Ab initio study of gap opening and screening effects in gated bilayer graphene

The electronic properties of doped bilayer graphene in presence of bottom and top gates have been studied and characterized by means of density-functional theory (DFT) calculations. Varying independently the bottom and top gates it is possible to control separately the total doping charge on the sample and the average external electric field acting on the bilayer. We show that, at fixed doping level, the band gap at the K point in the Brillouin zone depends linearly on the average electric field, whereas the corresponding proportionality coefficient has a nonmonotonic dependence on doping. We find that the DFT-calculated band gap at K, for small doping levels, is roughly half of the band gap obtained with standard tight-binding (TB) approach. We show that this discrepancy arises from an underestimate, in the TB model, of the screening of the system to the external electric field. In particular, on the basis of our DFT results we observe that, when bilayer graphene is in presence of an external electric field, both interlayer and intralayer screenings occur. Only the interlayer screening is included in TB calculations, while both screenings are fundamental for the description of the band-gap opening. We finally provide a general scheme to obtain the full band structure of gated bilayer graphene for an arbitrary value of the external electric field and of doping.