Josephson Currents in Quantum Hall Devices

TL;DR

This paper presents an exact analytical model for Josephson currents in quantum Hall devices, revealing that the current is independent of lead separation and bounded by the device perimeter, across all temperatures.

Contribution

It provides a comprehensive, all-orders analytic solution for Josephson currents in quantum Hall edge-based SNS junctions, extending previous perturbative results.

Findings

Josephson current is independent of the distance between leads.

Maximum Josephson current inversely proportional to device perimeter.

Results hold for all temperatures and coupling strengths.

Abstract

We consider a simple model for an SNS Josephson junction in which the "normal metal" is a section of a filling-factor $\nu=2$ integer quantum-Hall edge. We provide analytic expressions for the current/phase relations to all orders in the coupling between the superconductor and the quantum Hall edge modes, and for all temperatures. Our conclusions are consistent with the earlier perturbative study by Ma and Zyuzin [Europhysics Letters {\bf 21} 941-945 (1993)]: The Josephson current is independent of the distance between the superconducting leads, and the upper bound on the maximum Josephson current is inversely proportional to the perimeter of the Hall device.