Short Range Interaction Effects on the Density of States of Disordered Two Dimensional Crystals with a half--filled band

The Density of electronic States (DoS) of a two--dimensional square lattice with substitutional impurities is calculated in the presence of short--range electron--electron interactions. In the middle of the energy band, the Bragg reflections off the Brillouin zone boundary are shown to lead to additional quantum corrections to the DoS, the sign of which is opposite to the sign of the Altshuler--Aronov's logarithmic correction. The resulting quantum correction to the DoS at half--filling is positive, i.e. the DoS increases logarithmically as the Fermi energy is approached. However, far from the commensurate points where the Bragg reflections are suppressed, the negative logarithmic corrections to the DoS survive.