Electromagnetic attenuation of shear waves in superconductors

Abstract

A detailed analysis of the electromagnetic attenuation in superconductors has been carried out, with specific reference to type I materials. The rapid rise atTc predicted by Cullen and Ferrell is found to be most pronounced in superconductors with low acoustic velocities. Also, the effect occurs at lowest frequencies in these materials. It is demonstrated how the shape of the transition curve reflects anisotropies in electronic and elastic properties. Very close toTc the attenuation at low frequencies is inversely proportional to the real conductivity function, while at high frequencies it is proportional to that conductivity. Numerical results for Al, In, Pb, and Sn are presented. Although these materials are similar with regard to electronic structure, they are characteristically different with regard to electrodynamic properties as probed by ultrasonic phonons. From the present analysis it is concluded that ultrasonic probing of the electrodynamics of superconductors offers a sensitive and, at the present, unique way of determining the response of a superconductor to a single variable wave number. In addition the wave numbers available in this way are in a range where it has been most difficult to obtain such information by penetration depth studies, namely, in the transition region between pure local and nonlocal behavior.