Critical wave functions in disordered graphene

In order to elucidate the presence of non-localized states in doped graphene, an scaling analysis of the wave function moments known as inverse participation ratios is performed. The model used is a tight- binding hamiltonian considering nearest and next-nearest neighbors with random substitutional impurities. Our findings indicate the presence of non-normalizable wave functions that follow a critical (power-law) decay, which are between a metallic and insulating behavior. The power-law exponent distribution is robust against the inclusion of next-nearest neighbors and on growing the system size.