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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References
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.
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This is a summary of: Aseginolaza, U. et al. Bending rigidity, sound propagation and ripples in flat graphene. Nat. Phys. https://doi.org/10.1038/s41567-024-02441-z (2024).
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Rotational symmetry influences the mechanical properties of graphene. Nat. Phys. (2024). https://doi.org/10.1038/s41567-024-02442-y
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DOI: https://doi.org/10.1038/s41567-024-02442-y
