C₂₄ FULLERENE WITHIN THE HUBBARD MODEL

Silant'ev Anatoliy Vladimirovich, Senior lecturer, sub-department of physics and physics teaching technique, Mari State University (1 Lenina square, Yoshkar-Ola, Russia), kvvant@rambler.ru

538.1

10.21685/2072-3040-2016-3-7

Background. The Hubbard model is widely used for theoretical description of strongly correlated electronic systems. Investigations of carbon nanosystems within the Hubbard model demonstrate that theoretical results agree with experimental data. The purpose of this paper is to obtain and to investigate the energy spectrum of C₂₄ fullerene within the Hubbard model.
Materials and methods. Methods of quantum theoretical field were used to obtain the Green’s functions. The Green’s functions were found by the method of the motion equations for creation operators. Approximation of the mean field was used to obtain a closed system of differential equations for finding the creation operators.
Results. The energy spectrum and the degree of degeneracy of each energy level in C₂₄ fullerene were found by the Green’s functions. A classification of the energy levels in fullerene C₂₄ was realized by the group theory.
Conclusions. This work demonstrates that C₂₄ fullerene has ten energy levels and ten symmetrically enabled transitions between energy levels.

Hubbard model, Green’s functions, energy spectrum, fullerenes, nanosystems.

1. Dresselhaus M. S., Dresselhaus G., Eklund P. C. Science of fullerenes and carbon nanotubes. San Diego: Academic Press, 1996, p. 965.
2. Hisch A., Brettreich M. Fullerenes: Chemistry and Reactions. Weinheim: Wiley-VCH Verlag GmbH & Co. KGaA, 2005, p. 423.
3. Oku T., Kuno M., Kitahara H., Navita I. International Journal of Inorganic Materials. 2001, vol. 3, pp. 597–612.
4. Pokropivnyy V. V., Ivanovskiy A. L. Uspekhi khimii [Advances of chemistry].2008,vol.77,no.10,pp.899–937.
5. Kroto H. W. Nature. 1987, vol. 329, pp. 529–531.
6. Levin A. A. Vvedenie v kvantovuyu khimiyu tverdogo tela [Introduction into quantum solid state chemistry]. Moscow: Khimiya, 1974, p. 476.
7. Hubbard J. Proceedings of the Royal Society A. 1963, vol. 276, pp. 238–257.
8. Kuz'min E. V., Petrakovskiy G. A., Zavadskiy E. A. Fizika magnitouporyadochennykh veshchestv [Physics of magnetically ordered materials]. Novosibirsk: Nauka, 1976, p. 288.
9. Lieb E. H., Wu F. Y. Phys. Rev. 1968, vol. 20, no. 25, pp. 1445–1448.
10. Takahashi M. Prog. Theor. Phys. 1971, vol. 47, no. 1, pp. 69–82.
11. Silant'ev A. V. Izvestiya vuzov. Fizika [University proceedings. Physics]. 2014, vol. 57, no. 11, pp. 37–45.
12. Silant'ev A. V. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Fizikomatematicheskie nauki [University proceedings. Volga region. Physical and mathematical sciences]. 2015, no. 1 (33), pp. 168–182.
13. Izyumov Yu. A., Katsnel'son M. I., Skryabin Yu. N. Magnetizm kollektivizirovannykh elektronov [Magnetism of collective electrons]. Moscow: Nauka, 1994, p. 366.
14. Silant'ev A. V. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Fizikomatematicheskie nauki [University proceedings. Volga region. Physical and mathematical sciences]. 2016, no. 1 (37), 101–112.
15. Silant'ev A. V.Fizika metallov i metallovedenie[Physics of metals and physical metallurgy].2016,vol.117,no.10.
16. Ivanchenko G. S., Lebedev N. G. Fizika tverdogo tela [Solid state physics]. 2007, vol. 49, pp. 183–189.
17. Silant'ev A. V. Vestnik Mariyskogo gosudarstvennogo universiteta [Bulletin of Mari State University]. 2012, no. 8, pp. 18–21.
18. Silant'ev A. V. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Fizikomatematicheskie nauki [University proceedings. Volga region. Physical and mathematical sciences]. 2015, no. 2 (34), pp. 164–175.
19. Silant'ev A. V. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Fizikomatematicheskie nauki [University proceedings. Volga region. Physical and mathematical sciences]. 2013, no. 1 (25), pp. 135–143.
20. Silant'ev A. V. Vestnik Mariyskogo gosudarstvennogo universiteta [Bulletin of Mari State University]. 2012, no. 8, pp. 22–25.
21. Khamermesh M. Teoriya grupp i ee primenenie k fizicheskim problemam [Group theory and its application to physical problems]. Moscow: Mir, 1966, p. 587.