Ultrasonic Determination of the Superconducting Energy Gap in Thallium

The temperature-dependent energy gap 2Δ(T) in single crystals of high-purity thallium has been determined by measurements of the attenuation in the normal and superconducting states of longitudinal acoustic waves. Determinations were made for sound-wave propagation along the [0002], [101̄0], and [12̄10] crystallographic axes. The energy gap 2Δ(0) at 0^∘{}K for propagation along these axes, respectively, was found to be 3.76kTc±0.03kTc, 4.10kTc±0.03kTc, and 4.00kTc±0.10kTc. Ultrasonic attenuation gives a larger value for this limiting energy gap than that observed by other methods. The decrease in attenuation below Tc was found to be more abrupt than predicted by the Bardeen-Cooper-Schrieffer (BCS) theory. It is suggested that the simple BCS model does not give a complete picture of the ultrasonic attenuation in very pure superconductors.