Attenuation of flexural phonons in free-standing crystalline two-dimensional materials
We develop the theory for dynamics of the out-of-plane deformations in flexible two-dimensional materials. We focus on study of attenuation of flexural phonons in free-standing crystalline membranes. We demonstrate that the dynamical renormalization does not involve the ultraviolet divergent logarit...
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Zusammenfassung: | We develop the theory for dynamics of the out-of-plane deformations in
flexible two-dimensional materials. We focus on study of attenuation of
flexural phonons in free-standing crystalline membranes. We demonstrate that
the dynamical renormalization does not involve the ultraviolet divergent
logarithmic contributions contrary to the static ones. This fact allows us to
find the scaling form of the attenuation, determine its small and large
frequency asymptotes, and to derive the exact expression for the dynamical
exponent of flexural phonons in the long wave limit: $\textsf{z}{=}2{-}\eta/2$.
Here $\eta$ is the universal exponent controlling the static renormalization of
the bending rigidity. Also we determine the dynamical exponent for the
long-wave in-plane phonons: $\textsf{z}^\prime{=}(2{-}\eta)/(1{-}\eta/2)$. We
discuss implication of our results to experiments on phonon spectra in graphene
and dynamics of graphene-based nanomechanical resonators. |
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DOI: | 10.48550/arxiv.2312.04138 |