Optical conductivity of disordered graphene beyond the Dirac cone approximation

In this paper we systemically study the optical conductivity and density of states of disorded graphene beyond the Dirac cone approximation. The optical conductivity of graphene is computed by using the Kubo formula, within the framework of a full \pi-band tight-binding model. Different types of non-correlated and correlated disorders are considered, such as random or Gaussian potentials, random or Gaussian nearest-neighbor hopping parameters, randomly distributed vacancies or their clusters, and random adsorbed hydrogen atoms or their clusters. For a large enough concentration of resonant impurities, a new peak in the optical conductivity is found, associated to transitions between the midgap states and the Van Hove singularities of the main \pi-band. We further discuss the effect of doping on the spectrum, and find that small amounts of resonant impurities are enough to obtain a background contribution to the conductivity in the infra-red part of the spectrum, in agreement with recent experiments.