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

Presented by: 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.

Abstract
Résumé

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.

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.

Received: 2015-05-25
Accepted: 2015-10-13
Published online: 2015-11-04

DOI: 10.1016/j.crma.2015.10.007

Author's affiliations:

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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     author = {Vladimir A. Kozlov and Sergei A. Nazarov and Anna Orlof},
     title = {Trapped modes supported by localized potentials in the zigzag graphene ribbon},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {63--67},
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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/

References
Cited by

[1] A. Aslanian; L. Parnovskii; D. Vassiliev Q. J. Mech. Appl. Math., 53 (2000) no. 3, pp. 429-447

[2] L. Brey; H.A. Fertig Phys. Rev. B, 73 (2006)

[3] G. Cardone; S.A. Nazarov; K. Ruotsalainen Sb. Math., 203 (2012) no. 2, pp. 153-182

[4] D.V. Evans; M. Levitin; D. Vasil'ev J. Fluid Mech., 261 (1994), pp. 21-31

[5] I.V. Kamotskii; S.A. Nazarov J. Math. Sci., 111 (2002) no. 4, pp. 3657-3666

[6] S.A. Nazarov Theor. Math. Phys., 167 (2011) no. 2, pp. 606-627

[7] S.A. Nazarov Comput. Math. Math. Phys., 52 (2012) no. 3, pp. 598-632

[8] S.A. Nazarov Funct. Anal. Appl., 475 (2013) no. 3, pp. 195-209

[9] M.M. Vainberg; V.A. Trenogin Theory of Branching of Solutions of Non-linear Equations, Noordhoff International Publishing, Leyden, 1974

[10] M.D. VanDyke Perturbation Methods in Fluid Mechanics, Applied Mathematics and Mechanics, vol. 8, Academic Press, New York–London, 1964

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