The electronic properties of graphene and its bilayer

We present a discussion of some of the physical properties of graphene and its bilayer. In particular, we focus our attention on the calculation of the transparency of graphene and on the dependence of the energy gap of the biased graphene bilayer on the electronic density. We show that the transparency of graphene is controlled by the value of the fine structure constant over a frequency range from the infra-red to the ultra-violet. We derive the dependence of the energy gap of the graphene bilayer on the external applied electric field.