Nature of single particle states in disordered graphene

We analyse the nature of the single particle states, away from the Dirac point, in the presence of long-range charge impurities in a tight-binding model for electrons on a two-dimensional honeycomb lattice which is of direct relevance for graphene. We show that the low energy Hamiltonian at any point k has the same nature as that at the Dirac point. From the nature of the eigenfunctions it follows that a weak long range impurity will cause weak anti localization effects, which can be suppressed, giving localization if the strength of impurities is sufficiently large to cause inter-valley scattering. Since the inter valley spacing 2|k| increases as one moves in from the band edge towards the band center, the threshold V_{th} required to localize a single particle state of energy E(k) also increases, implying a mobility edge starting from the band edge for weak disorder and moving towards the band center as the disorder strength increases. We show its manifestation in various physical quantities calculated, like inverse participation ratio, charge conductivity and diffusion coefficient.