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Physics of Metals and Metallography

, Volume 119, Issue 6, pp 511–519 | Cite as

Influence of Deformation on the Energy Spectrum and the Optical Properties of Fullerene C20 within the Hubbard Model

  • A. V. Silant’ev
Theory of Metals
  • 15 Downloads

Abstract

The anticommutative Green’s functions and energy spectra of fullerene C20 with symmetry groups Ih, D5d, and D3d have been obtained in analytical form within the Hubbard model in the mean-field approximation. The methods of group theory have been used to classify energy states and identify allowed transitions in the energy spectra of C20.

Keywords

Hubbard model Green’s functions energy spectrum nanosystems fullerene С20 

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References

  1. 1.
    H. W. Kroto, J. R. Heath, S. C. O’Brien, R. F. Curl, and R. E. Smalley, “C60: Buckminsterfullerene,” Nature 318, 162–163 (2000).CrossRefGoogle Scholar
  2. 2.
    H. Prinzbach, A. Weller, P. Landenberger, F. Wahl, J. Worth, L. T. Scot, M. Gelmont, D. Olevano, and B. V. Issendorff, “Gas-phase production and photoelectron spectroscopy of the smallest fullerene C20,” Nature 407, 60–63 (2000).CrossRefGoogle Scholar
  3. 3.
    V. Parasuk and J. Almlof, “C20: the smallest fullerene?,” Chem. Phys. Lett. 184, 187–190 (1991).CrossRefGoogle Scholar
  4. 4.
    G. Galli, F. Gygi, and J-.C. Golaz, “Vibrational and electronic properties of neutral and negatively charged C20 clusters,” Phys. Rev. B 57, 1860–1867 (1998).CrossRefGoogle Scholar
  5. 5.
    O. E. Glukhova, A. I. Zhbanov, and A. G. Rezkov, “Rotation of the inner shell in a C20@C80 Nanoparticle,” Phys. Solid State 47, 390–396 (2005).CrossRefGoogle Scholar
  6. 6.
    V. I. Minkin, B. Ya. Simkin, and P. M. Minyaev, Theory of the Structure of Molecules (Feniks, Rostov-on-Don, 1997).Google Scholar
  7. 7.
    A. A. Levin, Introduction to Quantum Chemistry of Solids (Khimiya, Moscow, 1974) [in Russian].Google Scholar
  8. 8.
    R. O. Zaitsev, “On the superconductivity of planar carbon compounds,” JETP Lett. 94, 224–229 (2011).CrossRefGoogle Scholar
  9. 9.
    R. A. Harris and L. M. Falicov, “Self-consistent theory of bond alternation in polyenes: Normal state, chargedensity waves, and spin-density waves,” J. Chem. Phys. 51, 5034–5041 (1969).CrossRefGoogle Scholar
  10. 10.
    J. Hubbard, “Electron correlations in narrow energy bands,” Proc. R. Soc. London, Ser. A 276, 238–257 (1963).CrossRefGoogle Scholar
  11. 11.
    D. I. Khomskii, “Electronic correlations in narrow bands (the Hubbard model),” Fiz. Met. Metalloved. 29, 31–57 (1970) [in Russian].Google Scholar
  12. 12.
    Yu. A. Izyumov, M. I. Katsnel’son, and Yu. N. Skryabin, Magnetism of Itinerant Electrons (Nauka, Moscow, 1994) [in Russian].Google Scholar
  13. 13.
    J. Kanamori, “Electron correlations and ferromagnetism of transition metals,” Prog. Theor. Phys. 30, 275–289 (1963).CrossRefGoogle Scholar
  14. 14.
    M. C. Gutzwiller, “Effect of correlation on the ferromagnetism of transition metals,” Phys. Rev. Letters 10, 159–162 (1963).CrossRefGoogle Scholar
  15. 15.
    R. H. McKenzie, “A strongly correlated electron model for the layered organic superconductors k-(BEDT-TTF)2X,” Comm. Condens. Matter Phys. 18, 309–317 (1998).Google Scholar
  16. 16.
    I. I. Mazin, “Electronic structure of high-temperature superconductors in the normal state,” Usp. Fiz. Nauk 158, 155–161 (1989).CrossRefGoogle Scholar
  17. 17.
    G. S. Ivanchenko and N. G. Lebedev, “Electrical conductivity of double-walled carbon nanotubes in the framework of the Hubbard model,” Phys. Solid State 49, 189–196 (2007).CrossRefGoogle Scholar
  18. 18.
    A. V. Silant’ev, “Energy spectrum and optical properties of C60 fullerene within the Hubbard model,” Phys. Met. Metallogr. 118, 1–9 (2017).CrossRefGoogle Scholar
  19. 19.
    A. V. Silant’ev, “Energy spectrum and optical properties of C70 fullerene in Hubbard model,” Opt. Spektrosk. 124, 159–166 (2018).Google Scholar
  20. 20.
    A. V. Silant’ev, “Investigation of nanosystems in the Hubbard model in the mean-field approximation,” Izv. Vuzov. Povolzh. Region. Fiz.-Matem. Nauki, No 1, 102–112 (2016).Google Scholar
  21. 21.
    A. V. Silant’ev, “Dimer in the extended Hubbard model,” Russ. Phys. J., 57, 1491–1502 (2015).CrossRefGoogle Scholar
  22. 22.
    A. V. Silant’ev, “Dimer in the Hubbard model,” Izv. Vuzov. Povolzh. Region. Fiz.-Matem. Nauki, No. 1, 168–182 (2015).Google Scholar
  23. 23.
    S. V. Tyablikov, Methods of Quantum Theory of Magnetism (Nauka, Moscow, 1975) [in Russian].Google Scholar
  24. 24.
    M. Bühl and A. Hirsch, “Spherical aromaticity of fullerenes,” Chem. Rev. 101, 1153–1183 (2001).CrossRefGoogle Scholar
  25. 25.
    I. I. Sobel’man, Introduction to Theory of Atomic Spectra (Nauka, Moscow, 1977) [in Russian].Google Scholar
  26. 26.
    I. B. Bersuker, The Yahn–Teller Effect (Cambridge University Press, 2006).Google Scholar
  27. 27.
    I. G. Kaplan, Symmetry of Many-Electron Systems (Nauka, Moscow, 1969) [in Russian].Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Mari State UniversityYoshkar-OlaRussia

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