  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.
