Field distribution in a quantum Hall device

Abstract

The electric field strengths in a long rectangular device carrying a quantised Hall current are calculated. In the ideal system an analytic approximation for the field near the edge is obtained which is in agreement with the numerical results of MacDonald et al. (1983). It is pointed out that even a small departure of the Hall angle from pi /2 leads to a uniform field, and therefore current, across the system. Diamagnetic corrections are shown to be negligible. The fields in the source and drain are calculated, both for a two-dimensional electrode, for which an analytic solution is available, and for a three-dimensional electrode. In the three-dimensional case, most of the energy dissipation occurs within a distance l of two of the corners of the rectangle, where an expression for l is derived.