# 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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