Nonanalytic behavior of ultrasonic attenuation in disordered electronic systems

The sound attenuation coefficient {α} is calculated in perturbation theory around the Boltzmann result, α⁰, for two- and three-dimensional (3D) disordered electronic systems. For 3D systems we calculate impurity density corrections to α⁰ up to second order. The second-order correction is found to be nonanalytic in the impurity density. We also calculate the leading nonanalytic low-frequency corrections to α⁰ due to electron localization effects up to terms of second order in the impurity density. The theory suggests that for 2D systems there will be singular low-frequency corrections to α⁰ even in the presence of a magnetic field. The perturbation theory also shows that the behavior of {α} near an electronic mobility edge cannot be obtained by exponentiating an {ε} expansion around d=2.