Absence of backscattering in the quantum Hall effect in multiprobe conductors

Abstract

Under certain conditions, high magnetic fields in a two-dimensional conductor lead to a suppression of both elastic and inelastic backscattering. This, together with the formation of edge states, is used to develop a picture of the integer quantum Hall effect in open multiprobe conductors. We consider both ideal contacts without elastic scattering and also disordered contacts. Ideal contacts populate edge states equally whereas disordered contacts lead to an initial nonequilibrium population of the edge states. In Hall samples much larger than an inelastic length, and in the presence of disordered contacts, the sample edges become equipotential lines only an inelastic scattering length away from the current source and current drain contacts. Samples so small that the carriers can travel from one contact to the other without inelastic relaxation do not exhibit exact quantization if the contacts are disordered. In all cases we find that the quantum Hall effect occurs only if the sample exhibits at least two sets of equilibrated edge states which do not interact via elastic or inelastic scattering. The onset of interaction between the two sets of edge states leads to deviations from exact quantization and eventually to a breakdown of the quantum Hall effect.