Modeling disorder in graphene

We present a study of different models of local disorder in graphene. Our focus is on the main effects that vacancies (random, compensated, and uncompensated), local impurities, and substitutional impurities bring into the electronic structure of graphene. By exploring these types of disorder and their connections, we show that they introduce dramatic changes in the low energy spectrum of graphene, viz., localized zero modes, strong resonances, gap and pseudogap behaviors, and nondispersive midgap zero modes.