Spectral approach to transport in the 2D honeycomb lattice with substitutional disorder

The transport properties of a disordered two-dimensional (2D) honeycomb lattice are examined numerically using the spectral approach to the quantum percolation problem, characterized by an Anderson-type Hamiltonian. In our simulations, substitutional disorder (or doping) is represented by a modified bimodal probability distribution of the on-site energies. The results indicate the existence of extended energy states for nonzero disorder and the emergence of a transition towards localized behavior for critical doping concentration n_D>0.3%, in agreement with the experimentally observed metal-to-insulator transition in graphene sheet doped with hydrogen.