Ultrasonic attenuation in incommensurate solids due to order parameter fluctuations

Abstract

Abstract A theory for the dispersion and attenuation of sound waves due to amplitude and phase fluctuations of the order parameter in incommensurate solids is developed. Using Langevin equations for acoustic and order parameter modes we obtain a Debye behavior for the elastic response at “high” frequencies and a strongly non-Debye behavior at “low” frequencies due to infrared divergences of simple perturbation theory. The divergences are treated by summing up the leading diagrams of a 1/N expansion where N is the number of components of the order parameter. At low frequencies the dispersion of sound waves is only little affected by the divergences; however their absorption increases dramatically in pure systems, leading to diverging viscosities throughout the incommensurate phase and an anomalous ω3/2 law for the ultrasonic attenuation coefficient. We discuss also how the anomalous elastic response at low frequencies changes if a finite coherence length due to pinning effects is taken into account. Finall...