Effective Quantum Graph Models of Some Nonequilateral Graphyne Materials

de Oliveira, César R.; Rocha, Vinícius L.

doi:10.3390/c9030076

Open AccessArticle

Effective Quantum Graph Models of Some Nonequilateral Graphyne Materials

by

César R. de Oliveira

^*,†

and

Vinícius L. Rocha

^†

Departamento de Matemática, Universidade Federal de São Carlos, Cx. P. 676, São Carlos 13565-905, SP, Brazil

^*

Author to whom correspondence should be addressed.

^†

These authors contributed equally to this work.

C 2023, 9(3), 76; https://doi.org/10.3390/c9030076

Submission received: 25 May 2023 / Revised: 10 July 2023 / Accepted: 3 August 2023 / Published: 8 August 2023

(This article belongs to the Special Issue Advances in Modelling of Size Effects in Graphene and Carbon Nanotubes)

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Abstract

It is shown that it is possible to adapt the quantum graph model of graphene to some types of nonequilateral graphynes considered in the literature; we also discuss the corresponding nanotubes. The proposed models are, in fact, effective models and are obtained through selected boundary conditions and an ad hoc prescription. We analytically recover some results from the literature, in particular, the presence of Dirac cones for

α

-,

β

- and

(6, 6, 12)

-graphynes; for

γ

-graphyne, our model presents a band gap (according to the literature), but only for a range of parameters, with a transition at a certain point with quadratic touch and then the presence of Dirac cones.

Keywords: graphyne; graphyne nanotube; quantum graph; Dirac cone

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MDPI and ACS Style

de Oliveira, C.R.; Rocha, V.L. Effective Quantum Graph Models of Some Nonequilateral Graphyne Materials. C 2023, 9, 76. https://doi.org/10.3390/c9030076

AMA Style

de Oliveira CR, Rocha VL. Effective Quantum Graph Models of Some Nonequilateral Graphyne Materials. C. 2023; 9(3):76. https://doi.org/10.3390/c9030076

Chicago/Turabian Style

de Oliveira, César R., and Vinícius L. Rocha. 2023. "Effective Quantum Graph Models of Some Nonequilateral Graphyne Materials" C 9, no. 3: 76. https://doi.org/10.3390/c9030076

APA Style

de Oliveira, C. R., & Rocha, V. L. (2023). Effective Quantum Graph Models of Some Nonequilateral Graphyne Materials. C, 9(3), 76. https://doi.org/10.3390/c9030076

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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Effective Quantum Graph Models of Some Nonequilateral Graphyne Materials

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