Moire Superlattice Bands in Dirac Materials
When atomically thin two-dimensional (2D) materials are layered, they often form incommensurable noncrystalline structures that exhibit long-period moiré patterns when examined by scanning probes. In this presentation we will use graphene and hexagonal boron nitride as examples of gapless and gapped Dirac materials to illustrate how the moire superlattices due to interlayer coupling can alter the materials' intrinsic electronic properties. The derivation of the effective models for these van der Waals materials heterojunctions for arbitrary twist angles can benefit from input obtained from ab initio calculations carried out for commensurate short period crystalline structures. We will discuss how the moire pattern modified electronic structures give rise to a variety of experimentally measurable features including enhanced density of states through van Hove singularities, and flat bands, or to their suppression due to formation of band gaps.