Spectral approach to transport in the two-dimensional honeycomb lattice with substitutional disorder

Abstract

The transport properties of a disordered two-dimensional (2D) honeycomb lattice are examined numerically using the spectral approach to the 2D percolation problem, characterized by an Anderson-type Hamiltonian. In our model, disorder is represented by two parameters: a distribution of random on-site energies ε_i (positional disorder) and a concentration of doping energies p (substitutional disorder). 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 a graphene sheet doped with hydrogen