Effect of a Geometric Potential on the Eigenfunction and Eigenvalue of the Energy of State in a Twisted Graphene Nanoribbon

N. R. Sadykov; Садыков Н. Р.; Yu. A. Petrova; Петрова Ю. А.; I. A. Pilipenko; Пилипенко И. А.; R. S. Khrabrov; Храбров Р. С.; S. N. Skryabin; Скрябин С. Н.

doi:10.31857/S004445372302022X

Effect of a Geometric Potential on the Eigenfunction and Eigenvalue of the Energy of State in a Twisted Graphene Nanoribbon

Authors: Sadykov N.R.¹, Petrova Y.A.¹, Pilipenko I.A.¹, Khrabrov R.S.¹, Skryabin S.N.¹
Affiliations:
1. Snezhinsky Institute of Physics and Technology, National Research Nuclear University MEPhI
Issue: Vol 97, No 2 (2023)
Pages: 252-257
Section: ФИЗИЧЕСКАЯ ХИМИЯ НАНОКЛАСТЕРОВ, СУПРАМОЛЕКУЛЯРНЫХ СТРУКТУР И НАНОМАТЕРИАЛОВ
Submitted: 15.10.2023
Published: 01.02.2023
URL: https://ogarev-online.ru/0044-4537/article/view/136521
DOI: https://doi.org/10.31857/S004445372302022X
EDN: https://elibrary.ru/ELHIFX
ID: 136521

Cite item

Full Text

Open Access
Restricted Access

Access granted
Restricted Access

Subscription Access

Abstract
About the authors
References
Supplementary files
Statistics

Abstract

An expression is obtained for an effective geometric potential based on a coordinate system for a nanoribbon twisted in the form of a helicoid. The effective geometric potential for a Schrödinger equation is used to study a graphene nanoribbon of finite length with “armchair” edges under the action of an external electric field parallel to them. Solutions are calculated for the energy levels and wave functions of electrons in the vicinity of the Dirac point. It is shown there is only one state in the transverse direction.

Keywords

geometric potential, twisted nanoribbons, Weingarten equation, kp-type model

References

Jensen H., Koppe H. // Ann. Phys. 1971. V. 63. № 2. P. 586. https://doi.org/10.1016/0003-4916(71)90031-5
Costa R.C.T. // Phys. Rev. A. 1981. V. 23. № 4. P. 1982. https://doi.org/10.1103/PhysRevA.23.1982
Cantele G., Ninno D., Iadonisi G. // Phys. Rev. B. 2000. V. 61. P. 3730. https://doi.org/10.1103/PhysRevB.61.13730
Aoki H., Koshino M., Takeda D. et al. // Ibid. 2001. V. 65. P. 035102. https://doi.org/10.1103/PhysRevB.65.035102
Encinosa M., Mott L. // Phys. Rev. A. 2003. V. 68. P. 014102. https://doi.org/10.1103/PhysRevA.68.014102
Gravesen J., Willatzen M. // Ibid. 2005. V. 72. P. 032108. https://doi.org/10.1103/PhysRevA.72.032108
Marchi A., Reggiani S., Rudan M., Bertoni A. // Phys. Rev. B. 2005. V. 72. P. 035403. https://doi.org/10.1103/PhysRevB.72.035403
Ведерников А.И., Чаплик А.В. // ЖЭТФ. 2000. Т. 117. № 2. С. 449. http://www.jetp.ac.ru/cgi-bin/r/index/r/117/2/p449?a=list.
Ortix C., van den Brink J. // Phys. Rev. B. 2010. V. 81. P. 165419. https://doi.org/10.1103/PhysRevB.81.165419
Садыков Н.Р., Юдина Н.В. // Журн. технич. физики. 2020. Т. 90. Вып. 3. С. 387. https://doi.org/10.21883/JTF.2020.03.48921.62-19
Atanasov V., Saxena A. // Phys. Rev.B. 2015. B. V. 92. P. 035440. https://doi.org/journals.aps.org/prb/abstract/10.1103/ PhysRevB.92.035440.
Mohanty N., Moore D., Xu Z. et al. // Nat. Commun. 2012. V. 3. P. 844. https://doi.org/10.1038/ncomms1834
Dandoloff R., Truong T.T. // Phys. Lett. A. 2004. V. 325. P. 233. https://doi.org/10.1016/j.physleta.2004.03.050
Atanasov V., Dandoloff R., Saxena A. // Phys. Rev. B. 2009. V. 79. P. 033404. https://doi.org/10.1103/PhysRevB.79.033404
Burgess M., Jensen B. // Phys. Rev. A. 1993. V. 48. P. 1861. https://doi.org/10.1103/PhysRevA.48.1861
Atanasov V., Saxena A. // Phys. Rev. B. 2010. V. 81. P. 205409. https://doi.org/10.1103/PhysRevB.81.205409
Joglekar Y.N. and Saxena A. // Ibid. 2009. V. 80. P. 153405-4. https://doi.org/10.1103/PhysRevB.80.153405
Atanasov V., Saxena A.// J. Phys. Condens. Matter. 2011. V. 23. P. 175301.
Yang S.H. // Appl. Phys. Lett. 2020. V. 116. P. 120502 .
Yang S.H., Naaman R., Paltiel Y., Parkin S.S.P. // Nat. Rev. Phys. 2021. V. 3. P. 328.
Michaeli K., Kantor-Uriel N., Naamanm R., and Waldeck D.H.// Chem. Soc. Rev. 2016. V. 45. P. 6478
Naaman R. and Waldeck D.H.// Annu. Rev. Phys. Chem. 2015. V. 66. P. 263.
D’yachkova P.N. and D’yachkov E.P. // Appl. Phys. Lett. 2022. V. 120. P. 173101. https://doi.org/10.1063/5.008690
Kiricsi I., Fudala A., Konya et al. // Appl. Catal. 2000. A. 203. L. 1.
De Crescenzi M., Castrucci P., Scarselli M. et al. // Appl. Phys. Lett. 2005. V. 86. P. 231901.
Morata A., Pacios M., Gadea G. et al. // Nat. Commun. 2018. V. 9. P. 4759.
Wu H., Chan G., and Choi J.W. // Nat. Nanotechnol. 2012. V. 7. P. 310.
Chan C.K., Peng H., Liu G. et al. // Ibid. 2008. V. 3. P. 31.
Sadykov N.R., Muratov E.T., Pilipenko I.A., Aporoski A.V. // Physica E: Low-dimensional Systems and Nanostructures. 2020. V. 120. P. 114071. https://doi.org/10.1016/j.physe.2020.114071
Dubrovin B.A., Novikov S.P., and Fomenko A.T. // Modern Geometry: Methods and Applications, 2nd ed. M.: Fizmatlit, 1986.
Spivak M. A Comprehensive Introduction to Differential Geometry Publish or Perish, Boston, 1999.
Sadykov N.R. Quantum Electronics. 1996. V. 26 (3). P. 271. http://iopscience.iop.org/1063-7818/26/3/A24.
Будак Б.М., Самарский А.А., Тихонов А.Н. Сборник задач по математической физике. 4-е изд., испр. М.: ФИЗМАТЛИТ, 2004. 688 с. ISBN 5-9221-0311-3.
Onipko A. and Malysheva L. // Phys. Status Solidi. 2017. V. 255. P. 1700248. https://doi.org/10.1002/pssb.201700248
Boyd R.W. Nonlinear Optics. Academic Press, San Diego (2003).
Landau L.D., Lifshitz E.M. Course of Theoretical Physics. V. 3: Quantum Mechanics: Non-Relativistic Theory, 4th ed. (Oxford Univ. Press, Oxford, 1980) M.: Nauka, 1989.
Никифоров А.Ф., Уваров В.Б. Специальные функции математической физики. М.: Физматлит, 1978.
Садыков Н.Р. // Теоретическая и математическая физика. 2014. Вып. 180. № 3. С. 368. https://doi.org/10.4213/tmf8642