Chiral phase transition inQED3at finite temperature and impurity potential

Abstract

In a realistic interacting system described by ($2+1$)-dimensional quantum electrodynamics (${\mathrm{QED}}_{3}$), there is always a certain number of impurities by which fermions are scattered. In general, impurity scattering can generate a finite density of states at the Fermi level, which screens the temporal component of the gauge field. This effect is expected to weaken dynamical fermion mass generation. Within the Born approximation, by introducing a damping term in the energy component of the fermion propagator, the influences of finite temperature and impurity scattering on the chiral phase transition in ${\mathrm{QED}}_{3}$ are investigated. Pursuing this aim, we solve the Dyson-Schwinger equations for the fermion and boson propagators to the leading order in $1/{N}_{f}$ expansion at zero frequency and then calculate the chiral condensate, the chiral susceptibility, and the thermal susceptibility within a range of the impurity scattering rates $\mathrm{\ensuremath{\Gamma}}$ and the numbers of fermion flavors ${N}_{f}$. It is found that impurity scattering leads to an obvious suppression of the dynamical fermion mass generation and critical temperature ${T}_{c}$.