Dirac cones for bi- and trilayer Bernal-stacked graphene in a quantum graph model

@article{deOliveira2020DiracCF,
  title={Dirac cones for bi- and trilayer Bernal-stacked graphene in a quantum graph model},
  author={C{\'e}sar R. de Oliveira and Vin{\'i}cius L. Rocha},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2020},
  volume={53}
}
A quantum graph model for a single sheet of graphene is extended to bilayer and trilayer Bernal-stacked graphene; the spectra are characterized and the dispersion relations explicitly obtained; Dirac cones are then proven to be present only for trilayer graphene, although the bilayer has a gapless parabolic band component. Our model rigorously exhibits basic facts from tight-binding calculations, effective two-dimensional models and a π-orbital continuum model with nearest-neighbour tunnelling… 
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