Average density of states in disordered graphene systems

In this paper, the average density of states (ADOS) in graphene with binary alloy disorders is calculated by the recursion method. We observed an obvious resonant peak and a dip in ADOS curves near the Dirac point, which result from interactions with surrounding impurities. We also found that the resonance energy (Eᵣ) and the dip position (εdip) are strongly dependent on the concentration of disorders $(x)$ and their on-site potentials $(v)$. A linear relation, εdip=xv, holds when the impurity concentration is low. This relation can also be extended when the impurity concentration is high, but with certain constraints. We also compute ADOS with a finite density of vacancies.