Skip to main content
SpringerLink
Log in

Instability of vibrational modes in hexagonal lattice

  • Regular Article
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

The phenomenon of modulational instability is investigated for all four delocalized short-wave vibrational modes recently found for the two-dimensional hexagonal lattice with the help of a group-theoretic approach. The polynomial pair potential with hard-type quartic nonlinearity (β-FPU potential with β > 0) is used to describe interactions between atoms. As expected for the hard-type anharmonic interactions, for all four modes the frequency is found to increase with the amplitude. Frequency of the modes I and III bifurcates from the upper edge of the phonon spectrum, while that of the modes II and IV increases from inside the spectrum. It is also shown that the considered model supports spatially localized vibrational mode called discrete breather (DB) or intrinsic localized mode. DB frequency increases with the amplitude above the phonon spectrum. Two different scenarios of the mode decay were revealed. In the first scenario (for modes I and III), development of the modulational instability leads to a formation of long-lived DBs that radiate their energy slowly until thermal equilibrium is reached. In the second scenario (for modes II and IV) a transition to thermal oscillations of atoms is observed with no formation of DBs.

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. S. Flach, A.V. Gorbach, Phys. Rep. 467, 1 (2008)

    Article  ADS  Google Scholar 

  2. S.V. Dmitriev, E.A. Korznikova, J.A. Baimova, M.G. Velarde, Phys. Usp. 59, 446 (2016)

    Article  ADS  Google Scholar 

  3. G.M. Chechin, V.P. Sakhnenko. Physica D 117, 43 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  4. M.G. Velarde, A.P. Chetverikov, W. Ebeling, S.V. Dmitriev, V.D. Lakhno, Eur. Phys. J. B 89, 233 (2016)

    Article  ADS  Google Scholar 

  5. E.A. Korznikova, S.Y. Fomin, E.G. Soboleva, S.V. Dmitriev, J. Exp. Theor. Phys. Lett. 103, 277 (2016)

    Article  Google Scholar 

  6. S.Yu. Fomin, E.A. Korznikova, Lett. Mater. 6, 57 (2016)

    Article  Google Scholar 

  7. S.V. Dmitriev, J. Micromech. Mol. Phys. 1, 1630001 (2016)

    Article  Google Scholar 

  8. V.M. Burlakov, S.A. Kiselev, V.I. Rupasov, Phys. Lett. A 147, 130 (1990)

    Article  ADS  Google Scholar 

  9. V.M. Burlakov, S.A. Kiselev, V.I. Rupasov, J. Exp. Theor. Phys. Lett. 51, 544 (1990)

    Google Scholar 

  10. T. Cretegny, T. Dauxois, S. Ruffo, A. Torcini, Physica D 121, 109 (1998)

    Article  ADS  Google Scholar 

  11. T. Dauxois, R. Khomeriki, F. Piazza, S. Ruffo, Chaos 15, 015110 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  12. Yu.A. Kosevich, G. Corso, Physica D 170, 1 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  13. Yu.A. Kosevich, S. Lepri, Phys. Rev. B 61, 299 (2000)

    Article  ADS  Google Scholar 

  14. K. Ikeda, Y. Doi, B.F. Feng, T. Kawahara, Physica D 225, 184 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  15. L.Z. Khadeeva, S.V. Dmitriev, Phys. Rev. B 81, 214306 (2010)

    Article  ADS  Google Scholar 

  16. L. Kavitha, E. Parasuraman, D. Gopi, A. Prabhu, R.A. Vicencio, J. Magn. Magn. Mater. 401, 394 (2016)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  18. M. Inagaki, F. Kang, J. Mater. Chem. A 2, 13193 (2014)

    Article  Google Scholar 

  19. C. Gonzalez, Y.J. Dappe, B. Biel, J. Phys. Chem. C 120, 17115 (2016)

    Article  Google Scholar 

  20. A.A. Kistanov, Y. Cai, K. Zhou, S.V. Dmitriev, Y.W. Zhang, J. Phys. Chem. C 120, 6876 (2016)

    Article  Google Scholar 

  21. J. Zhao, H. Liu, Z. Yu, R. Quhe, S. Zhou, Y. Wang, C.C. Liu, H. Zhong, N. Han, J. Lu, Y. Yao, K. Wu, Prog. Mater. Sci. 83, 24 (2016)

    Article  Google Scholar 

  22. J.A. Baimova, E.A. Korznikova, I.P. Lobzenko, S.V. Dmitriev, Rev. Adv. Mater. Sci. 42, 68 (2015)

    Google Scholar 

  23. B. Liu, J.A. Baimova, S.V. Dmitriev, X. Wang, H. Zhu, K. Zhou, J. Phys. D 46, 305302 (2013)

    Article  Google Scholar 

  24. G.M. Chechin, S.V. Dmitriev, I.P. Lobzenko, D.S. Ryabov, Phys. Rev. B 90, 045432 (2014)

    Article  ADS  Google Scholar 

  25. J.A. Baimova, S.V. Dmitriev, Russ. Phys. J. 58, 785 (2015)

    Article  Google Scholar 

  26. J.A. Baimova, R.T. Murzaev, I.P. Lobzenko, S.V. Dmitriev, K. Zhou, J. Exp. Theor. Phys. 122, 869 (2016)

    Article  ADS  Google Scholar 

  27. Y. Yamayose, Y. Kinoshita, Y. Doi, A. Nakatani, T. Kitamura, Europhys. Lett. 80, 40008 (2007)

    Article  ADS  Google Scholar 

  28. Y. Kinoshita, Y. Yamayose, Y. Doi, A. Nakatani, T. Kitamura, Phys. Rev. B 77, 024307 (2008)

    Article  ADS  Google Scholar 

  29. T. Shimada, D. Shirasaki, T. Kitamura, Phys. Rev. B 81, 035401 (2010)

    Article  ADS  Google Scholar 

  30. T. Shimada, D. Shirasaki, Y. Kinoshita, Y. Doi, A. Nakatani, T. Kitamura, Physica D 239, 407 (2010)

    Article  ADS  Google Scholar 

  31. Y. Doi, A. Nakatani, Procedia Engineering 10, 3393 (2011)

    Article  Google Scholar 

  32. Y. Doi, A. Nakatani, Lett. Mater. 6, 49 (2016)

    Article  Google Scholar 

  33. L.Z. Khadeeva, S.V. Dmitriev, Yu.S. Kivshar, J. Exp. Theor. Phys. Lett. 94, 539 (2011)

    Article  Google Scholar 

  34. E.A. Korznikova, A.V. Savin, Y.A. Baimova, S.V. Dmitriev, R.R. Mulyukov, J. Exp. Theor. Phys. Lett. 96, 222 (2012)

    Article  Google Scholar 

  35. E.A. Korznikova, J.A. Baimova, S.V. Dmitriev, Europhys. Lett. 102, 60004 (2013)

    Article  ADS  Google Scholar 

  36. I.P. Lobzenko, G.M. Chechin, G.S. Bezuglova, Yu.A. Baimova, E.A. Korznikova, S.V. Dmitriev, Phys. Solid State 58, 633 (2016)

    Article  ADS  Google Scholar 

  37. V. Hizhnyakov, M. Klopov, A. Shelkan, Phys. Lett. A 380, 1075 (2016)

    Article  ADS  Google Scholar 

  38. A. Fraile, E.N. Koukaras, K. Papagelis, N. Lazarides, G.P. Tsironis, Chaos Solitons Fractals 87, 262 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  39. W. Liang, G.M. Vanacore, A.H. Zewail, Proc. Natl. Acad. Sci. USA 111, 5491 (2014)

    Article  ADS  Google Scholar 

  40. G. Chechin, D. Ryabov, S. Shcherbinin, Lett. Mater. 6, 9 (2016)

    Article  Google Scholar 

  41. A. Chetverikov, W. Ebeling, M.G. Velarde, Lett. Mater. 6, 82 (2016)

    Article  Google Scholar 

  42. A.P. Chetverikov, W. Ebeling, M.G. Velarde, Springer Ser. Mater. Sci. 221, 321 (2015)

    Article  Google Scholar 

  43. S.V. Dmitriev, A.P. Chetverikov, M.G. Velarde, Phys. Status Solidi B 252, 1682 (2015)

    Article  ADS  Google Scholar 

  44. J. Bajars, J.C. Eilbeck, B. Leimkuhler, Physica D 301-302, 8 (2015)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Metals Superplasticity Problems RAS, Khalturin St. 39, 450001, Ufa, Russia

    Elena A. Korznikova, Dmitry V. Bachurin & Sergey V. Dmitriev

  2. Institute for Applied Materials, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, 76344, Eggenstein-Leopoldshafen, Germany

    Dmitry V. Bachurin

  3. Ufa State Aviation Technical University, Karl Marx St. 12, 450077, Ufa, Russia

    Sergey Yu. Fomin

  4. National Research Saratov State University, Department of Physics, Astrakhanskaya 83, 410012, Saratov, Russia

    Alexander P. Chetverikov

  5. National Research Tomsk State University, Lenin Avenue 36, 634050, Tomsk, Russia

    Sergey V. Dmitriev

Authors
  1. Elena A. Korznikova
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dmitry V. Bachurin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sergey Yu. Fomin
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Alexander P. Chetverikov
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Sergey V. Dmitriev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Elena A. Korznikova.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Korznikova, E.A., Bachurin, D.V., Fomin, S.Y. et al. Instability of vibrational modes in hexagonal lattice. Eur. Phys. J. B 90, 23 (2017). https://doi.org/10.1140/epjb/e2016-70595-2

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/e2016-70595-2

Keywords

Search

Navigation