Impurity band induced by point defects in graphene

It is pointed out that point defects on graphene are strongly correlated and can not be treated as independent scatters. In particular, for large on-site defect potential, it is shown that defects induce an impurity band with density of state characterized by the Wigner semi-circle law. We find that the impurity band enhances conductivity to the order of $4 e^2 /h $ and explains the absence of strong localization. Furthermore,the impurity band supports ferromagnetism with the induced magnetic moment approaching 1$\mu_B$ per defect in the limit of infinite quasi-particle lifetime.