Abstract
The electronic structure of semiconducting double-wall carbon nanotubes (CNTs) is calculated using the linearized augmented cylindrical wave method. The consideration is performed in the framework of the local density functional theory and the muffin-tin (MT) approximation for the one-electron Hamiltonian. The electronic spectrum of a double-wall CNT is determined by the free motion of electrons in the interatomic space of the two cylindrical layers, scattering by the MT spheres, and tunneling through the classically impenetrable region. Calculated results for double-wall CNTs of the (n, 0)@(n′, 0) zigzag type indicate that the shift of the band-gap width depends on whether n and n′ are divided by 3 with a remainder of 1 or 2. It is found that, regardless of the type of the inner tube, the energy gap E g of the outer tube decreases by 0.15–0.22 eV if the tube belongs to the sequence n = 2 (mod 3). For the outer tubes of the sequence n = 1 (mod 3), the shifts of the band gap ΔE g are always negative −0.15 ≤ ΔE g ≤ −0.05 eV. In both cases, the shifts ΔE g weakly oscillate rather than decrease in going to tubes of a larger diameter d. For the inner tubes, the changes in the band gap ΔE g are more sensitive to the diameter. At 10 ≤ n ≤ 16, the shifts ΔE g are positive and the maximum value of ΔE g equals 0.39 and 0.32 for the sequences n = 2 (mod 3) and n = 1 (mod 3), respectively. In going to the inner tubes of a larger diameter, ΔE g rapidly drops and then oscillates in the range from −0.05 to 0.06 eV. The calculated results indicate that the shifts of the optical band gaps in core and shell tubes upon the formation of double-wall CNTs are significant, which must hinder the identification of double-wall CNTs by optical methods. On the other hand, the obtained results open up possibilities for a more detailed classification of double-wall nanotubes.
Similar content being viewed by others
References
R. Saito, G. Dresselhaus, and M. S. Dresselhaus, Physical Properties of Carbon Nanotubes (Imperial College Press, London, 1998).
A. V. Eletskiĭ, Usp. Fiz. Nauk 167, 945 (1997) [Phys. Usp. 40, 899 (1997)].
J. W. Mintmire, B. I. Dunlap, and C. T. White, Phys. Rev. Lett. 68, 631 (1992).
P. N. D’yachkov, Carbon Nanotubes: Structure, Properties, and Applications (Binom, Moscow, 2006) [in Russian].
A. N. Enyashin, G. Seifert, and A. L. Ivanovskiĭ, Pis’ma Zh. Éksp. Teor. Fiz. 80, 709 (2004) [JETP Lett. 80, 608 (2004)].
S. Bandow, K. Hirahara, T. Hiraoka, et al., MRS Bull. 29(4), 260 (2004).
T. Hertel, A. Hagen, V. Talalaev, et al., Nano Lett. 5, 511 (2005).
P. N. D’yachkov, O. M. Kepp, and A. V. Nikolaev, Dokl. Akad. Nauk 365, 215 (1999).
P. N. D’yachkov and D. V. Kirin, Dokl. Akad. Nauk 369, 639 (1999).
P. N. D’yachkov, in Encyclopedia of Nanoscience and Nanotechnology, Ed. by Hari Singh Nalwa (Am. Sci., Los Angeles, CA, 2003), Vol. 1, p. 191.
O. K. Andersen, Phys. Rev. B 12, 3060 (1975).
D. D. Koelling and G. O. Arbman, J. Phys. F: Met. Phys. 5, 2041 (1975).
P. N. D’yachkov, H. Hermann, and D. V. Kirin, Appl. Phys. Lett. 81, 5228 (2002).
P. N. D’yachkov and H. Hermann, J. Appl. Phys. 95, 399 (2004).
A. Yu. Golovocheva and P. N. D’yachkov, Pis’ma Zh. Éksp. Teor. Fiz. 82, 834 (2005) [JETP Lett. 82, 737 (2005)].
P. N. D’yachkov and D. V. Makaev, Phys. Rev. B 71, 081101(R) (2005).
R. Saito, G. Dresselhaus, and M. S. Dresselhaus, J. Appl. Phys. 73, 494 (1993).
Ph. Lambin, L. Philippe, J. C. Charlier, and J. P. Michenaud, Comput. Mater. Sci. 2, 350 (1994).
Y.-K. Kwon and D. Tomanek, Phys. Rev. B 58, R16 001 (1998).
Y. Miyamoto, S. Saito, and D. Tomanek, Phys. Rev. B 65, 041402(R) (2001).
S. Sanvito, Y.-K. Kwon, D. Tomanek, and C. J. Lambert, Phys. Rev. Lett. 84, 1974 (2000).
S. Frank, P. Poncharal, Z. L. Wang, and W. A. de Heer, Science 280, 1744 (1998).
B. Shan and K. Cho, Phys. Rev. B 73, 081401(R) (2006).
D. Östling, D. Tomanek, and A. Rosèn, Phys. Rev. B 55, 13 980 (1997).
R. C. Tatar and S. Rabii, Phys. Rev. B 25, 4126 (1982).
S. M. Bachilo, M. S. Strano, C. Kittrell, et al., Science 298, 2361 (2002).
Author information
Authors and Affiliations
Additional information
Original Russian Text © D.V. Makaev, P.N. D’yachkov, 2006, published in Pis’ma v Zhurnal Éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2006, Vol. 84, No. 6, pp. 397–402.
Rights and permissions
About this article
Cite this article
Makaev, D.V., D’yachkov, P.N. Band structure and optical transitions in semiconducting double-wall carbon nanotubes. Jetp Lett. 84, 335–339 (2006). https://doi.org/10.1134/S0021364006180123
Received:
Issue Date:
DOI: https://doi.org/10.1134/S0021364006180123