Skip to main content
SpringerLink
Log in

Analysis of the stability of states of semiconductor superlattice in the presence of tilted magnetic field

  • Theoretical and Mathematical Physics
  • Published:
Technical Physics Aims and scope Submit manuscript

Abstract

A method to calculate the spectrum of the Lyapunov exponents for a periodic semiconductor nanostructure (superlattice) described in the framework of a semiclassical approach is proposed. The analysis of the stability of a stationary state in such a system is performed for autonomous dynamics and in the presence of a tilted magnetic field. The method of the Lyapunov exponents is used to study the effect of the tilted magnetic field on the stability of the stationary state and the characteristics of subterahertz oscillation regimes.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. L. Esaki and R. Tsu, IBM J. Res. Dev. 14 1, 61 (1970).

    Article  Google Scholar 

  2. M. I. Ovsyannikov, et al., Sov. Phys. Semicond. 4, 1919 (1970).

    Google Scholar 

  3. A. Ya. Shik, Sov. Phys. Semicond. 8, 1195 (1974).

    Google Scholar 

  4. L. L. Bonilla and H. T. Grahn, Rep. Prog. Phys. 68, 577 (2005).

    Article  ADS  Google Scholar 

  5. T. M. Greenaway, et al., Phys. Rev. B 80, 205 318 (2009).

    Article  Google Scholar 

  6. T. Hyart, et al., Phys. Rev. Lett. 103, 117 401 (2010).

    Google Scholar 

  7. B. K. Ridley, Proc. Phys. Soc. London 82, 954 (1963).

    Article  ADS  Google Scholar 

  8. A. A. Koronovskii, et al., Phys. Wave Phenom. 21 1, 48 (2013).

    Article  ADS  Google Scholar 

  9. A. Sibille, et al., Phys. Rev. Lett. 64, 52 (1990).

    Article  ADS  Google Scholar 

  10. H. Kroemer, IEEE Trans. Electron Devices 15, 819 (1968).

    Article  Google Scholar 

  11. A. G. Balanov, et al., Phys. Rev. E 77, 026 209 (2008).

    Article  Google Scholar 

  12. S. P. Kuznetsov, Dynamic Chaos, Ser. Modern Theory of Waves and Oscillations (Fizmatlit, Moscow, 2001).

    Google Scholar 

  13. V. V. Makarov, et al., Izv. Vyssh. Uchebn. Zaved., Prikl. Nelineinaya Din. 64 5, 40 (2013).

    Google Scholar 

  14. S. Lepri, et al., Chaos 7, 701 (1997).

    Article  ADS  MathSciNet  Google Scholar 

  15. S. P. Kuznetsov and D. I. Trubetskov, Radiophys. Quantum Electron. 47 341 (2004).

    Article  ADS  Google Scholar 

  16. T. M. Fromhold, et al., Nature 428, 726 (2004).

    Article  ADS  Google Scholar 

  17. A. O. Selskii, et al., Phys. Rev. B 84, 235 311 (2011).

    Article  Google Scholar 

  18. A. E. Hramov, et al., Phys. Rev. Lett. 112, 116 603 (2014).

    Article  Google Scholar 

  19. A. O. Sel’skii and G. V. Osipov, Tech. Phys. Lett. 41, 98 (2015).

    Article  Google Scholar 

  20. M. Butiker and H. Thomas, Phys. Rev. Lett. 38 2, 78 (1977).

    Article  ADS  Google Scholar 

  21. G. Benettin, et al., Meccanica 15, 9 (1980).

    Article  ADS  Google Scholar 

  22. A. A. Koronovskii, et al., Phys. Rev. B 88, 165 304 (2013).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Yuri Gagarin State Technical University of Saratov, Politekhnicheskaya ul. 77, Saratov, 410054, Russia

    V. A. Maksimenko, V. V. Makarov, A. A. Koronovskii & A. E. Hramov

  2. Saratov State University, Astrakhanskaya ul. 83, Saratov, 410012, Russia

    A. A. Koronovskii & A. E. Hramov

Authors
  1. V. A. Maksimenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. V. Makarov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. A. Koronovskii
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. E. Hramov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. E. Hramov.

Additional information

Original Russian Text © V.A. Maksimenko, V.V. Makarov, A.A. Koronovskii, A.E. Hramov, 2016, published in Zhurnal Tekhnicheskoi Fiziki, 2016, Vol. 86, No. 3, pp. 1–7.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Maksimenko, V.A., Makarov, V.V., Koronovskii, A.A. et al. Analysis of the stability of states of semiconductor superlattice in the presence of tilted magnetic field. Tech. Phys. 61, 317–323 (2016). https://doi.org/10.1134/S1063784216030154

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063784216030154

Keywords

Search

Navigation