Nonanalytic behavior of ultrasonic attenuation in disordered electronic systems

Abstract

The sound attenuation coefficient α is calculated in perturbation theory around the Boltzmann result, ${\alpha }^0$, for two- and three-dimensional (3D) disordered electronic systems. For 3D systems we calculate impurity density corrections to ${\alpha }^0$ 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 ${\alpha }^0$ 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 ${\alpha }^0$ 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.