected two-dimensional quantum Hall system in the low magnetic field regime

Abstract

In a preceding paper [Phys. Rev. B 72, 035334 (2005)], experimental results for the so-called ``anti-Hall bar within a Hall bar'' configuration have been compared with numerical simulations for the high magnetic field regime. The sample structure is a doubly connected, double-boundary electronic system that has been experimentally investigated by Mani. The application of a network model for magnetotransport allows us to evaluate the longitudinal and Hall voltages in this geometry. Thus, within our network model, we rebuild the experimental configuration, including the sample geometry and the two independent floating current sources. In this paper we extend our calculations to the low magnetic field regime, where the quantum Hall effect is not yet established. Like in the high magnetic field regime, we realize the Hall voltages and longitudinal voltages at both the inner and outer boundaries to behave 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 both injected currents.