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 s of graphene with resonant scatterers. In the case of smooth resonant impurities the symmetry class is identified as DIII and s grows logarithmically with increasing impurity concentration. For vacancies (or strong on-site potential impurities, class BDI) s saturates at a constant value that depends on the vacancy distribution among two sublattices. © 2010 The American Physical Society.