Dynamic interplay of Berry’s phase and spectral flow in the current-voltage characteristics of a restricted class of large SNS annular Josephson junctions

Abstract

It has been argued that a competition arises between the Berry phase and spectral flow effects in a restricted class of large SNS annular Josephson junctions. A crossover is expected to occur in the junction response at the temperature ${T}_{*}$ where the superconducting dynamics enters the hydrodynamic limit. For $Tg{T}_{*},$ spectral flow occurs in the weak link and masks the Berry phase effects; while for $T\ensuremath{\ll}{T}_{*},$ spectral flow does not occur allowing Berry phase effects to freely influence junction dynamics. In this paper we focus on temperatures $T\ensuremath{\lesssim}{T}_{*}$ where spectral flow masking of Berry phase effects begins to switch off. In the case where a single vortex is present in the weak link, we numerically calculate the I--V curves for a restricted class of annular Josephson junctions in which nonvanishing Berry phase effects are expected to occur. We find that as Berry phase effects strengthen, distinctive shifts appear in the I--V curves which are the signature of the crossover, and provide clear targets for an experimental test of the underlying theory. We estimate ${T}_{*}$ for a clean junction, summarize the restrictions defining the class of annular junctions in which nonvanishing Berry phase effects are expected to occur, and show how the I--V curve shifts can be understood as a consequence of: (1) a Berry phase contribution to the tunneling current density; (2) the magnetic structure of the vortex core; and (3) Bernoulli's theorem.