Vortices in superconducting films: Statistics and fractional quantum Hall effect

We present a 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 reanalyzed. The Magnus force can be interpreted as an interaction with the effective magnetic field. The effective magnetic field may be even of the order 10(6)T/Angstrom. We discuss a possibility of the fractional quantum Hall effect (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 quantized values. The mere existence of the FQHE does not depend on vortex quantum statistics, 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 resistivity.