Abstract
The energy spectra of single-wall carbon nanotubes (CNTs) with chiralities of (10, 10), (11, 9), and (12, 8) are calculated in the static fluctuation approximation for the Hubbard model. The choice of these systems for investigation was dictated by the fact that these systems are the most typical of heterogeneous samples obtained by synthesis. It is shown that in the chosen model and approximation, the type of conduction is independent of chirality, which contradicts the generally accepted opinion concerning the critical dependence of the CNT conduction current on the chirality indices. The optical absorption spectra of the CNTs under investigation are calculated using the resultant energy spectra. The shape of the optical absorption spectrum averaged over the known weight composition is in good agreement with experimental data. The results of investigation suggest that the rule according to which CNTs exhibit metal-type conductivity when the difference in the chirality indices is a multiple of three; otherwise, they have the semiconductor-type conductivity, is in all probability not general, but has applicability limits that can be established by rigorous calculations based on the Hubbard model.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. A. Levin, Solid-State Quantum Chemistry (Khimiya, Moscow, 1974; McGraw-Hill, New York, 1977).
R. Saito, M. Fujita, G. Dresselhaus, and M. S. Dresselhaus, Phys. Rev. B: Condens. Matter 46, 1804 (1992).
M. S. Dresselhaus, G. Dresselhaus, and R. Saito, Carbon 33, 883 (1992).
N. Hamad, S. Sawada, and A. Oshiyama, Phys. Rev. Lett. 68, 1579 (1992).
P. R. Wallace, Phys. Rev. 71, 622 (1947).
J. Hubbard, Proc. R. Soc. London, Ser. A 276, 238 (1963).
T. O. Wehling, E. Sasioglu, C. Friedrich, A. I. Lichtenstein, M. I. Katsnelson, and S. Blugel, Phys. Rev. Lett. 106, 236805 (2011).
A. V. Eletskii, Phys.—Usp. 52(3), 209 (2009).
Min Ouyang, Jin-Lin Huang, Chin Li Cheung, and C. M. Lieber, Science (Washington) 292, 702 (2001).
J. W. G. Wildoer, L. C. Venema, A. G. Rinzler, R. E. Smalley, and C. Dekker, Nature (London) 391, 59 (1998).
Yu. A. Izyumov and V. I. Sadovskii, Electronic Structure of Strongly Correlated Compounds (Regular and Chaotic Dynamics, Izhevsk, Russia, 2009) [in Russian].
R. O. Zaitsev, Diagrammatic Method in the Theory of Superconductivity and Ferromagnetism (Editorial URSS, Moscow, 2004), p. 175.
R. O. Zaitsev, JETP Lett. 94(3), 206 (2011).
V. A. Loskutov, G. I. Mironov, and R. R. Nigmatullin, Low Temp. Phys. 22(3), 220 (1997).
G. I. Mironov, Phys. Solid State 41(6), 864 (1999).
R. R. Nigmatullin, A. A. Khamzin, and I. I. Popov, J. Exp. Theor. Phys. 114(2), 314 (2012).
G. I. Mironov and A. I. Murzashev, Phys. Solid State 53(11), 2393 (2011).
A. I. Murzashev, Russ. Phys. J. 55(5), 524 (2012).
B. V. Lobanov and A. I. Murzashev, Phys. Solid State 55(4), 868 (2013).
A. I. Murzashev and E. O. Shadrin, Phys. Solid State 55(1), 205 (2013).
A. I. Murzashev and E. O. Shadrin, Russ. Phys. J. 56(7), 793 (2013).
J. M. Cowley, P. Nikolaev, A. Thess, and R. E. Smalley, Chem. Phys. Lett. 265, 379 (1997).
S. V. Tyablikov, Methods in the Quantum Theory of Magnetism (Nauka, Moscow, 1975; Springer-Verlag, New York, 1995).
T. E. Arutyunova, G. I. Mironov, and A. I. Murzashev, Phys. Solid State 54(9), 1917 (2012).
H. Kataura, Y. Kumazawa, I. Umezu, S. Suzuki, Y. Ohtsuka, and Y. Achiba, Synth. Met. 103, 2555 (1999).
Seok Ho Jeong, Ki Kang Kima, Seok Jin Jeong, Kay Hyeok Ana, Seung Hee Lee, and Young Hee Lee, Synth. Met. 157, 570 (2007).
O. Jost, A. A. Gorbunov, and W. Pompe, Appl. Phys. Lett. 75, 2217 (1999).
T. Movlarooy, A. Kompany, S. M. Hosseini, and N. Shahtahmasebi, Comput. Mater. Sci. 49, 450 (2010).
V. Adamyan and S. Tishchenko, J. Phys.: Condens. Matter 19, 186206 (2007).
A. G. Marinopoulos, L. Wirtz, A. Marini, V. Olevano, A. Rubio, and L. Reining, Appl. Phys. A: Mater. Sci. Process. 78, 1157 (2004).
E. Malić, M. Hirtschulz, F. Milde, A. Knorr, and S. Reich, Phys. Rev. B: Condens. Matter 74, 195431 (2006).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.I. Murzashev, E.O. Shadrin, 2014, published in Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2014, Vol. 145, No. 6, pp. 1061–1071.
Rights and permissions
About this article
Cite this article
Murzashev, A.I., Shadrin, E.O. Energy spectrum and optical absorption spectra of carbon nanotubes with chiralities of (10, 10), (11, 9), and (12, 8). J. Exp. Theor. Phys. 118, 935–944 (2014). https://doi.org/10.1134/S1063776114050148
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063776114050148