Optical Transparency in an effective model for Graphene

Motivated by experiments confirming that the optical transparency of graphene is defined through the fine structure constant and that it could be fully explained within the relativistic Dirac fermions in 2D picture, in this article we investigate how this property is affected by next-to-nearest neighbor coupling in the low-energy continuum description of graphene. A detailed calculation within the linear response regime allows us to conclude that, somewhat surprisingly, the zero-frequency limit of the optical conductivity that determines the transparency remains robust up to this correction.