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Dirac cones for graph models of multilayer AA-stacked graphene sheets

  • César R. de Oliveira ORCID logo and Vinícius L. Rocha ORCID logo
Published/Copyright: February 15, 2021
Zeitschrift für Naturforschung A
From the journal Zeitschrift für Naturforschung A Volume 76 Issue 4

Abstract

We propose an extension, of a quantum graph model for a single sheet of graphene, to multilayer AA-stacked graphene and also to a model of the bulk graphite. Spectra and Dirac cones are explicitly characterized for bilayer and trilayer graphene, as well as for graphite. For weak layer interaction (as proposed in the text), simple perturbation arguments also cover any number of layers and it mathematically recovers basic cone existences from the theoretical and experimental physics literature; its main strength is its simplicity.

Keywords: Dirac cones; multilayer graphene; quantum graph model; spectral analysis
Corresponding author: César R. de Oliveira, Departamento de Matemática, UFSCar, São Carlos, SP, 13560-970Brazil, E-mail:

Funding source: Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Funding source: Conselho Nacional de Desenvolvimento Científico e Tecnológico

Award Identifier / Grant number: 303503/2018-1

  1. Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: CRdO thanks the partial support by Conselho Nacional de Desenvolvimento Científico e Tecnológico (a Brazilian government agency, under contract 303503/2018-1). VLR thanks the financial support by Coordenaçãoo de Aperfeiçoamento de Pessoal de Nível Superior (a Brazilian government agency).

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

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Received: 2020-12-01
Accepted: 2021-01-20
Published Online: 2021-02-15
Published in Print: 2021-04-27

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/zna-2020-0330
Keywords for this article
Dirac cones; multilayer graphene; quantum graph model; spectral analysis

Articles in the same Issue

  1. Frontmatter
  2. General
  3. Rapid Communication
  4. All waves have a zero tunneling time
  5. Atomic, Molecular & Chemical Physics
  6. Studies of local structures for Cu2+ centers in M2Zn(SO4)2·6H2O (M = NH4 and Rb) crystals
  7. Dynamical Systems & Nonlinear Phenomena
  8. Dynamics of liquid drop on a vibrating micro-perforated plate
  9. Inverse scattering method for the Kundu-Eckhaus equation with zero/nonzero boundary conditions
  10. Evolution of nonlinear stationary formations in a quantum plasma at finite temperature
  11. Solid State Physics & Materials Science
  12. Effect of ZnO nanoparticles on optical textures and image analysis properties of 7O.O5 liquid crystalline compound
  13. First-principles study on band gaps and transport properties of van der Waals WSe2/WTe2 heterostructure
  14. Dirac cones for graph models of multilayer AA-stacked graphene sheets
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