Effective Quantum Graph Models of Some Nonequilateral Graphyne Materials
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 a...
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| Format: | Article |
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MDPI AG
2023-08-01
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| Online Access: | https://www.mdpi.com/2311-5629/9/3/76 |
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| author | César R. de Oliveira Vinícius L. Rocha |
| author_facet | César R. de Oliveira Vinícius L. Rocha |
| author_sort | César R. de Oliveira |
| collection | DOAJ |
| description | 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula>- and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mn>6</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>12</mn><mo>)</mo></mrow></semantics></math></inline-formula>-graphynes; for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula>-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. |
| first_indexed | 2024-03-10T22:55:55Z |
| format | Article |
| id | doaj.art-0bf5b9ea5f3a4777ba2fbf6706f4de66 |
| institution | Directory Open Access Journal |
| issn | 2311-5629 |
| language | English |
| last_indexed | 2024-03-10T22:55:55Z |
| publishDate | 2023-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | C |
| spelling | doaj.art-0bf5b9ea5f3a4777ba2fbf6706f4de662023-11-19T09:57:17ZengMDPI AGC2311-56292023-08-01937610.3390/c9030076Effective Quantum Graph Models of Some Nonequilateral Graphyne MaterialsCésar R. de Oliveira0Vinícius L. Rocha1Departamento de Matemática, Universidade Federal de São Carlos, Cx. P. 676, São Carlos 13565-905, SP, BrazilDepartamento de Matemática, Universidade Federal de São Carlos, Cx. P. 676, São Carlos 13565-905, SP, BrazilIt 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula>- and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mn>6</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>12</mn><mo>)</mo></mrow></semantics></math></inline-formula>-graphynes; for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula>-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.https://www.mdpi.com/2311-5629/9/3/76graphynegraphyne nanotubequantum graphDirac cone |
| spellingShingle | César R. de Oliveira Vinícius L. Rocha Effective Quantum Graph Models of Some Nonequilateral Graphyne Materials C graphyne graphyne nanotube quantum graph Dirac cone |
| title | Effective Quantum Graph Models of Some Nonequilateral Graphyne Materials |
| title_full | Effective Quantum Graph Models of Some Nonequilateral Graphyne Materials |
| title_fullStr | Effective Quantum Graph Models of Some Nonequilateral Graphyne Materials |
| title_full_unstemmed | Effective Quantum Graph Models of Some Nonequilateral Graphyne Materials |
| title_short | Effective Quantum Graph Models of Some Nonequilateral Graphyne Materials |
| title_sort | effective quantum graph models of some nonequilateral graphyne materials |
| topic | graphyne graphyne nanotube quantum graph Dirac cone |
| url | https://www.mdpi.com/2311-5629/9/3/76 |
| work_keys_str_mv | AT cesarrdeoliveira effectivequantumgraphmodelsofsomenonequilateralgraphynematerials AT viniciuslrocha effectivequantumgraphmodelsofsomenonequilateralgraphynematerials |