Ultrasonic Attenuation in the Superconducting State of High-Purity Thallium

Abstract

The electronic attenuation of longitudinal ultrasonic waves (10 to 130 MHz) was measured in the superconducting state of high-purity thallium by the pulse echo technique. $\frac{{\ensuremath{\alpha}}_{s}}{{\ensuremath{\alpha}}_{n}}$, the ratio of superconducting- to normal-state attenuation, decreased faster with decreasing $\frac{T}{{T}_{c}}$ in the temperature region just below the transition temperature ${T}_{c}$ than predicted by the BCS theory. The zero-temperature energy gaps, based on the low-temperature data, were $(3.90\ifmmode\pm\else\textpm\fi{}0.1)k{T}_{c}$, $(3.52\ifmmode\pm\else\textpm\fi{}0.15)k{T}_{c}$, and $(3.70\ifmmode\pm\else\textpm\fi{}0.20)k{T}_{c}$ for propagation along the [0001], [$\overline{1}2\overline{1}0$], and [$10\overline{1}0$] directions, respectively. No frequency effects were observed in $\frac{{\ensuremath{\alpha}}_{s}}{{\ensuremath{\alpha}}_{n}}$ versus $\frac{T}{{T}_{c}}$ for propagation along the [0001] and [$\overline{1}2\overline{1}0$] directions. For $\mathrm{q}\ensuremath{\parallel}[10\overline{1}0]$, however, $\frac{{\ensuremath{\alpha}}_{s}}{{\ensuremath{\alpha}}_{n}}$ varied with frequency, dropping faster as $T$ was lowered below ${T}_{c}$ and as the frequency became lower. The attenuation was found to be amplitude-independent in the superconducting and normal states.