The low energy electronic band structure of bilayer graphene

We employ the tight binding model to describe the electronic band structure of bilayer graphene and we explain how the optical absorption coefficient of a bilayer is influenced by the presence and dispersion of the electronic bands, in contrast to the featureless absorption coefficient of monolayer graphene. We show that the effective low energy Hamiltonian is dominated by chiral quasiparticles with a parabolic dispersion and Berry phase 2 pi. Layer asymmetry produces a gap in the spectrum but, by comparing the charging energy with the single particle energy, we demonstrate that an undoped, gapless bilayer is stable with respect to the spontaneous opening of a gap. Then, we describe the control of a gap in the presence of an external gate voltage. Finally, we take into account the influence of trigonal warping which produces a Lifshitz transition at very low energy, breaking the isoenergetic line about each valley into four pockets.