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Condens. Matter 2018, 3(2), 11; https://doi.org/10.3390/condmat3020011

Electronic Properties of Curved Few-Layers Graphene: A Geometrical Approach

1,†,* , 2,†
and
3,†
1
Departamento de Física, Universidade Federal de Ouro Preto, 35400-000 Ouro Preto MG, Brazil
2
School of Science and Technology, Mathematics Division, University of Camerino, 62032 Camerino, Italy
3
School of Pharmacy, Physics Unit, University of Camerino, 62032 Camerino, Italy
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Received: 19 December 2017 / Revised: 21 March 2018 / Accepted: 30 March 2018 / Published: 5 April 2018
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Abstract

We show the presence of non-relativistic Lévy-Leblond fermions in flat three- and four-layers graphene with AB stacking, extending the results obtained in Cariglia et al. 2017 for bilayer graphene. When the layer is curved we obtain a set of equations for Galilean fermions that are a variation of those of Lévy-Leblond with a well defined combination of pseudospin, and that admit Lévy-Leblond spinors as solutions in an approriate limit. The local energy of such Galilean fermions is sensitive to the intrinsic curvature of the surface. We discuss the relationship between two-dimensional pseudospin, labelling layer degrees of freedom, and the different energy bands. For Lévy-Leblond fermions, an interpretation is given in terms of massless fermions in an effective 4D spacetime, and in this case the pseudospin is related to four dimensional chirality. A non-zero energy band gap between conduction and valence electronic bands is obtained for surfaces with positive curvature. View Full-Text
Keywords: few-layers graphene; Lévy-Leblond equations; non-relativistic fermions; Eisenhart lift; curved systems few-layers graphene; Lévy-Leblond equations; non-relativistic fermions; Eisenhart lift; curved systems
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Cariglia, M.; Giambò, R.; Perali, A. Electronic Properties of Curved Few-Layers Graphene: A Geometrical Approach. Condens. Matter 2018, 3, 11.

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