Non-adiabatic Josephson Dynamics in Junctions with in-Gap Quasiparticles

TL;DR

This paper develops a framework to include low energy quasiparticles in Josephson junction dynamics, revealing their significant impact on nonlinear behavior, especially in systems with in-gap states or high transparency channels.

Contribution

It introduces a general approach to model non-adiabatic quasiparticle effects in Josephson junctions, extending beyond traditional adiabatic assumptions.

Findings

Low energy quasiparticles significantly influence Josephson dynamics.

Resonant quasiparticle interactions dominate at small amplitudes.

In-gap states alter the nonlinear behavior of Josephson junctions.

Abstract

Conventional models of Josephson junction dynamics rely on the absence of low energy quasiparticle states due to a large superconducting gap. With this assumption the quasiparticle degrees of freedom become "frozen out" and the phase difference becomes the only free variable, acting as a fictitious particle in a local in time Josephson potential related to the adiabatic and non-dissipative supercurrent across the junction. In this article we develop a general framework to incorporate the effects of low energy quasiparticles interacting non-adiabatically with the phase degree of freedom. Such quasiparticle states exist generically in constriction type junctions with high transparency channels or resonant states, as well as in junctions of unconventional superconductors. Furthermore, recent experiments have revealed the existence of spurious low energy in-gap states in tunnel junctions of conventional superconductors - a system for which the adiabatic assumption typically is assumed to hold. We show that the resonant interaction with such low energy states rather than the Josephson potential defines nonlinear Josephson dynamics at small amplitudes.