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

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In order to manipulate the properties of graphene, its very important to understand the electronic structure in 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 augmented space recursion method. Extrinsic off-diagonal disorder is shown to have dramatic effects on the two-dimensional Dirac-cone, including asymmetries in the band structures as well as the presence of discontinuous bands in certain limits. Disorder-induced broadening, related to the scattering length (or life-time) of electrons, is modified significantly with the increasing strength of disorder. We propose that our theory is suitable to study the effects of disorder in other 2D materials, e.g., a boron nitride monolayer.