Increase of the Anisotropy of the Energy Gap in Superconducting Thallium under Pressure

A study has been made of the dependence of the superconducting transition temperature of thallium on the density of lattice defects due to plastic deformation, as a function of hydrostatic pressures up to 4 kbar. The change in critical temperature with resistivity ratio is found to be pressure-dependent. It can be accounted for by a theory of gap anisotropy given by Markowitz and Kadanoff and yields a strongly pressure-dependent anisotropy parameter $\lambda 〈a^2〉$ which varies from 0.0008 at zero pressure to 0.007 at $p=4\mathrm{}$ kbar. Only a little change in the "valence" effect with pressure is observed. The well-known anomalous enhancement of the transition temperature of thallium at pressures up to 2 kbar can be explained quantitatively by this increase of the gap anisotropy under pressure.