Effect of disorder on the electronic properties of graphene: A theoretical approach

In order to manipulate the properties of graphene, it is very important to understand the electronic structure in the presence of disorder. We investigate, within a tight-binding description, the effects of disorder in the on-site (diagonal disorder) term in the Hamiltonian as well as in the hopping integral (off-diagonal disorder) on the electronic dispersion and density of states by the augmented space recursion method. Extrinsic off-diagonal disorder is shown to have dramatic effects on the two-dimensional (2D) Dirac cone, including asymmetries in the band structures as well as the presence of discontinuous bands (because of resonances) in certain limits. Disorder-induced broadening, related to the scattering length (or lifetime) of Bloch electrons, is modified significantly with increasing strength of disorder. We propose that our methodology is suitable for the study of the effects of disorder in other 2D materials, such as a boron nitride monolayer.