Controlled formation of an isolated miniband in bilayer graphene on an almost commensurate $\sqrt{3} \times \sqrt{3}$ substrate

TL;DR

This paper theoretically explores how a perpendicular electric field and incommensurability at the interface influence the electronic properties of bilayer graphene on a nearly commensurate substrate, leading to tunable miniband formation.

Contribution

It demonstrates the possibility of controlling miniband structures in bilayer graphene through substrate-induced moiré patterns and electric fields, a novel approach for electronic property engineering.

Findings

Miniband structures can be tuned from overlapping to isolated narrow bands.

A single narrow miniband can be formed and separated by gaps from other bands.

The interplay of electric field and moiré perturbation enables band structure control.

Abstract

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 then 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 moir\'{e} 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 moir\'{e} perturbation, the miniband structure can be tuned from that with a single band gap at the neutrality point and over-lapping 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.