To the theory of electronic states of an epitaxial graphene bilayer

The energy spectrum of an epitaxial graphene bilayer is investigated. The most general case of spontaneous breaking of the $P$ symmetry within and between the layers is considered. The influence of the gate voltage on the energy spectrum is studied. It is shown that a general profile of this influence substantially depends on the ratio between bandgaps corresponding to different layers. At a certain value of the Coulomb potential caused by the transition of a charge from the substrate, the bandgap collapses. These studies are carried out for two types of layer packing in the bilayer, namely, the $AB$ and $AA$ packings.