Generic Miniband Structure of Graphene on a Hexagonal Substrate

TL;DR

This paper classifies the generic miniband structures of electrons in graphene on hexagonal substrates, revealing conditions for isolated minibands with mini Dirac points and their effects on Hall coefficient behavior.

Contribution

It introduces a symmetry-based classification of miniband structures in graphene on hexagonal substrates, identifying conditions for isolated minibands with mini Dirac points.

Findings

First miniband can be separated by mini Dirac points.

Hall coefficient shows two sign alternations with charge density.

Conditions depend on substrate symmetry and moiré pattern.

Abstract

Using a general symmetry-based approach, we provide a classification of generic miniband structures for electrons in graphene placed on substrates with the hexagonal Bravais symmetry. In particular, we identify conditions at which the first moir\'e miniband is separated from the rest of the spectrum by either one or a group of three isolated mini Dirac points and is not obscured by dispersion surfaces coming from other minibands. In such cases the Hall coefficient exhibits two distinct alternations of its sign as a function of charge carrier density.