Chiral supercurrent through a quantum Hall weak link

TL;DR

This paper models the unique chiral supercurrent in quantum Hall weak links, revealing its dependence on both edges, its unusual current-phase relation with a doubled period, and its robustness to interactions, aligning with recent experiments.

Contribution

It provides a microscopic calculation of the chiral supercurrent, demonstrating its distinct properties and robustness, and compares theoretical results with experimental data.

Findings

Chiral supercurrent requires both edges for mediation.

Supercurrent exhibits a 2φ₀ periodicity in the current-phase relation.

Quantitative agreement with experiments achieved through interface assumptions.

Abstract

We use a microscopic 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, chiral supercurrent was previously shown to obey an unusual current-phase relation with period $2 \phi_0=h/e$, which is twice as large as 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 of Amet et al [Science, 352(6288)] and find that quantitative agreement in magnitude of the supercurrent can be attained by making reasonable but critical assumptions about the superconductor quantum Hall interface.