  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.
