Dynamical chiral symmetry breaking in QED$_{3}$ at finite density and impurity potential

TL;DR

This paper investigates how finite chemical potential and impurity scattering influence dynamical mass generation in (2+1)-dimensional QED, revealing suppression of critical fermion flavor and mass due to these effects.

Contribution

It provides a detailed analysis of the impact of chemical potential and impurities on chiral symmetry breaking in QED3, including the static length development and damping effects.

Findings

Finite chemical potential and impurities suppress the critical fermion flavor N_c.

Impurity scattering introduces a finite damping rate for fermions.

The dynamical fermion mass is significantly reduced by these effects.

Abstract

We study the effects of finite chemical potential and impurity scattering on dynamical fermion mass generation in (2+1)-dimensional quantum electrodynamics. In any realistic systems, these effects usually can not be neglected. The longitudinal component of gauge field develops a finite static length produced by chemical potential and impurity scattering, while the transverse component remains long-ranged because of the gauge invariance. Another important consequence of impurity scattering is that the fermions have a finite damping rate, which reduces their lifetime staying in a definite quantum state. By solving the Dyson-Schwinger equation for fermion mass function, it is found that these effects lead to strong suppression of the critical fermion flavor $N_c$ and the dynamical fermion mass in the symmetry broken phase.