Ultrasonic attenuation at 500 kHz in superconducting tin

Abstract

The temperature dependence of the longitudinal ultrasonic attenuation in single crystals of white tin has been measured by a resonance technique at a frequency of 500 kHz between 1 and 4.2 °K, for propagation along (100) and (001). The resistance ratio of the samples varied from 800 to 30000 and in all cases the electronic mean free path is smaller than the ultrasonic wavelength. No difference is found between propagation along (100) and (001) in the most heavily doped samples, in contrast to the suggestion of Kadanoff & Pippard, although in this case the normalized attenuation curve lies above the form found by Bardeen, Cooper & Schrieffer (B.C.S.). A systematic decrease of attenuation with increasing purity is found, so that in the most pure samples the curve lies well below the B.C.S. form. This effect is more marked for (001) propagation. A simple model is used to calculate the details of elastic scattering in the anisotropic superconductor, and it is shown that scattering across the Fermi surface can account for the lack of any orientational differences. The free path of the excitations is modified by the anisotropy: this brings the theory into very good agreement with the present results, and also increases the theoretical anisotropy of thermal conductivity in tin so as to agree with experiment. Phonon scattering across the Fermi surface is shown to account for the variation of attenuation with purity; the anisotropy of this effect is consistent with the gap anisotropy.