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Effects of rotation in the energy spectrum of C60

  • Jonas R. F. LimaEmail author
  • Júlio Brandão
  • Márcio M. Cunha
  • F. Moraes
Regular Article

Abstract

In this paper, motivated by the experimental evidence of rapidly rotating C60 molecules in fullerite, we study the low-energy electronic states of rotating fullerene within a continuum model. In this model, the low-energy spectrum is obtained from an effective Dirac equation including non-Abelian gauge fields that simulate the pentagonal rings of the molecule. Rotation is incorporated into the model by solving the effective Dirac equation in the rotating referential frame. The exact analytical solution for the eigenfunctions and energy spectrum is obtained, yielding the previously known static results in the no rotation limit. Due to the coupling between rotation and total angular momentum, that appears naturally in the rotating frame, the zero modes of static C60 are shifted and also suffer a Zeeman splitting whithout the presence of a magnetic field.

Keywords

Molecular Physics and Chemical Physics 

References

  1. 1.
    C.S. Yannoni, R.D. Johnson, G. Meijer, D.S. Bethune, J.R. Salem, J. Phys. Chem. 95, 9 (1991)CrossRefGoogle Scholar
  2. 2.
    D.A. Neumann et al., Phys. Rev. Lett. 67, 3808 (1991)ADSCrossRefGoogle Scholar
  3. 3.
    Y. Zou et al., Proc. Natl. Acad. Sci. 106, 22135 (2009)ADSCrossRefGoogle Scholar
  4. 4.
    C. Sanchez et al., Chem. Eur. J. 18, 7382 (2012)CrossRefGoogle Scholar
  5. 5.
    J.M. Hawkins, A. Meyer, T.A. Lewis, S. Loren, F.J. Hollander, Science 252, 312 (1991)ADSCrossRefGoogle Scholar
  6. 6.
    P.J. Fagan, J.C. Calabrese, B. Malone, Science 252, 1160 (1991)ADSCrossRefGoogle Scholar
  7. 7.
    R.D. Johnson, C.S. Yannoni, H.C. Dorn, J.R. Salem, D.S. Bethune, Science 255, 1235 (1992)ADSCrossRefGoogle Scholar
  8. 8.
    Q. Liang, O.K.C. Tsui, Y. Xu, H. Li, X. Xiao, Phys. Rev. Lett. 90, 146102 (2003)ADSCrossRefGoogle Scholar
  9. 9.
    J.-M. Yan, Z.-J. Xu, J. Mol. Struct.: Theochem 312, 179 (1994)CrossRefGoogle Scholar
  10. 10.
    M.A. Strzhemechny, E.A. Katz, Fuller. Nanotub. Carbon Nanostructures 12, 281 (2005)CrossRefGoogle Scholar
  11. 11.
    J.Q. Shen, S. He, F. Zhuang, Eur. Phys. J. D 33, 35 (2005)ADSCrossRefGoogle Scholar
  12. 12.
    J.-Q. Shen, S.-L. He, Phys. Rev. B 68, 195421 (2003)ADSCrossRefGoogle Scholar
  13. 13.
    J. Gonzalez, F. Guinea, M. Vozmediano, Nucl. Phys. B 406, 771 (1993)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    J. Gonzalez, F. Guinea, M.A.H. Vozmediano, Phys. Rev. Lett. 69, 172 (1992)ADSCrossRefGoogle Scholar
  15. 15.
    D.V. Kolesnikov, V.A. Osipov, Eur. Phys. J. B 49, 465 (2006)ADSCrossRefGoogle Scholar
  16. 16.
    P.R. Wallace, Phys. Rev. 71, 622 (1947)ADSCrossRefzbMATHGoogle Scholar
  17. 17.
    D.P. DiVincenzo, E.J. Mele, Phys. Rev. B 29, 1685 (1984)ADSCrossRefGoogle Scholar
  18. 18.
    A.H. Castro Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov, A.K. Geim, Rev. Mod. Phys. 81, 109 (2009)ADSCrossRefGoogle Scholar
  19. 19.
    J.A.G. Vickers, Class. Quant. Grav. 4, 1 (1987)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  20. 20.
    C. Furtado, F. Moraes, A.M.d.M. Carvalho, Phys. Lett. A 372, 5368 (2008)ADSCrossRefzbMATHGoogle Scholar
  21. 21.
    V. Osipov, Phys. Lett. A 164, 327 (1992)ADSCrossRefMathSciNetGoogle Scholar
  22. 22.
    M.O. Katanaev, Phys. Usp. 48, 675 (2005)ADSCrossRefGoogle Scholar
  23. 23.
    E.A. Kochetov, V.A. Osipov, J. Phys. A: Math. Gen. 32, 1961 (1999)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  24. 24.
    P.E. Lammert, V.H. Crespi, Phys. Rev. B 69, 035406 (2004)ADSCrossRefGoogle Scholar
  25. 25.
    A.A. Abrikosov, Int. J. Mod. Phys. A 17, 885 (2002)ADSCrossRefMathSciNetGoogle Scholar
  26. 26.
    L. Landau, E. Lifshits, Mechanics, 2nd edn. (Pergamon, Oxford, 1969)Google Scholar
  27. 27.
    F.W. Hehl, W.-T. Ni, Phys. Rev. D 42, 2045 (1990)ADSCrossRefGoogle Scholar
  28. 28.
    J. Jackson, Classical electrodynamics, 3rd edn. (Wiley, New York, 1998)Google Scholar
  29. 29.
    P. Goddard, J. Nuyts, D. Olive, Nucl. Phys. B 125, 1 (1977)ADSCrossRefMathSciNetGoogle Scholar
  30. 30.
    Y. Aharonov, G. Carmi, Found. Phys. 3, 493 (1973)ADSCrossRefGoogle Scholar
  31. 31.
    Y. Aharonov, G. Carmi, Found. Phys. 4, 75 (1974)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Jonas R. F. Lima
    • 1
    Email author
  • Júlio Brandão
    • 1
  • Márcio M. Cunha
    • 2
  • F. Moraes
    • 1
  1. 1.Departamento de Física, CCENUniversidade Federal da ParaíbaJoão PessoaBrazil
  2. 2.Departamento de Física, CCENUniversidade Federal de PernambucoRecifeBrazil

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