Sound attenuation and anharmonic damping in solids with correlated disorder

Abstract

We study via self-consistent Born approximation a model for sound waves in a disordered environment, in which the local fluctuations of the shear modulus G are spatially correlated with a certain correlation length ξ. The theory predicts an enhancement of the density of states over Debye's ω2 law (boson peak) whose intensity increases for increasing correlation length, and whose frequency position is shifted downwards as 1/ξ. Moreover, the predicted disorder-induced sound attenuation coefficient Γ(k) obeys a universal scaling law ξ Γ(k) = f(kξ) for a given variance of G. Finally, the inclusion of the lowest-order contribution to the anharmonic sound damping into the theory allows us to reconcile apparently contradictory recent experimental data in amorphous SiO2.