Ultrasonic studies of the electronic structure of hexagonal metal crystals II. Superconducting state in zinc and cadmium

Abstract

Measurements have been made of the temperature dependence of the attenuation of longitudinal ultrasound in the superconducting states of pure zinc and cadmium for propagation along the and <0001>, <101 ¯ 0> and <112 ¯ 0> directions, at frequencies from 40 to 160 MHz. This temperature dependence has been interpreted in terms of an energy gap parameter A = 2∆(0)/ kT c . In zinc, for T < ½ T c , A was found to be 3.41 ± 0.1, 3.79 ± 0.1 and 3.64 ± 0.1 for the <0001>, <101 ¯ 0> and <122 ¯ 0> directions respectively. The corresponding values for cadmium were 3.29 ± 0.1, 2.80 ± 0.1 and 3.87 ± 0.1. A simple model proposed by Hays for the distribution of the energy gaps on the Fermi surface of zinc does not explain these results, and a more realistic model has been proposed. The main features of the proposed energy-gap distributions in zinc and cadmium are that the electrons on the third band lens have larger energy gaps than those on the second band monster, over which there is a large and complicated variation.