Josephson effect in superconductor-normal dot-superconductor junctions driven out of equilibrium by quasiparticle injection

TL;DR

This paper theoretically investigates how quasiparticle injection influences the supercurrent in superconductor-normal dot-superconductor junctions, revealing a voltage-induced transition to $ ext{π}$-junction behavior due to competing contributions to the supercurrent.

Contribution

It introduces a detailed theoretical analysis of supercurrent variations caused by quasiparticle injection, identifying conditions for a sign reversal and $ ext{π}$-junction transition in such junctions.

Findings

Supercurrent decomposes into subgap and outside-gap contributions.

A critical voltage exists where the supercurrent sign reverses.

The effect persists under certain temperature and relaxation conditions.

Abstract

We study theoretically the large variations of the supercurrent through a normal dot that are induced by a small quasiparticle injection current from normal leads connected to the dot. We find that the supercurrent decomposes into a subgap contribution, which depends on the voltages applied to the normal leads, as well as a contribution with opposite sign from energies outside the gap, which is insensitive to the voltages. As the voltages gradually suppress the subgap contribution, a critical voltage exists above which the contribution from energies outside the gap dominates, leading to a sign reversal of the current-phase relation, namely a transition to a so-called $\pi$-junction behavior. We determine the critical voltage and analyze the robustness of the effect with respect to temperature and inelastic relaxation in the dot.