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The adhesion of graphene on slightly lattice-mismatched surfaces, forinstance of hexagonal boron nitride (hBN) or Ir(111), gives rise to a complexlandscape of sublattice symmetry-breaking potentials for the Dirac fermions.Whereas a gap at the Dirac point opens for perfectly lattice-matched grapheneon hBN, we show that the small lattice incommensurability prevents the openingof this gap and rather leads to a renormalized Dirac dispersion with a trigonalwarping. This warping breaks the effective time reversal symmetry in a singlevalley. On top of this a new set of massless Dirac fermions is generated, whichare characterized by a group velocity that is half the one of pristinegraphene.

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