Optical conductivity of graphene in the visible region of the spectrum

We compute the optical conductivity of graphene beyond the usual Dirac-cone approximation, giving results that are valid in the visible region of the conductivity spectrum. The effect of next-nearest-neighbor hopping is also discussed. Using the full expression for the optical conductivity, the transmission and reflection coefficients are given. We find that even in the optical regime the corrections to the Dirac-cone approximation are surprisingly small (a few percent). Our results help in the interpretation of the experimental results reported by Nair et al. [Science 320, 1308 (2008)].