Skip to main content
Log in

Ultrashort optical pulses in carbon nanotubes and graphene with periodic impurities

  • Fullerenes and Atomic Clusters
  • Published:
Physics of the Solid State Aims and scope Submit manuscript

Abstract

The dispersion law for electrons has been derived by the Green’s function method using the Anderson periodic model, which has been proposed to describe the electron subsystem in carbon nanotubes and graphene with impurities. The combined dynamics of electrons and an electromagnetic field has been considered in the low-temperature limit, and the effective equation describing the propagation of ultrashort optical pulses has been obtained. The solutions to this equation as functions of the parameters of the problem have been presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science (Washington) 306, 666 (2004).

    Article  ADS  Google Scholar 

  2. P. J. F. Harris, Carbon Nanotubes and Related Structures: New Materials for the Twenty-First Century (Cambridge University Press, Cambridge, 1999; Tekhnosfera, Moscow, 2003).

    Book  Google Scholar 

  3. Y. Zhang, J. W. Tan, H. L. Stormer, and P. Kim, Nature (London) 438, 201 (2005).

    Article  ADS  Google Scholar 

  4. S. Stankovich, D. A. Dikin, G. H. B. Dommett, K. M. Kohlhaas, E. J. Zimney, E. A. Stach, R. D. Piner, S. B. T. Nguyen, and R. S. Ruoff, Nature (London) 442, 282 (2006).

    Article  ADS  Google Scholar 

  5. B. Partoens and F. M. Peeters, Phys. Rev. B: Condens. Matter 74, 075404 (2006).

    ADS  Google Scholar 

  6. S. V. Morozov, K. S. Novoselov, F. Schedin, D. Jiang, A. A. Firsov, and A. K. Geim, Phys. Rev. B: Condens. Matter 72, 201401 (2005).

    ADS  Google Scholar 

  7. M. B. Belonenko, E. V. Demushkina, and N. G. Lebedev, J. Russ. Laser Res. 27, 457 (2006).

    Article  Google Scholar 

  8. M. B. Belonenko, E. V. Demushkina, and N. G. Lebedev, Fiz. Tverd. Tela (St. Petersburg) 50(2), 367 (2008) [Phys. Solid State 50 (2), 383 (2008)].

    Google Scholar 

  9. P.W. Anderson. Phys. Rev. 124, 41 (1961).

    Article  MathSciNet  ADS  Google Scholar 

  10. Yu. A. Izyumov, I. I. Chashchin, and D. S. Alekseev, The Theory of Strongly Correlated Systems: The Generating Functional Method (Research Scientific Center “Regular and Chaotic Dynamics,” Institute of Computer Sciences, Moscow-Izhevsk, 2006) [in Russian].

    Google Scholar 

  11. N. F. Stepanov, Quantum Mechanics and Quantum Chemistry (Mir, Moscow, 2001) [in Russian].

    Google Scholar 

  12. S. V. Tyablikov, Methods in the Quantum Theory of Magnetism (Plenum, New York, 1967; Nauka, Moscow, 1975).

    Google Scholar 

  13. N. N. Bogolyubov and N. N. Bogolyubov, Jr., Introduction to Quantum Statistical Mechanics (Nauka, Moscow, 1984; Gordon and Breach, London, 1992).

    MATH  Google Scholar 

  14. S. A. Maksimenko and G. Ya. Slepyan, in Handbook of Nanotechnology. Nanometer Structure: Theory, Modeling, and Simulation, Ed. by A. Lakhatakia (SPIE Press, Bellingham, Washington, United States, 2004), p. 145.

    Chapter  Google Scholar 

  15. Yu. A. Il’inskiĭ and L. V. Keldysh, Interaction of Electromagnetic Radiation with Substance (Moscow State University, Moscow, 1989).

    Google Scholar 

  16. Solitons, Ed. by R. Bullough and Ph. Caudry (Springer, Heidelberg, 1980; Mir, Moscow, 1983).

    MATH  Google Scholar 

  17. N. S. Bakhvalov, Numerical Methods: Analysis, Algebra, and Ordinary Differential Equations (Nauka, Moscow, 1975; Mir, Moscow, 1977).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. B. Belonenko.

Additional information

Original Russian Text © M.B. Belonenko, N.G. Lebedev, N.N. Yanyushkina, 2010, published in Fizika Tverdogo Tela, 2010, Vol. 52, No. 8, pp. 1656–1661.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Belonenko, M.B., Lebedev, N.G. & Yanyushkina, N.N. Ultrashort optical pulses in carbon nanotubes and graphene with periodic impurities. Phys. Solid State 52, 1780–1786 (2010). https://doi.org/10.1134/S1063783410080330

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063783410080330

Keywords

Navigation