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

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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.

About the authors

N. R. Sadykov

Snezhinsky Institute of Physics and Technology, National Research Nuclear University MEPhI

Email: n.r.sadykov@rambler.ru
456776, Snezhinsk, Russia

Yu. A. Petrova

Snezhinsky Institute of Physics and Technology, National Research Nuclear University MEPhI

Email: n.r.sadykov@rambler.ru
456776, Snezhinsk, Russia

I. A. Pilipenko

Snezhinsky Institute of Physics and Technology, National Research Nuclear University MEPhI

Email: n.r.sadykov@rambler.ru
456776, Snezhinsk, Russia

R. S. Khrabrov

Snezhinsky Institute of Physics and Technology, National Research Nuclear University MEPhI

Email: n.r.sadykov@rambler.ru
456776, Snezhinsk, Russia

S. N. Skryabin

Snezhinsky Institute of Physics and Technology, National Research Nuclear University MEPhI

Author for correspondence.
Email: n.r.sadykov@rambler.ru
456776, Snezhinsk, Russia

References

  1. Jensen H., Koppe H. // Ann. Phys. 1971. V. 63. № 2. P. 586. https://doi.org/10.1016/0003-4916(71)90031-5
  2. Costa R.C.T. // Phys. Rev. A. 1981. V. 23. № 4. P. 1982. https://doi.org/10.1103/PhysRevA.23.1982
  3. Cantele G., Ninno D., Iadonisi G. // Phys. Rev. B. 2000. V. 61. P. 3730. https://doi.org/10.1103/PhysRevB.61.13730
  4. Aoki H., Koshino M., Takeda D. et al. // Ibid. 2001. V. 65. P. 035102. https://doi.org/10.1103/PhysRevB.65.035102
  5. Encinosa M., Mott L. // Phys. Rev. A. 2003. V. 68. P. 014102. https://doi.org/10.1103/PhysRevA.68.014102
  6. Gravesen J., Willatzen M. // Ibid. 2005. V. 72. P. 032108. https://doi.org/10.1103/PhysRevA.72.032108
  7. Marchi A., Reggiani S., Rudan M., Bertoni A. // Phys. Rev. B. 2005. V. 72. P. 035403. https://doi.org/10.1103/PhysRevB.72.035403
  8. 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.
  9. Ortix C., van den Brink J. // Phys. Rev. B. 2010. V. 81. P. 165419. https://doi.org/10.1103/PhysRevB.81.165419
  10. 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
  11. 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.
  12. Mohanty N., Moore D., Xu Z. et al. // Nat. Commun. 2012. V. 3. P. 844. https://doi.org/10.1038/ncomms1834
  13. Dandoloff R., Truong T.T. // Phys. Lett. A. 2004. V. 325. P. 233. https://doi.org/10.1016/j.physleta.2004.03.050
  14. Atanasov V., Dandoloff R., Saxena A. // Phys. Rev. B. 2009. V. 79. P. 033404. https://doi.org/10.1103/PhysRevB.79.033404
  15. Burgess M., Jensen B. // Phys. Rev. A. 1993. V. 48. P. 1861. https://doi.org/10.1103/PhysRevA.48.1861
  16. Atanasov V., Saxena A. // Phys. Rev. B. 2010. V. 81. P. 205409. https://doi.org/10.1103/PhysRevB.81.205409
  17. Joglekar Y.N. and Saxena A. // Ibid. 2009. V. 80. P. 153405-4. https://doi.org/10.1103/PhysRevB.80.153405
  18. Atanasov V., Saxena A.// J. Phys. Condens. Matter. 2011. V. 23. P. 175301.
  19. Yang S.H. // Appl. Phys. Lett. 2020. V. 116. P. 120502 .
  20. Yang S.H., Naaman R., Paltiel Y., Parkin S.S.P. // Nat. Rev. Phys. 2021. V. 3. P. 328.
  21. Michaeli K., Kantor-Uriel N., Naamanm R., and Waldeck D.H.// Chem. Soc. Rev. 2016. V. 45. P. 6478
  22. Naaman R. and Waldeck D.H.// Annu. Rev. Phys. Chem. 2015. V. 66. P. 263.
  23. D’yachkova P.N. and D’yachkov E.P. // Appl. Phys. Lett. 2022. V. 120. P. 173101. https://doi.org/10.1063/5.008690
  24. Kiricsi I., Fudala A., Konya et al. // Appl. Catal. 2000. A. 203. L. 1.
  25. De Crescenzi M., Castrucci P., Scarselli M. et al. // Appl. Phys. Lett. 2005. V. 86. P. 231901.
  26. Morata A., Pacios M., Gadea G. et al. // Nat. Commun. 2018. V. 9. P. 4759.
  27. Wu H., Chan G., and Choi J.W. // Nat. Nanotechnol. 2012. V. 7. P. 310.
  28. Chan C.K., Peng H., Liu G. et al. // Ibid. 2008. V. 3. P. 31.
  29. 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
  30. Dubrovin B.A., Novikov S.P., and Fomenko A.T. // Modern Geometry: Methods and Applications, 2nd ed. M.: Fizmatlit, 1986.
  31. Spivak M. A Comprehensive Introduction to Differential Geometry Publish or Perish, Boston, 1999.
  32. Sadykov N.R. Quantum Electronics. 1996. V. 26 (3). P. 271. http://iopscience.iop.org/1063-7818/26/3/A24.
  33. 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.
  34. Onipko A. and Malysheva L. // Phys. Status Solidi. 2017. V. 255. P. 1700248. https://doi.org/10.1002/pssb.201700248
  35. Boyd R.W. Nonlinear Optics. Academic Press, San Diego (2003).
  36. 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.
  37. Никифоров А.Ф., Уваров В.Б. Специальные функции математической физики. М.: Физматлит, 1978.
  38. Садыков Н.Р. // Теоретическая и математическая физика. 2014. Вып. 180. № 3. С. 368. https://doi.org/10.4213/tmf8642

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Copyright (c) 2023 Н.Р. Садыков, Ю.А. Петрова, И.А. Пилипенко, Р.С. Храбров, С.Н. Скрябин

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