VORTICES IN SUPERCONDUCTING FILMS - STATISTICS AND FRACTIONAL QUANTUMHALL-EFFECT

We present a derivation of the Berry phase picked up during exchange o f parallel vortices. This derivation is based on the Bogolubov-de Genn es formalism. The origin of the Magnus force is also critically reanal yzed. The Magnus force can be interpreted as an interaction with the e ffective magnetic field. The effective magnetic field may be even of t he order 10(6)T/Angstrom. We discuss a possibility of the fractional q uantum Hall effect (FQHE) in vortex systems. As the real magnetic fiel d is varied to drive changes in vortex density, the vortex density wil l prefer to stay at some quantized values. The mere existence of the F QHE does not depend on vortex quantum statistics, although the pattern of the plateaux does. We also discuss how the density of anyonic vort ices can lower the effective strengh of the Magnus force, what might b e observable in measurements of Hall resistivity.