Effect of Torsional Deformations on the Spin States of Carbon Nanotubes with Metallic Conductivity

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription or Fee Access

Abstract

The formation of spin levels upon torsional deformation of nonchiral (n, n) carbon nanotubes has been theoretically studied. In the absence of mechanical deformation, nanotubes have inversion symmetry and a metallic band structure with a spin-degenerate state near the Fermi level. The twisting deformation breaks the inversion symmetry, so that the tube becomes chiral. As a result, due to the Rashba effect, the degeneracy of the levels is completely lifted and spin gaps are formed between the bands of predominantly α and β types.

About the authors

E. P. D’yachkov

Institute of General and Inorganic Chemistry, Russian Academy of Sciences

Email: p_dyachkov@rambler.ru
119991, Moscow, Russia

N. A. Lomakin

Institute of General and Inorganic Chemistry, Russian Academy of Sciences

Email: p_dyachkov@rambler.ru
119991, Moscow, Russia

P. N. D’yackov

Institute of General and Inorganic Chemistry, Russian Academy of Sciences

Author for correspondence.
Email: p_dyachkov@rambler.ru
119991, Moscow, Russia

References

  1. Ando T. // J. Phys. Soc. Jpn. 2000. V. 69. P. 1757. https://doi.org/10.1143/JPSJ.69.1757
  2. Chico L., Lopez-Sancho M.P., Munoz M.C. // Phys. Rev. Lett. 2004. V. 93. P. 176402. https://doi.org/10.1103/PhysRevLett.93.176402
  3. Huertas-Hernando D., Guinea F., Brataas A. // Phys. Rev. B. 2006. V. 74. P. 155426. https://doi.org/10.1103/PhysRevB.74.155426
  4. Kuemmeth F., Ilani S., Ralph D. et al. // Nature. 2008. V. 452. P. 448. https://doi.org/10.1038/ncomms2584
  5. Ilani S., McEuen P.L. // Annu. Rev. Condens. Matter. Phys. 2010. V. 1. P. 1. https://doi.org/10.1146/annurev-conmatphys-070909-103928
  6. Jhang S.H., Marganska M., Skuorsky Y. et al. // Phys. Rev. B. 2010. V. 82. P. 041404. https://doi.org/10.1103/PhysRevB.82.041404
  7. Jespersen T., Grove-Rusmussen K., Paaske J. // Nature Physics. 2011. V. 7. P. 348. https://doi.org/10.1038/nphys1880
  8. Steele G.A., Pei F., Laird E.A. et al. // Nature Commun. 2013. V. 4. P. 1573. https://doi.org/10.1038/ncomms2584
  9. Wunsch B. // Phys. Rev. B. 2009. V. 79. P. 235408. https://doi.org/10.1103/PhysRevB.79.235408
  10. Merchant C., Markovic N. // Phys. Rev. Lett. 2008. V. 100. P. 156601. https://doi.org/10.1103/PhysRevLett.100.156601
  11. Wang K.Y., Blackburn A.M., Wang H.F. et al. // Appl. Phys. Lett. 2013. V. 102. P. 093508. https://doi.org/10.1063/1.4794535
  12. Guimaraes F.S.M., Kirwan D.F., Costa A.T. et al. // Phys. Rev. B. 2010. V. 81. P. 153408. https://doi.org/10.1103/PhysRevB.81.153408
  13. Flensberg K., Marcus C. // Phys. Rev. B. 2010. V. 81. P. 195418. https://doi.org/10.1103/PhysRevB.81.195418
  14. Gunlycke D., Jefferson J.H., Bailey S.W.D et al. // J. Phys.: Condens. Matter. 2006. V. 18. P. S843. https://doi.org/10.1088/0953-8984/18/21/S10
  15. Hueso L.E., Pruneda J.M., Ferrari V. // Nature. 2007. V. 445. P. 410. https://doi.org/10.1038/nature05507
  16. Galland C., Imamoglu A. // Phys. Rev. Lett. 2008. V. 101. P. 157404. https://doi.org/10.1103/PhysRevLett.101.157404
  17. Bulaev D., Trauzettel B., Loss D. // Phys. Rev. B. 2008. V. 77. P. 235301. https://doi.org/10.1103/PhysRevB.77.235301
  18. Laird E.A., Pei F., Kouwenhoven L.P. // Nat. Nanotechnol. 2013. V. 8. P. 565. https://doi.org/10.1038/nnano.2013.140
  19. Schulz A., De Martino A., Egger R. // Phys. Rev. B. 2010. V. 82. P. 033407. https://doi.org/10.1103/PhysRevB.82.033407
  20. Galpin M.R., Jayatilaka F.W., Logan D.E. // Phys. Rev. B. 2010. V. 81. P. 075437. https://doi.org/10.1103/PhysRevB.81.075437
  21. Lim J., Lopez R., Aguado R. // Phys. Rev. Lett. 2011. V. 107. P. 196801. https://doi.org/10.1103/PhysRevLett.107.196801
  22. Palyi A., Struck P., Rudner M. et al. // Phys. Rev. Lett. 2012. V. 108. P. 206811. https://doi.org/10.1103/PhysRevLett.108.206811
  23. Ohm C., Stampfer C., Splettstoesser J. et al. // Appl. Phys. Lett. 2012. V. 100. P. 143103. https://doi.org/10.1063/1.3698395
  24. Alam K.M., Pramanik S. // Adv. Funct. Mater. 2015. V. 25. P. 3210. https://doi.org/10.1002/adfm.201500494
  25. Alam K.M. Pramanik S. // Nanoscale. 2017. V. 9. P. 5155. https://doi.org/10.1039/C6NR09395G
  26. Rahman Md.W., Alam K.M., Pramanik S. // ACS Omega. 2018. V. 3. P. 17108. https://doi.org/10.1021/acsomega.8b02237
  27. Rahman Md.W., Firouzeh S., Mujica V. et al. // ACS Nano. 2020. V. 14. P. 3389. https://doi.org/10.1021/acsnano.9b09267
  28. Yang S.H. // Appl. Phys. Lett. 2021. V. 16. P. 120502. https://doi.org/10.1063/5.0039147
  29. Yang S.H., Naaman R., Paltiel Y. et al. // Nat. Rev. Phys. 2021. V. 3. P. 328. https://doi.org/10.1038/s42254-021-00302-9
  30. Michaeli K., Kantor-Uriel N., Naamanm R. et al. // Chem. Soc. Rev. 2016. V. 45. P. 6478. https://doi.org/10.1039/C6CS00369A
  31. Naaman R., Waldeck D.H. // Annu. Rev. Phys. Chem. 2015. V. 66. P. 263. https://doi.org/10.1146/annurev-physchem-040214-121554
  32. Joselevich E. // ChemPhysChem. 2006. V. 7. P. 1405. https://doi.org/10.1002/cphc.200600206
  33. D’yachkov P.N. // Russ. J. Inorg. Chem. 2021. V. 66. P. 852. https://doi.org/10.1134/S0036023621110048
  34. D’yachkov P.N. // Appl. Func. Mater. 2022. V. 2. P. 35. https://doi.org/10.35745/afm2022v02.02.0006
  35. D’yachkov P.N., Makaev D.V. // Phys. Rev. B. 2007. V. 76. P. 195411. https://doi.org/10.1103/PhysRevB.76.195411
  36. D’yachkov P.N., Makaev D.V. // Int. J. Quantum Chem. 2016. V. 116. P. 316. https://doi.org/10.1002/qua.25030
  37. D’yachkov P.N. // Quantum Chemistry of Nanotubes: Electronic Cylindrical Waves. London: Taylor and Francis, 2019. 212 p.
  38. Дьячков П.Н. // Углеродные нанотрубки: строение, свойства, применения. М.: БИНОМ. Лаборатория знаний, 2006. 203 с.
  39. Cohen-Karni T., Segev L., Srur-Lavi O. et al. // Nature Nanotechnol. 2006. V. 1. P. 36. https://doi.org/10.1038/nnano.2007.179
  40. Changa T. // Appl. Phys. Lett. 2007. V. 90. P. 201910. https://doi.org/10.1063/1.2739325
  41. Zhang D.-B., James R.D., Dumitrică T. // Phys. Rev. B. 2009. V. 80. P. 155418. https://doi.org/10.1103/PhysRevB.80.115418
  42. Bercioux D., Lucignano P. // Rep. Prog. Phys. 2015. V. 78. P. 106001. https://https://doi.org/10.1088/0034-4885/78/10/106001
  43. Koo H.C., Nitta J., Frolov S. M. et al. // Nat. Mater. 2015. V. 14. P. 871. https://doi.org/10.1038/nmat4360
  44. Koo H.C., Kim S.B., Kim H. et al. // Adv. Mater. 2020. V. 32. P. 2002117. https://doi.org/10.1002/adma.202002117
  45. Рашба E.И., Шека В.И. // Физ. тверд. тела. 1959. Т. 2. С. 162.
  46. D’yachkov P.N., D’yachkov E.P. // Appl. Phys. Lett. 2022. V. 120. P. 173101. https://doi.org/10.1063/5.0086902
  47. D’yachkov P.N. // Russ. J. Inorg. Chem. 2022. V. 67. P. 1606. https://doi.org/10.1134/S0036023622600678
  48. Martin W.C. Notional Bureau of Standards A. Phys. Chem. 1971. V. 7SA.

Supplementary files

Supplementary Files
Action
1. JATS XML
Download
2.

Download (266KB)
Indexing metadata
3.

Download (163KB)
Indexing metadata
4.

Download (370KB)
Indexing metadata

Copyright (c) 2023 Е.П. Дьячков, Н.А. Ломакин, П.Н. Дьячков