Instability of vibrational modes in hexagonal lattice

  • Elena A. Korznikova
  • Dmitry V. Bachurin
  • Sergey Yu. Fomin
  • Alexander P. Chetverikov
  • Sergey V. Dmitriev
Regular Article
  • 73 Downloads

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.

Keywords

Statistical and Nonlinear Physics 

References

  1. 1.
    S. Flach, A.V. Gorbach, Phys. Rep. 467, 1 (2008)ADSCrossRefGoogle Scholar
  2. 2.
    S.V. Dmitriev, E.A. Korznikova, J.A. Baimova, M.G. Velarde, Phys. Usp. 59, 446 (2016)ADSCrossRefGoogle Scholar
  3. 3.
    G.M. Chechin, V.P. Sakhnenko. Physica D 117, 43 (1998)ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    M.G. Velarde, A.P. Chetverikov, W. Ebeling, S.V. Dmitriev, V.D. Lakhno, Eur. Phys. J. B 89, 233 (2016)ADSCrossRefGoogle Scholar
  5. 5.
    E.A. Korznikova, S.Y. Fomin, E.G. Soboleva, S.V. Dmitriev, J. Exp. Theor. Phys. Lett. 103, 277 (2016)CrossRefGoogle Scholar
  6. 6.
    S.Yu. Fomin, E.A. Korznikova, Lett. Mater. 6, 57 (2016)CrossRefGoogle Scholar
  7. 7.
    S.V. Dmitriev, J. Micromech. Mol. Phys. 1, 1630001 (2016)CrossRefGoogle Scholar
  8. 8.
    V.M. Burlakov, S.A. Kiselev, V.I. Rupasov, Phys. Lett. A 147, 130 (1990)ADSCrossRefGoogle Scholar
  9. 9.
    V.M. Burlakov, S.A. Kiselev, V.I. Rupasov, J. Exp. Theor. Phys. Lett. 51, 544 (1990)Google Scholar
  10. 10.
    T. Cretegny, T. Dauxois, S. Ruffo, A. Torcini, Physica D 121, 109 (1998)ADSCrossRefGoogle Scholar
  11. 11.
    T. Dauxois, R. Khomeriki, F. Piazza, S. Ruffo, Chaos 15, 015110 (2005)ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    Yu.A. Kosevich, G. Corso, Physica D 170, 1 (2002)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    Yu.A. Kosevich, S. Lepri, Phys. Rev. B 61, 299 (2000)ADSCrossRefGoogle Scholar
  14. 14.
    K. Ikeda, Y. Doi, B.F. Feng, T. Kawahara, Physica D 225, 184 (2007)ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    L.Z. Khadeeva, S.V. Dmitriev, Phys. Rev. B 81, 214306 (2010)ADSCrossRefGoogle Scholar
  16. 16.
    L. Kavitha, E. Parasuraman, D. Gopi, A. Prabhu, R.A. Vicencio, J. Magn. Magn. Mater. 401, 394 (2016)ADSCrossRefGoogle Scholar
  17. 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)ADSCrossRefGoogle Scholar
  18. 18.
    M. Inagaki, F. Kang, J. Mater. Chem. A 2, 13193 (2014)CrossRefGoogle Scholar
  19. 19.
    C. Gonzalez, Y.J. Dappe, B. Biel, J. Phys. Chem. C 120, 17115 (2016)CrossRefGoogle Scholar
  20. 20.
    A.A. Kistanov, Y. Cai, K. Zhou, S.V. Dmitriev, Y.W. Zhang, J. Phys. Chem. C 120, 6876 (2016)CrossRefGoogle Scholar
  21. 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)CrossRefGoogle Scholar
  22. 22.
    J.A. Baimova, E.A. Korznikova, I.P. Lobzenko, S.V. Dmitriev, Rev. Adv. Mater. Sci. 42, 68 (2015)Google Scholar
  23. 23.
    B. Liu, J.A. Baimova, S.V. Dmitriev, X. Wang, H. Zhu, K. Zhou, J. Phys. D 46, 305302 (2013)CrossRefGoogle Scholar
  24. 24.
    G.M. Chechin, S.V. Dmitriev, I.P. Lobzenko, D.S. Ryabov, Phys. Rev. B 90, 045432 (2014)ADSCrossRefGoogle Scholar
  25. 25.
    J.A. Baimova, S.V. Dmitriev, Russ. Phys. J. 58, 785 (2015)CrossRefGoogle Scholar
  26. 26.
    J.A. Baimova, R.T. Murzaev, I.P. Lobzenko, S.V. Dmitriev, K. Zhou, J. Exp. Theor. Phys. 122, 869 (2016)ADSCrossRefGoogle Scholar
  27. 27.
    Y. Yamayose, Y. Kinoshita, Y. Doi, A. Nakatani, T. Kitamura, Europhys. Lett. 80, 40008 (2007)ADSCrossRefGoogle Scholar
  28. 28.
    Y. Kinoshita, Y. Yamayose, Y. Doi, A. Nakatani, T. Kitamura, Phys. Rev. B 77, 024307 (2008)ADSCrossRefGoogle Scholar
  29. 29.
    T. Shimada, D. Shirasaki, T. Kitamura, Phys. Rev. B 81, 035401 (2010)ADSCrossRefGoogle Scholar
  30. 30.
    T. Shimada, D. Shirasaki, Y. Kinoshita, Y. Doi, A. Nakatani, T. Kitamura, Physica D 239, 407 (2010)ADSCrossRefGoogle Scholar
  31. 31.
    Y. Doi, A. Nakatani, Procedia Engineering 10, 3393 (2011)CrossRefGoogle Scholar
  32. 32.
    Y. Doi, A. Nakatani, Lett. Mater. 6, 49 (2016)CrossRefGoogle Scholar
  33. 33.
    L.Z. Khadeeva, S.V. Dmitriev, Yu.S. Kivshar, J. Exp. Theor. Phys. Lett. 94, 539 (2011)CrossRefGoogle Scholar
  34. 34.
    E.A. Korznikova, A.V. Savin, Y.A. Baimova, S.V. Dmitriev, R.R. Mulyukov, J. Exp. Theor. Phys. Lett. 96, 222 (2012)CrossRefGoogle Scholar
  35. 35.
    E.A. Korznikova, J.A. Baimova, S.V. Dmitriev, Europhys. Lett. 102, 60004 (2013)ADSCrossRefGoogle Scholar
  36. 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)ADSCrossRefGoogle Scholar
  37. 37.
    V. Hizhnyakov, M. Klopov, A. Shelkan, Phys. Lett. A 380, 1075 (2016)ADSCrossRefGoogle Scholar
  38. 38.
    A. Fraile, E.N. Koukaras, K. Papagelis, N. Lazarides, G.P. Tsironis, Chaos Solitons Fractals 87, 262 (2016)ADSMathSciNetCrossRefGoogle Scholar
  39. 39.
    W. Liang, G.M. Vanacore, A.H. Zewail, Proc. Natl. Acad. Sci. USA 111, 5491 (2014)ADSCrossRefGoogle Scholar
  40. 40.
    G. Chechin, D. Ryabov, S. Shcherbinin, Lett. Mater. 6, 9 (2016)CrossRefGoogle Scholar
  41. 41.
    A. Chetverikov, W. Ebeling, M.G. Velarde, Lett. Mater. 6, 82 (2016)CrossRefGoogle Scholar
  42. 42.
    A.P. Chetverikov, W. Ebeling, M.G. Velarde, Springer Ser. Mater. Sci. 221, 321 (2015)CrossRefGoogle Scholar
  43. 43.
    S.V. Dmitriev, A.P. Chetverikov, M.G. Velarde, Phys. Status Solidi B 252, 1682 (2015)ADSCrossRefGoogle Scholar
  44. 44.
    J. Bajars, J.C. Eilbeck, B. Leimkuhler, Physica D 301-302, 8 (2015)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Elena A. Korznikova
    • 1
  • Dmitry V. Bachurin
    • 1
    • 2
  • Sergey Yu. Fomin
    • 3
  • Alexander P. Chetverikov
    • 4
  • Sergey V. Dmitriev
    • 1
    • 5
  1. 1.Institute for Metals Superplasticity Problems RASUfaRussia
  2. 2.Institute for Applied Materials, Karlsruhe Institute of TechnologyEggenstein-LeopoldshafenGermany
  3. 3.Ufa State Aviation Technical UniversityUfaRussia
  4. 4.National Research Saratov State University, Department of PhysicsSaratovRussia
  5. 5.National Research Tomsk State UniversityTomskRussia

Personalised recommendations