Journal
CONDENSED MATTER
Volume 3, Issue 2, Pages -Publisher
MDPI
DOI: 10.3390/condmat3020011
Keywords
few-layers graphene; Levy-Leblond equations; non-relativistic fermions; Eisenhart lift; curved systems
Categories
Funding
- CNPq [303923/2015-6]
- Pesquisador Mineiro project [PPM-00630-17]
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We show the presence of non-relativistic Levy-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 Levy-Leblond with a well defined combination of pseudospin, and that admit Levy-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 Levy-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.
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