  Graphene and other two-dimensional materials display remarkable optical
properties, including a simple light transparency of $T \approx 1 - \pi \alpha$
for light in the visible region. Most theoretical rationalizations of this
"universal" opacity employ a model coupling light to the electron's crystal
momentum and put emphasis on the linear dispersion of the graphene bands.
However, such a formulation of interband absorption is not allowable within
band structure theory, because it conflates the crystal momentum label with the
canonical momentum operator. We show that the physical origin of the optical
behavior of graphene can be explained within a straightforward picture with the
correct use of canonical momentum coupling. Its essence lies in the
two-dimensional character of the density of states rather than in the precise
dispersion relation, and therefore the discussion is applicable to other
systems such as semiconductor membranes. At higher energies the calculation
predicts a peak corresponding to a van Hove singularity as well as a specific
asymmetry in the absorption spectrum of graphene, in agreement with previous
results.

Mesoscale and Nanoscale Physics;Materials Science