Graphene on incommensurate substrates: trigonal warping and emerging Dirac cone replicas with halved group velocity

TLDR: In this paper, it was shown that the small lattice incommensurability prevents the opening of this gap and rather leads to a renormalized Dirac dispersion with a trigonal warping, which breaks the effective time-reversal symmetry in a single valley.

Abstract: 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 an additional set of massless Dirac fermions is generated, which is characterized by a group velocity that is about half the one of pristine graphene.