Continuum model of the twisted graphene bilayer

The continuum model of the twisted graphene bilayer (Phys. Rev. Lett. 99, 256802, 2007) is extended to include all types of commensurate structures. The essential ingredient of the model, the Fourier components of the spatially modulated hopping amplitudes, can be calculated analytically, for any ty...

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Detalhes bibliográficos
Autor principal: Santos, J. M. B. Lopes dos (author)
Outros Autores: Peres, N. M. R. (author), Castro Neto, A. H. (author)
Formato: article
Idioma:eng
Publicado em: 2012
Assuntos:
Texto completo:http://hdl.handle.net/1822/21069
País:Portugal
Oai:oai:repositorium.sdum.uminho.pt:1822/21069
Descrição
Resumo:The continuum model of the twisted graphene bilayer (Phys. Rev. Lett. 99, 256802, 2007) is extended to include all types of commensurate structures. The essential ingredient of the model, the Fourier components of the spatially modulated hopping amplitudes, can be calculated analytically, for any type of commensurate structures in the low twist angle limit. We show that the Fourier components that could give rise to a gap in the SE-even structures discussed by Mele (Phys. Rev. B 81, 161405 2010) vanish linearly with angle, whereas the amplitudes that saturate to finite values, as $\theta\to0$, ensure that all low angle structures share essentially the same physics. We extend our previous calculations beyond the validity of perturbation theory, to discuss the disappearance of Dirac cone structure at angles below 1^{\circ}.