Next Article in Journal
Decadal Climate Change in Ny-Ålesund, Svalbard, A Representative Area of the Arctic
Next Article in Special Issue
Microscopic Linear Response Theory of Spin Relaxation and Relativistic Transport Phenomena in Graphene
Previous Article in Journal
Electromagnetic Field in Hybrid Quantum Plasmonic-Photonic Systems
Previous Article in Special Issue
Nanoscale Phase Separation and Lattice Complexity in VO2: The Metal–Insulator Transition Investigated by XANES via Auger Electron Yield at the Vanadium L23-Edge and Resonant Photoemission
Article Menu

Export Article

Open AccessArticle
Condens. Matter 2018, 3(2), 11;

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

1,*,†, 2,† and 3,†
Departamento de Física, Universidade Federal de Ouro Preto, 35400-000 Ouro Preto MG, Brazil
School of Science and Technology, Mathematics Division, University of Camerino, 62032 Camerino, Italy
School of Pharmacy, Physics Unit, University of Camerino, 62032 Camerino, Italy
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Received: 19 December 2017 / Revised: 21 March 2018 / Accepted: 30 March 2018 / Published: 5 April 2018
PDF [2433 KB, uploaded 5 April 2018]


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

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

Share & Cite This Article

MDPI and ACS Style

Cariglia, M.; Giambò, R.; Perali, A. Electronic Properties of Curved Few-Layers Graphene: A Geometrical Approach. Condens. Matter 2018, 3, 11.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Metrics

Article Access Statistics



[Return to top]
Condens. Matter EISSN 2410-3896 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top