Interaction-induced supercurrent in quantum Hall setups

TL;DR

This paper explores how electron-electron interactions induce supercurrents in quantum Hall edge channels, especially in complex multi-terminal setups, revealing non-local effects and interference phenomena.

Contribution

It extends previous models to include scattering between opposite channels and multiple contacts, providing a comprehensive relation for the interaction-induced supercurrent.

Findings

Supercurrent can be mediated by nonlocal electron-electron interactions.

Supercurrent sensitivity to scattering demonstrates its non-local nature.

Interference of Andreev reflections influences phase dependence of supercurrents.

Abstract

Recently we have proposed an unusual mechanism of superconducting current that is specific for Quantum Hall Edge channels connected to superconducting electrodes. We have shown that the supercurrent can be mediated by a nonlocal electon-electon interaction that provide an opportunity for a long-distance information transfer in the direction opposite to the electron flow. A convenient model for such interaction is that of an external circuit. The consideration has been done for the case of a single channel. In this work, we extend these results to more sophisticated setups that include the scattering between Quantum Hall channels of opposite direction and multiple superconducting contacts. For a single Quantum Hall constriction, we derive a general and comprehensive relation for the interaction- induced supercurrent in terms of scattering amplitudes and demonstrate the non-local nature of the current by considering its sensitivity to scattering. We understand the phase dependences of the supercurrents in multi-terminal setups in terms of interference of Andreev reflection processes. For more complex setups encompassing at least two constrictions we find an interplay between non-interacting and interaction-induced currents and contibutions of complex interference processes.