Charge Condensation in QED$_3$ with a Chern-Simons Term

TL;DR

This paper investigates charge condensation in QED3 with a Chern-Simons term, revealing that spontaneous magnetization occurs only when fermion masses approach zero, linking magnetization to fermion mass.

Contribution

It introduces a functional method to analyze charge condensation and spontaneous magnetization in QED3 with a Chern-Simons term, highlighting the role of fermion mass.

Findings

Stable vacuum with nonzero charge condensation exists only when fermion mass approaches zero.

Spontaneous magnetization is closely related to the fermion mass.

Charge condensation can remain nonzero at zero chemical potential under certain conditions.

Abstract

Introducing a chemical potential in the functional method, we construct the effective action of QED$_3$ with a Chern-Simons term. We examine a possibility that charge condensation $\langle\psi^\dagger\psi \rangle$ remains nonzero at the limit of the zero chemical potential. If it happens, spontaneous magnetization occurs due to the Gauss' law constraint which connects the charge condensation to the background magnetic field. It is found that the stable vacuum with nonzero charge condensation is realized only when fermion masses are sent to zero, keeping it lower than the chemical potential. This result suggests that the spontaneous magnetization is closely related to the fermion mass.