Vortices in superconducting films are anyons

TL;DR

This paper demonstrates that vortices in superconducting films exhibit anyonic statistics due to their incompressibility, contrasting with vortices in superfluid helium which are not anyons.

Contribution

It clarifies the origin of anyonic behavior in vortices of superconducting films and distinguishes it from superfluid helium vortices, emphasizing the role of incompressibility.

Findings

Vortices in superfluid helium are not anyons due to compressibility.

Superconducting vortices are anyons because of the normal state in the vortex core.

Linking of vortex loops in 3D does not produce a topological phase invariant.

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.