The adhesion of graphene on slightly lattice-mismatched surfaces, for instance of hexagonal boron nitride (hBN) or Ir(111), gives rise to a complex landscape of sublattice symmetry-breaking potentials for the Dirac fermions. Whereas a gap at the Dirac point opens for perfectly lattice-matched graphene on hBN, we show that the small lattice incommensurability prevents the opening of this gap and rather leads to a renormalized Dirac dispersion with a trigonal warping. This warping breaks the effective time reversal symmetry in a single valley. On top of this a new set of massless Dirac fermions is generated, which are characterized by a group velocity that is half the one of pristine graphene.
@article{arxiv.1111.0399,
title = {Graphene on incommensurate substrates: trigonal warping and emerging Dirac cone replicas with halved group velocity},
author = {Carmine Ortix and Liping Yang and Jeroen van den Brink},
journal= {arXiv preprint arXiv:1111.0399},
year = {2015}
}