Bosonic Chern-Simons Field Theory of Anyon Superconductivity

TL;DR

This paper develops a quantum field theory model for anyon superconductivity using bosonic particles coupled to a Chern-Simons gauge field, revealing vortex lattice solutions and stability conditions related to quantum corrections.

Contribution

It introduces a mean field solution with vortex lattice structure for bosons coupled to Chern-Simons fields, and analyzes stability conditions for anyon superconductivity.

Findings

Mean field solution exhibits vortex lattice with single quantum flux

Stability of the solution requires Chern-Simons coefficient to be an integer

Provides insights into the Meissner effect in anyon superconductors

Abstract

We study the Quantum Field Theory of nonrelativistic bosons coupled to a Chern--Simons gauge field at nonzero particle density. This field theory is relevant to the study of anyon superconductors in which the anyons are described as {\bf bosons} with a statistical interaction. We show that it is possible to find a mean field solution to the equations of motion for this system which has some of the features of bose condensation. The mean field solution consists of a lattice of vortices each carrying a single quantum of statistical magnetic flux. We speculate on the effects of the quantum corrections to this mean field solution. We argue that the mean field solution is only stable under quantum corrections if the Chern--Simons coefficient $N=2\pi\theta/g^2$ is an integer. Consequences for anyon superconductivity are presented. A simple explanation for the Meissner effect in this system is discussed.