Abstract

We develop the theory for dynamics of the out-of-plane deformations in flexible two-dimensional materials. We focus on studying the attenuation of flexural phonons in free-standing crystalline membranes. We demonstrate that dynamic renormalization does not involve the ultraviolet divergent logarithmic contributions, contrary to static ones. This fact allows us to find the scaling form of the attenuation, determine its small- and large-frequency asymptotes, and derive the exact expression for the dynamical exponent of flexural phonons in the long-wave limit. Furthermore, we demonstrate that the presence of nonzero tension strongly reduces the relative magnitude of the attenuation and, consequently, results in parametrical narrowing of the phonon spectral line due to stress-controlled suppression of the retardation effects in the dynamically screened inter-phonon interaction. We predict the specific power-law dependence of the spectral-line width on temperature and tension. We speculate that suppression of the phonon attenuation by nonzero tension might be responsible for higher quality factors of mechanical nanoresonators based on flexural two-dimensional materials. We discuss the implications of our results for experiments on phonon spectra in graphene and the dynamics of graphene-based nanomechanical resonators.