Spectral Flow, Magnus Force and Mutual Friction via the Geometric Optics Limit of Andreev Reflection

TL;DR

This paper investigates how spectral flow and Andreev reflection influence vortex dynamics in superfluids, revealing that discrete core states cause Bloch oscillations that prevent spectral flow, with implications for mutual friction.

Contribution

It introduces a geometric optics approach to analyze vortex core states and derives mutual friction coefficients considering relaxation processes.

Findings

Discrete vortex core states cause Bloch oscillations.

Spectral flow is hindered by state discreteness, affecting momentum transfer.

Mutual friction coefficients are derived from relaxation mechanisms.

Abstract

The notion of spectral flow has given new insight into the motion of vortices in superfluids and superconductors. For a BCS superconductor the spectrum of low energy vortex core states is largely determined by the geometric optics limit of Andreev reflection. We use this to follow the evolution of the states when a stationary vortex is immersed in a transport supercurrent. If the core spectrum were continuous, spectral flow would convert the momentum flowing into the core via the Magnus effect into unbound quasiparticles --- thus allowing the vortex to remain stationary without a pinning potential or other sink for the inflowing momentum. The discrete nature of the states, however, leads to Bloch oscillations which thwart the spectral flow. The momentum can escape only via relaxation processes. Taking these into account permits a physically transparent derivation of the mutual friction coefficients.