Josephson Effect in the Quantum Hall Regime

Abstract

We consider a SNS junction, where the normal metal is taken to be in the quantum Hall regime. The induced supercurrent is carried by the edge states which are always extended. The coherence length along the direction of the edge state is determined by the drift velocity due to the surface electric field, and is much larger than the magnetic length. In a point contact junction, the critical supercurrent is independent of the positions of the leads, and depends only on the junction perimeter. We estimate the magnitude of this effect and comment on its experimental realizability.