Ultrasonic Attenuation in Dirty Superconductors

Abstract

The attenuation coefficients of acoustic waves have been calculated for small-gap superconductors for the case where the electron mean free path $l$ is much smaller than the pure superconductor coherence length ${\xi }_0$. The emphasis in this paper is placed on a study of longitudinal acoustic waves. It is shown that attenuation in this case arises from both electromagnetic absorption and the collision drag effect. In the transverse case the electromagnetic absorption is negligible in the low-frequency limit $\frac{\left|\Delta \right|}{\omega }\gg 1$. The results of the calculation have been applied to the Abrikosov mixed state and the superconducting surface sheath. Measurement of the attenuation in these regimes will determine the upper critical fields $H_{c2\mathrm{}}$ and $H_{c3\mathrm{}}$ as well as the averaged amplitude of the energy gap.