Ultrasonic Shear Wave Attenuation in Superconducting Tin

Abstract

The superconducting attenuation of transverse ultrasonic waves was studied experimentally in single crystal tin. The "residual" attenuation was found to be consistent with the relation $\frac{{\alpha }_s}{{\alpha }_n}\propto \exp (-\frac{\mathcal{E}}{\mathrm{kT}})$ at low reduced temperatures in tin; $\frac{{\alpha }_s}{{\alpha }_n}$ is the superconducting-to-normal attenuation ratio and $\mathcal{E}$ is the superconducting energy gap. This functional form satisfied the low-temperature observations for all principal propagation and polarization orientations. Anisotropy in the apparent superconducting energy gap was demonstrated. It was found that anisotropy can be associated with polarization orientation as well as propagation orientation of the transverse lattice waves. Observed values of total and residual shear wave attenuation were found to suggest the importance of shear deformation interactions between the electron system and lattice waves in tin.