Gate-tunable bandgap in bilayer graphene

The tight-binding model of bilayer graphene is used to find the gap between the conduction and valence bands as a function of both the gate voltage and the doping level by donors or acceptors. The total Hartree energy is minimized and an equation for the gap is obtained. This equation for the ratio of the gap to the chemical potential is determined only by the screening constant. Therefore, the gap is strictly proportional to the gate voltage or the carrier concentration in the absence of donors or acceptors. But in the case where the donors or acceptors are present, the gap demonstrates an asymmetric behavior on the electron and hole sides of the gate bias. A comparison with experimental data obtained by Kuzmenko et al. demonstrates a good agreement.