Physics of the Solid State

, Volume 61, Issue 11, pp 2139–2144 | Cite as

Dynamics of a Three-Component Delocalized Nonlinear Vibrational Mode in Graphene

  • S. A. Shcherbinin
  • M. N. Semenova
  • A. S. Semenov
  • E. A. Korznikova
  • G. M. Chechin
  • S. V. DmitrievEmail author


The dynamics of a three-component nonlinear delocalized vibrational mode in graphene is studied with molecular dynamics. This mode, being a superposition of a root and two one-component modes, is an exact and symmetrically determined solution of nonlinear equations of motion of carbon atoms. The dependences of a frequency, energy per atom, and average stresses over a period that appeared in graphene are calculated as a function of amplitude of a root mode. We showed that the vibrations become periodic with certain amplitudes of three component modes, and the vibrations of one-component modes are close to periodic one and have a frequency twice the frequency of a root mode, which is noticeably higher than the upper boundary of a spectrum of low-amplitude vibrations of a graphene lattice. The data obtained expand our understanding of nonlinear vibrations of graphene lattice.


nonlinear dynamics graphene delocalized oscillations second harmonic generation 



A.S. Semenov (calculations together with discussion of results) is grateful to Russian Science Foundation (project no. 18-72-00006). E.A. Korznikova is grateful to Russian Foundation for Basic Research (grant no. 18-32-20158 mol_a_ved) for financial support (discussion of results and writing the article). This work was partially supported by the State Assignment of the Institute for Metals Superplasticity Problems (Russian Academy of Sciences).


The authors declare that they have no conflicts of interest.


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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  • S. A. Shcherbinin
    • 1
  • M. N. Semenova
    • 2
  • A. S. Semenov
    • 2
  • E. A. Korznikova
    • 3
  • G. M. Chechin
    • 1
  • S. V. Dmitriev
    • 3
    • 4
    Email author
  1. 1.Southern Federal UniversityRostov-on-DonRussia
  2. 2.Ammosov North-Eastern Federal UniversityMirnyRussia
  3. 3.Institute for Metals Superplasticity Problems, Russian Academy of SciencesUfaRussia
  4. 4.National Research Tomsk State UniversityTomskRussia

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