Dynamical Generation of Fermion Mass and Magnetic Field in Three-Dimensional QED with Chern-Simons Term

TL;DR

This paper investigates how a Chern-Simons term in three-dimensional QED influences dynamical symmetry breaking, leading to the generation of fermion mass and magnetic fields under specific conditions, revealing new vacuum phases.

Contribution

It introduces a novel phase where both fermion mass and magnetic field are dynamically generated in 3D QED with a CS term, depending on the CS coefficient value.

Findings

A new vacuum phase with both fermion mass and magnetic field generated.

Fermion remains massless with only magnetic field induced at specific CS coefficient.

Spontaneous magnetization is absent when the CS coefficient is zero.

Abstract

We study dynamical symmetry breaking in three-dimensional QED with a Chern-Simons (CS) term, considering the screening effect of $N$ flavor fermions. We find a new phase of the vacuum, in which both the fermion mass and a magnetic field are dynamically generated, when the coefficient of the CS term $\kappa$ equals $N e^2/4 \pi$. The resultant vacuum becomes the finite-density state half-filled by fermions. For $\kappa=N e^2/2 \pi$, we find the fermion remains massless and only the magnetic field is induced. For $\kappa=0$, spontaneous magnetization does not occur and should be regarded as an external field.