Quasiparticle trapping, Andreev level population dynamics, and charge imbalance in superconducting weak links

TL;DR

This paper develops a comprehensive theoretical framework for understanding quasiparticle dynamics and charge imbalance in superconducting weak links, highlighting the effects of environmental phase fluctuations and nonequilibrium distributions.

Contribution

It introduces a self-consistent approach that accounts for nonequilibrium quasiparticle distributions and analyzes their impact on charge imbalance and current in superconducting weak links.

Findings

Charge imbalance caused by phase fluctuations induces quasiparticle current.

The theory predicts phase-dependent quasiparticle currents in realistic models.

It enables analysis of quantum coherent evolution from arbitrary initial states.

Abstract

We present a comprehensive theoretical framework for the Andreev bound state population dynamics in superconducting weak links. Contrary to previous works, our approach takes into account the generated nonequilibrium distribution of the continuum quasiparticle states in a self-consistent way. As application of our theory, we show that the coupling of the superconducting contact to environmental phase fluctuations induces a charge imbalance of the continuum quasiparticle population. This imbalance is due to the breaking of the left-right symmetry in the rates connecting continuum quasiparticles and the Andreev bound state system, and causes a quasiparticle current on top of the Josephson current in a ring geometry. We evaluate the phase dependence of the quasiparticle current for realistic choices of the model parameters. Our theory also allows one to analyze the quantum coherent evolution of the system from an arbitrary initial state.