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# Graphene on incommensurate substrates: trigonal warping and emergingDirac cone replicas with halved group velocity

Physical Review B (Impact Factor: 3.77). 11/2011; DOI:10.1103/PhysRevB.86.081405
Source: arXiv

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.

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##### Article: Topological Signatures in the Electronic Structure of Graphene Spirals
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ABSTRACT: Topology is familiar mostly from mathematics, but also natural sciences have found its concepts useful. Those concepts have been used to explain several natural phenomena in biology and physics, and they are particularly relevant for the electronic structure description of topological insulators and graphene systems. Here, we introduce topologically distinct graphene forms - graphene spirals - and employ density-functional theory to investigate their geometric and electronic properties. We found that the spiral topology gives rise to an intrinsic Rashba spin-orbit splitting. Through a Hamiltonian constrained by space curvature, graphene spirals have topologically protected states due to time-reversal symmetry. In addition, we argue that the synthesis of such graphene spirals is feasible and can be achieved through advanced bottom-up experimental routes that we indicate in this work.
Scientific Reports 01/2013; 3:1632. · 2.93 Impact Factor