Narrowing of the Flexural Phonon Spectral Line in Stressed Crystalline Two-Dimensional Materials

We develop the microscopic theory for the attenuation of out-of-plane phonons in stressed flexible two-dimensional crystalline materials. 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 high quality factors of mechanical nanoresonators based on flexural two-dimensional materials.