Nonadiabatic Josephson dynamics in junctions with in-gap quasiparticles

Abstract

Conventional models of Josephson junction dynamics rely on the absence of low-energy quasiparticle states owing to a large superconducting gap. With this assumption the quasiparticle degrees of freedom are ⟪frozen out⟫ and the phase difference becomes the only free variable, acting as a fictitious particle in a temporally localized Josephson potential related to the adiabatic and nondissipative supercurrent across the junction. In this article we develop a general framework to incorporate the effects of low-energy quasiparticles interacting nonadiabatically with the phase degree of freedom. These quasiparticle states typically exist in constriction type junctions with high transparency channels or resonant states, as well as in junctions of unconventional superconductors. Recent experiments have also revealed the existence of spurious low-energy in-gap states in tunnel junctions of conventional superconductors—a system for which the adiabatic assumption is typically assumed to be valid. We show that a resonant interaction with these low-energy states, rather than the Josephson potential, determines the nonlinear Josephson dynamics at small amplitudes.