Dynamical chiral symmetry breaking inQED3at finite density and impurity potential

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 cannot be neglected. The longitudinal component of the 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. By solving the Dyson-Schwinger equation for the 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.