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.
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References
H. W. Kroto, J. R. Heath, S. C. O’Brien, R. F. Curl, and R. E. Smalley, “C60: Buckminsterfullerene,” Nature 318, 162–163 (2000).
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).
V. Parasuk and J. Almlof, “C20: the smallest fullerene?,” Chem. Phys. Lett. 184, 187–190 (1991).
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).
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).
V. I. Minkin, B. Ya. Simkin, and P. M. Minyaev, Theory of the Structure of Molecules (Feniks, Rostov-on-Don, 1997).
A. A. Levin, Introduction to Quantum Chemistry of Solids (Khimiya, Moscow, 1974) [in Russian].
R. O. Zaitsev, “On the superconductivity of planar carbon compounds,” JETP Lett. 94, 224–229 (2011).
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).
J. Hubbard, “Electron correlations in narrow energy bands,” Proc. R. Soc. London, Ser. A 276, 238–257 (1963).
D. I. Khomskii, “Electronic correlations in narrow bands (the Hubbard model),” Fiz. Met. Metalloved. 29, 31–57 (1970) [in Russian].
Yu. A. Izyumov, M. I. Katsnel’son, and Yu. N. Skryabin, Magnetism of Itinerant Electrons (Nauka, Moscow, 1994) [in Russian].
J. Kanamori, “Electron correlations and ferromagnetism of transition metals,” Prog. Theor. Phys. 30, 275–289 (1963).
M. C. Gutzwiller, “Effect of correlation on the ferromagnetism of transition metals,” Phys. Rev. Letters 10, 159–162 (1963).
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).
I. I. Mazin, “Electronic structure of high-temperature superconductors in the normal state,” Usp. Fiz. Nauk 158, 155–161 (1989).
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).
A. V. Silant’ev, “Energy spectrum and optical properties of C60 fullerene within the Hubbard model,” Phys. Met. Metallogr. 118, 1–9 (2017).
A. V. Silant’ev, “Energy spectrum and optical properties of C70 fullerene in Hubbard model,” Opt. Spektrosk. 124, 159–166 (2018).
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).
A. V. Silant’ev, “Dimer in the extended Hubbard model,” Russ. Phys. J., 57, 1491–1502 (2015).
A. V. Silant’ev, “Dimer in the Hubbard model,” Izv. Vuzov. Povolzh. Region. Fiz.-Matem. Nauki, No. 1, 168–182 (2015).
S. V. Tyablikov, Methods of Quantum Theory of Magnetism (Nauka, Moscow, 1975) [in Russian].
M. Bühl and A. Hirsch, “Spherical aromaticity of fullerenes,” Chem. Rev. 101, 1153–1183 (2001).
I. I. Sobel’man, Introduction to Theory of Atomic Spectra (Nauka, Moscow, 1977) [in Russian].
I. B. Bersuker, The Yahn–Teller Effect (Cambridge University Press, 2006).
I. G. Kaplan, Symmetry of Many-Electron Systems (Nauka, Moscow, 1969) [in Russian].
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Original Russian Text © A.V. Silant’ev, 2018, published in Fizika Metallov i Metallovedenie, 2018, Vol. 119, No. 6, pp. 541–549.
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Silant’ev, A.V. Influence of Deformation on the Energy Spectrum and the Optical Properties of Fullerene C20 within the Hubbard Model. Phys. Metals Metallogr. 119, 511–519 (2018). https://doi.org/10.1134/S0031918X18060133
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DOI: https://doi.org/10.1134/S0031918X18060133