Ultrasonic attenuation and sound velocity of the excitonic state

Ultrasonic attenuation and sound velocity of a metal in the excitonic state are investigated theoretically in the limitq1 1 and/T_c 1, whereq is the sound-wave vector,1 is the electron mean-free path, is the phonon energy, andT_c is the transition temperature of the excitonic state. The attenuation coefficient of the longitudinal wave increases drastically upon entrance into the excitonic state, then passes a maximum and decreases exponentially as temperature tends to 0 K. The attenuation coefficient of the transverse wave, on the other hand, is described in terms of the electric conductivity in the limitq1 1 and generally increases in the excitonic state. Furthermore, we find that the sound velocity of the longitudinal wave increases rapidly in the excitonic state, which is a simple manifestation of the anomaly of the dielectric function in the excitonic state.