Moir\'e minibands in graphene heterostructures with almost commensurate sqrt3 x sqrt3 hexagonal crystals

TL;DR

This paper develops a phenomenological model for low-energy moiré minibands in graphene on nearly commensurate hexagonal substrates, revealing how slight incommensurability affects Dirac cones and band gaps.

Contribution

It introduces a theory describing how near-commensurate superlattices influence Dirac electrons and miniband structures in graphene heterostructures.

Findings

Incommensurability causes periodic intervalley scattering.

Zero energy Dirac cones remain intact despite superlattice perturbation.

Band gaps can open asymmetrically at moiré subband edges.

Abstract

We present a phenomenological theory of the low energy moir\'e minibands of Dirac electrons in graphene placed on an almost commensurate hexagonal underlay with a unit cell pproximately three times larger than that of graphene.A slight incommensurability results in a periodically modulated intervalley scattering for electrons in graphene. In contrast to the perfectly commensurate Kekul\'e distortion of graphene, such supperlattice perturbation leaves the zero energy Dirac cones intact, but is able to open a band gap at the edge of the first moir\'e subbband, asymmetrically in the conduction and valence bands.