Critical wavefunctions in disordered graphene

In order to elucidate the presence of non-localized states in doped graphene, a scaling analysis of the wavefunction 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 wavefunctions that follow a critical (power-law) decay, which show a behavior intermediate between those of metals and insulators. The power-law exponent distribution is robust against the inclusion of next-nearest neighbors and growing the system size.