Ultrasonic attenuation in superconductors

Abstract

The theory of ultrasonic attenuation in a superconductor, particularly its relation to the attenuation in the normal state of the same metal, is developed for rather general conditions, by means of a Boltzmann-equation approach. In principle no special assumptions are made about the shape of the Fermi surface or the scattering function, but in order to obtain simple results it is found necessary to assume the energy gap to take the same value at all points on the Fermi surface, and to consider elastic scattering only. It is then found that for all values of ql the attenuation of longitudinal waves follows the original B.C.S.law, $\alpha_s$/$\alpha_n$ = 2f($\Delta$), f being the Fermi function, while for other than purely longitudinal waves there should be a discontinuity in $\alpha_s$/$\alpha_n$ at the transition temperature, with the residual attenuation below the discontinuity also varying as f($\Delta$). Considerable attention is paid to the special case ql $\simeq$ I, since here the behaviour is particularly sensitive to violations of the conditions assumed; variations of $\Delta$ especially can lead in principle to quite different forms of $\alpha_s$/$\alpha_n$.