Density of states of disordered two-dimensional crystals with half-filled band

A diagrammatic method is applied to study the effects of commensurability in two-dimensional disordered crystalline metals by using the particle-hole symmetry with respect to the nesting vector P-0 = {+/- pi/a, pi/a) for a half-filled electronic band. The density of electronic states (DoS) is shown to have nontrivial corrections due to both nesting and elastic impurity scattering processes, and as a result the Van Hove singularity is preserved in the center of the band. However, the energy dependence of the DoS is significantly changed. A small offset from the middle of the band gives rise to the disappearance of quantum corrections to the DoS.