Vortices in superconducting films - statistics and fractional quantum Hall effect

TL;DR

This paper derives the Berry phase for vortex exchange in superconducting films, reanalyzes the Magnus force, and explores the potential for fractional quantum Hall effects in vortex systems, highlighting novel interactions and quantization phenomena.

Contribution

It provides a new derivation of the Berry phase using the Bogolubov-de Gennes formalism and discusses the implications for vortex quantum statistics and fractional quantum Hall effects.

Findings

Berry phase derivation for vortex exchange

Magnus force interpreted as interaction with effective magnetic field

Potential for fractional quantum Hall effect in vortex systems

Abstract

We present a new derivation of the Berry phase picked up during exchange of parallel vortices. This derivation is based on the Bogolubov - de Gennes formalism. The origin of the Magnus force is also critically reanalised. The Magnus force can be interpreted as interaction with effective magnetic field. The efective magnetic field may be even of the order $10^{6} T/\AA$. We discuss a possibility of the FQHE in vortex systems. As the real magnetic field is varied to drive changes in vortex density, the vortex density will prefer to stay at some quantised values. The mere existence of the FQHE does not depend on vortex quantumstatistics although the pattern of the plateaux does. We also discuss how the density of anyonic vortices can lower the effective strengh of the Magnus force, what might be observable in measurements of Hall resitivity.