Abstract

We study the influence of the Coulomb interaction on the optical conduc-
tivity of graphene at zero temperature. In order to calculate the corrections to
the conductivity, one needs to evaluate two divergent diagrams, the self-energy
diagram and the vertex diagram. Previous studies show that the value of the
corrections depends on the regularization scheme used. In the literature we
find mainly two different values for the corrections. We present a regulariza-
tion scheme, combining dimensional regularization and a deformation of the
Coulomb potential, which is able to reproduce both values depending on the
order of limits taken. Finally, in order to determine which of the two values is
correct, we perform a tight-binding calculation where we determine the correc-
tion to the optical conductivity on the lattice.