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Rotational symmetry influences the mechanical properties of graphene

Rotational symmetry is shown to protect the quadratic dispersion of out-of-plane flexural vibrations in graphene and other two-dimensional materials against phonon–phonon interactions, making the bending rigidity of these materials non-divergent. The quadratic dispersion is then consistent with the propagation of sound in the graphene plane.

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Fig. 1: Bending and ripples in graphene.


  1. Paulatto, L., Mauri, F. & Lazzeri, M. Anharmonic properties from a generalized third-order ab initio approach: Theory and applications to graphite and graphene. Phys. Rev. B 87, 214303 (2013). This paper shows that, in the standard perturbation theory built on the harmonic solution, the lifetimes of the in-plane modes do not vanish at small momenta, making it impossible for sound to propagate.

    Article  ADS  Google Scholar 

  2. Nelson, D. R. & Peliti, L. Fluctuations in membranes with crystalline and hexatic order. J. Phys. France 48, 1085–1092 (1987). This paper is a classic reference that shows how anharmonic effects can linearize the flexural modes and consequently make the bending rigidity divergent.

    Article  Google Scholar 

  3. Fasolino, A., Los, J. H. & Katsnelson, M. I. Intrinsic ripples in graphene. Nat. Mater. 6, 858–861 (2007). An article that presents atomistic simulations on the formation of ripples in graphene.

    Article  ADS  Google Scholar 

  4. Amorim, B. et al. Novel effects of strains in graphene and other two dimensional materials. Phys. Rep. 617, 1–54 (2016). A review article that presents in good detail the current understanding of the mechanical properties of graphene.

    Article  ADS  MathSciNet  Google Scholar 

  5. Monacelli, L. et al. The stochastic self-consistent harmonic approximation: calculating vibrational properties of materials with full quantum and anharmonic effects. J. Phys. Condens. Matter 33, 363001 (2021). This review article covers our stochastic SCHA method in full detail.

    Article  Google Scholar 

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This is a summary of: Aseginolaza, U. et al. Bending rigidity, sound propagation and ripples in flat graphene. Nat. Phys. (2024).

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Rotational symmetry influences the mechanical properties of graphene. Nat. Phys. (2024).

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