najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМОnajo-1231Research ArticleMATHEMATICSМАТЕМАТИКАScattering by a junction of “zig-zag” and “armchair” nanotubesРассеяние на стыке нанотрубок «зигзаг» и «кресло»ЛобановИ. С.LobanovI, S.

Санкт-Петербург.

I.S. Lobanov - Ph.D, Associate Professor,

Saint-Petersburg.

lobanov.igor@gmail.comПоповИ. Ю.PopovI. Yu.

Санкт-Петербург.

I.Yu. Popov –  D.Sc., Professor,

Saint-Petersburg.

popov1955@gmail.comСанкт-Петербургский национальный исследовательский университет информационных технологий, механики и оптикиSaint-Petersburg National Research University of Information Technologies, Mechanics and Optics20122008202532626Copyright © Lobanov I.S., Popov I.Y., 20252025Лобанов И.С., Попов И.Ю.Lobanov I.S., Popov I.Y.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/1231

The quantum graph model of junction of zig-zag and armchair signle-wall carbon nanotubes is considered. The spectrum is completely described. A condition on appearance of stateslocalized near the interface is provided. All localized states are explicitly calculated. 

Рассматривается модель квантовых графов сочленения однослойных нанотрубок типа «зигзаг» и «кресло». Дается полное описание спектра. Находятся условия возникновения связанного состояния на соединении нанотрубок. Приводится полное описание всех локализованных состояний.

соединение нанотрубокоднослойные углеродные нанотрубкиквантовый графcarbone nanotubequantum graphscatteringРабота поддержана ФЦП «Научные и научно-педагогические кадры инновационной России на 2009-2013 годы» (контракты Р689 NK-526P, 14.740.11.0879, 16,740,11,0030), грантом 11-08-00267 РФФИ.ReferencesA. Badanin, J. Bruning, E. Korotyaev, I. Lobanov. Schrodinger operators on armchair nanotubes. I.¨ arXiv:0707.3909A. Badanin, J. Bruning, E. Korotyaev, I. Lobanov. Schrodinger operators on armchair nanotubes. I.¨ arXiv:0707.3909Chuanhong Jin, Kazu Suenaga, Sumio Iijima Plumbing carbon nanotubes // Nature Nanotechnology 3, 17 21. – 2008. Published online: 9 December 2007 doi: 10.1038/nnano.2007.406Chuanhong Jin, Kazu Suenaga, Sumio Iijima Plumbing carbon nanotubes // Nature Nanotechnology 3, 17 21. – 2008. Published online: 9 December 2007 doi: 10.1038/nnano.2007.406E. Korotyaev. Lattice Dislocations in a 1-Dimensional Model // Commun. Math. Phys. – 2000. – 213. – P. 471-489.E. Korotyaev. Lattice Dislocations in a 1-Dimensional Model // Commun. Math. Phys. – 2000. – 213. – P. 471-489.E. Korotyaev. Schrodinger operator with a junction of two 1-dimensional periodic potentials // Asymptotic¨ Analysis. – 2000. – 45. – P. 73-97.E. Korotyaev. Schrodinger operator with a junction of two 1-dimensional periodic potentials // Asymptotic¨ Analysis. – 2000. – 45. – P. 73-97.E. Korotyaev, I. Lobanov. Schrodinger Operators on Zigzag Nanotubes // Journal Annales Henri Poincare. –¨ 2007. – 8 (6). – P. 1151-1176.E. Korotyaev, I. Lobanov. Schrodinger Operators on Zigzag Nanotubes // Journal Annales Henri Poincare. –¨ 2007. – 8 (6). – P. 1151-1176.A. Rochefort, P. Avouris. Quantum Size Effects in Carbon Nanotube Intramolecular Junctions // Nano Letters.– 2002. – 2 (3). – pp 253-256 DOI: 10.1021/nl015705tA. Rochefort, P. Avouris. Quantum Size Effects in Carbon Nanotube Intramolecular Junctions // Nano Letters.– 2002. – 2 (3). – pp 253-256 DOI: 10.1021/nl015705tH. Santos, A. Ayuela, W. Jaskolski, M. Pelc, L. Chico. Interface States in Carbon Nanotube Junctions: Rolling up graphene // Phys. Rev. B. – 2009. – 80. – 035436.H. Santos, A. Ayuela, W. Jaskolski, M. Pelc, L. Chico. Interface States in Carbon Nanotube Junctions: Rolling up graphene // Phys. Rev. B. – 2009. – 80. – 035436.Wang, R. N., Zheng, X. H., Song, L. L. and Zeng, Z., Ab initio study on the electronic transport properties of carbon nanotube intramolecular junctions // Physica status solidi (a). 2011. – 208: 2803-2808. doi: 10.1002/pssa.201127314Wang, R. N., Zheng, X. H., Song, L. L. and Zeng, Z., Ab initio study on the electronic transport properties of carbon nanotube intramolecular junctions // Physica status solidi (a). 2011. – 208: 2803-2808. doi: 10.1002/pssa.201127314Wei, D. and Liu, Y., The Intramolecular Junctions of Carbon Nanotubes // Advanced Materials. 2008.– 20: 2815-2841. doi: 10.1002/adma.200800589Wei, D. and Liu, Y., The Intramolecular Junctions of Carbon Nanotubes // Advanced Materials. 2008.– 20: 2815-2841. doi: 10.1002/adma.200800589Yagang Yao, Qingwen Li, Jin Zhang, Ran Liu, Liying Jiao, Yuntian T. Zhu, Zhongfan Liu. Temperaturemediated growth of single-walled carbon-nanotube intramolecular junctions // Nature Materials. – 2007. – 6.– P. 283–286. Published online: 18 March 2007 doi: 10.1038/nmat1865Yagang Yao, Qingwen Li, Jin Zhang, Ran Liu, Liying Jiao, Yuntian T. Zhu, Zhongfan Liu. Temperaturemediated growth of single-walled carbon-nanotube intramolecular junctions // Nature Materials. – 2007. – 6.– P. 283–286. Published online: 18 March 2007 doi: 10.1038/nmat1865

The authors declare that there are no conflicts of interest present.