Chiral supercurrent through a quantum Hall weak link

Abstract

We use an effective model to calculate properties of the supercurrent carried by chiral edge states of a quantum Hall weak link. This ``chiral'' supercurrent is qualitatively distinct from the usual Josephson supercurrent in that it cannot be mediated by a single edge alone, i.e., both right- and left-going edges are needed. Moreover, the chiral supercurrent was previously shown to obey an unusual current-phase relation with period $2{\ensuremath{\phi}}_{0}=h/e$, which is twice the period of conventional Josephson junctions. We show that the ``chiral'' nature of this supercurrent is sharply defined, and is robust to interactions to infinite order in perturbation theory. We compare our results with recent experimental findings [Amet et al., Science 352 966 (2016)] and find that quantitative agreement in the magnitude of the supercurrent can be attained by making reasonable but critical assumptions about the superconductor quantum Hall interface.