Frustration effects on the electronic density of states of a random binary alloy

We examine the tight-binding density of states of a random binary alloy in a square lattice. In the split-band limit, which is similar to the model used for studing the quantum percolation problem, numerical calculations show that there is a pseudogap at the center of the lower subband, near and beyond the geometrical percolation threshold. This behavior is studied in two ways, by analyzing the first spectral moments of the lower subband, and by taking advantage of the bipartite nature of the lattice to renormalize half of the sites. This shows that the pseudogap in the split band limit appears because of frustration effects in the renormalized lattice.