Effect of magnetic pair breaking on Andreev bound states and resonant supercurrent in quantum dot Josephson junctions

TL;DR

This paper models how magnetic pair-breaking affects Andreev bound states and supercurrent in quantum dot Josephson junctions, highlighting the impact of magnetic fields and spin-flip scattering on supercurrent behavior.

Contribution

It introduces a model incorporating pair-breaking effects into the analysis of Josephson tunneling through quantum dots, extending understanding of magnetic field influences.

Findings

Supercurrent and phase relation are significantly affected by pair-breaking.

Magnetic field dependence persists despite suppressed orbital effects.

Model aligns with recent experiments on carbon nanotube junctions.

Abstract

We propose a model for resonant Josephson tunneling through quantum dots that accounts for Cooper pair-breaking processes in the superconducting leads caused by a magnetic field or spin-flip scattering. The pair-breaking effect on the critical supercurrent $I_c$ and the Josephson current-phase relation $I(\phi)$ is largely due to the modification of the spectrum of Andreev bound states below the reduced (Abrikosov-Gorkov) quasiparticle gap. For a quantum dot formed in a quasi-one-dimensional channel, both $I_c$ and $I(\phi)$ can show a significant magnetic field dependence induced by pair breaking despite the suppression of the orbital magnetic field effect in the channel. This case is relevant to recent experiments on quantum dot Josephson junctions in carbon nanotubes. Pair-breaking processes are taken into account via the relation between the Andreev scattering matrix and the quasiclassical Green functions of the superconductors in the Usadel limit.