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

TL;DR

This paper investigates how slight lattice mismatch in graphene on substrates like hBN or Ir(111) causes trigonal warping of Dirac cones and generates new Dirac fermions with reduced group velocity, without opening a gap.

Contribution

It reveals that incommensurate substrates prevent gap opening and induce trigonal warping and new Dirac cones with halved group velocity in graphene.

Findings

Lattice incommensurability prevents Dirac gap opening.

Trigonal warping breaks effective time reversal symmetry.

Emergence of new massless Dirac fermions with halved velocity.

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 a new set of massless Dirac fermions is generated, which are characterized by a group velocity that is half the one of pristine graphene.