Vortices in superconducting films - statistics and fractional quantum Hall effect

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.