  We study the band dispersion of graphene with randomly distributed structural
defects using two complementary methods, exact diagonalization of the
tight-binding Hamiltonian and implementing a self-consistent T matrix
approximation. We identify three distinct types of impurities resulting in
qualitatively different spectra in the vicinity of the Dirac point. First,
resonant impurities, such as vacancies or 585 defects, lead to stretching of
the spectrum at the Dirac point with a finite density of localized states. This
type of spectrum has been observed in epitaxial graphene by photoemission
spectroscopy and discussed extensively in the literature. Second, nonresonant
(weak) impurities, such as paired vacancies or Stone-Wales defects, do not
stretch the spectrum but provide a line broadening that increases with energy.
Finally, disorder that breaks sublattice symmetry, such as vacancies placed in
only one sublattice, open a gap around the Dirac point and create an impurity
band in the middle of this gap. We find good agreement between the results of
the two methods and also with the experimentally measured spectra.
