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

• URL: http://arxiv.org/abs/2011.08658v1
• Date: Tue, 17 Nov 2020 14:41:07 GMT
• Title: Dirac cones for bi- and trilayer Bernal-stacked graphene in a quantum graph model
• Authors: Cesar R. de Oliveira, Vinicius L. Rocha
• Abstract summary: A quantum graph model for a single sheet of graphene is extended to bilayer and trilayer Bernal-stacked graphene. Dirac cones are then proven to be present only for trilayer graphene, although the bilayer has a gapless parabolic band component.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 $\pi$-orbital continuum model with nearest-neighbour tunneling that have been discussed in the physics literature.

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