Trapped modes supported by localized potentials in the zigzag graphene ribbon

Vladimir A. Kozlov; Sergei A. Nazarov; Anna Orlof

doi:10.1016/j.crma.2015.10.007

Partial differential equations/Mathematical physics

Trapped modes supported by localized potentials in the zigzag graphene ribbon
[Modes piégés supportés par des potentiels localisés dans des bandes de graphène en zigzag]

Présenté par : the Editorial Board

Vladimir A. Kozlov ¹ ; Sergei A. Nazarov ^2,^3,⁴ ; Anna Orlof ¹

¹ Department of Mathematics, Linköping University, SE-58183 Linköping, Sweden
² Saint-Petersburg State University, Universitetskaya nab., 7-9, 199034, St. Petersburg, Russia
³ Saint-Petersburg State Polytechnical University, Polytechnicheskaya ul., 29, 195251, St. Petersburg, Russia
⁴ Institute of Problems of Mechanical Engineering RAS, V.O., Bol'shoi pr., 61, 199178, St. Petersburg, Russia

Comptes Rendus. Mathématique, Volume 354 (2016) no. 1, pp. 63-67.

Résumé
Abstract

On construit des potentiels localisés pour les équations de Dirac décrivant le comportement des électrons dans une bande de graphène en zigzag, pour lesquels des modes piégés existent, tels que les valeurs propres correspondantes sont plongées dans le spectre continu.

Localized potentials in the Dirac equation for the electron dynamics in a zigzag graphene ribbon are constructed to support trapped modes while the corresponding eigenvalues are embedded into the continuous spectrum.

Reçu le : 2015-05-25
Accepté le : 2015-10-13
Publié le : 2015-11-04

DOI : 10.1016/j.crma.2015.10.007

Affiliations des auteurs :

Vladimir A. Kozlov ¹ ; Sergei A. Nazarov ^{2, 3, 4} ; Anna Orlof ¹

¹ Department of Mathematics, Linköping University, SE-58183 Linköping, Sweden
² Saint-Petersburg State University, Universitetskaya nab., 7-9, 199034, St. Petersburg, Russia
³ Saint-Petersburg State Polytechnical University, Polytechnicheskaya ul., 29, 195251, St. Petersburg, Russia
⁴ Institute of Problems of Mechanical Engineering RAS, V.O., Bol'shoi pr., 61, 199178, St. Petersburg, Russia

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     title = {Trapped modes supported by localized potentials in the zigzag graphene ribbon},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {63--67},
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     language = {en},
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Vladimir A. Kozlov; Sergei A. Nazarov; Anna Orlof. Trapped modes supported by localized potentials in the zigzag graphene ribbon. Comptes Rendus. Mathématique, Volume 354 (2016) no. 1, pp. 63-67. doi : 10.1016/j.crma.2015.10.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.10.007/

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S. A. Nazarov Trapping of a wave in a curved cylindrical acoustic waveguide with constant cross-section, St. Petersburg Mathematical Journal, Volume 31 (2020) no. 5, pp. 865-885 | DOI:10.1090/spmj/1626 | Zbl:1450.35200
V. A. Kozlov; S. A. Nazarov Model of a saccular aneurysm of the bifurcation node of an artery, Journal of Mathematical Sciences (New York), Volume 238 (2019) no. 5, pp. 676-688 | DOI:10.1007/s10958-019-04266-1 | Zbl:1421.35387
S. A. Nazarov Various manifestations of wood anomalies in locally distorted quantum waveguides, Computational Mathematics and Mathematical Physics, Volume 58 (2018) no. 11, pp. 1838-1855 | DOI:10.1134/s096554251811009x | Zbl:1421.78020

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