▎ 摘　　要

We investigate theoretically the interplay between the effects of a perpendicular electric field and incommensurability at the interface on the electronic properties of a heterostructure of bilayer graphene and a semiconducting substrate with a unit cell almost three times larger than that of graphene. It is known that the former introduces an asymmetry in the distribution of the electronic wave function between the layers and opens a band gap in the electronic spectrum. The latter generates a long wavelength periodic moire perturbation of graphene electrons which couples states in inequivalent graphene Brillouin zone corners and leads to the formation of minibands. We show that, depending on the details of the moire perturbation, the miniband structure can be tuned from that with a single band gap at the neutrality point and overlapping minibands on the conduction/valence band side to a situation where a single narrow miniband is separated by gaps from the rest of the spectrum.