Diffusion and Criticality in Undoped Graphene with Resonant Scatterers

A general theory is developed to describe graphene with an arbitrary number of isolated impurities. The theory provides a basis for an efficient numerical analysis of the charge transport and is applied to calculate the Dirac-point conductivity sigma of graphene with resonant scatterers. In the case of smooth resonant impurities the symmetry class is identified as DIII and sigma grows logarithmically with increasing impurity concentration. For vacancies (or strong on-site potential impurities, class BDI) sigma saturates at a constant value that depends on the vacancy distribution among two sublattices.