Vortices in superconducting films are anyons

Abstract

We point out that nontrivial quantumstatistics of vortices in planar superfluid systems has its origin in the Schrodinger equation rather then the Chern-Simons term. Vortices in superfluid helium films are not anyons because helium films are compressible. Quantum Hall effect layers admit vortices with nontrivial statistical interactions thanks to their incompressibility. We consider type II planar superconductors described by time-dependent nonlinear Schrodinger equation. Inside of a vortex core superconductor is in the normal state. Because of that vortices in superconducting films are anyons. We consider also vortex loops in 3 dimensions but a phase factor due to linking of vortex loops' worldsheets is not a topological invariant.