Unconventional behavior of Dirac fermions in three-dimensional gauge theory

We study the unconventional behavior of massless Dirac fermions due to interaction with a U(1) gauge field in two spatial dimensions. At zero chemical potential, the longitudinal and transverse components of gauge interaction are both long-ranged. There is no fermion velocity renormalization since the system respects Lorentz invariance. At finite chemical potential, the Lorentz invariance is explicitly broken by the finite Fermi surface. The longitudinal gauge interaction is statically screened and becomes unimportant, whereas the transverse gauge interaction remains long-ranged and leads to singular renormalization of fermion velocity. The anomalous dimension of fermion velocity is calculated by means of the renormalization group method. We then examine the influence of singular velocity renormalization on several physical quantities, and show that they exhibit different behavior at zero and finite chemical potential.Comment: 9 pages, 4 figure

Dynamical chiral symmetry breaking in QED3_{3} at finite density and impurity potential

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.Comment: 8 pages, 4 figure