Effect of magnetic pair breaking on Andreev bound states and resonant supercurrent in quantum dot Josephson 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 $I(\ensuremath{\varphi})$ 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 $I(\ensuremath{\varphi})$ 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.