Anisotropy and Strong-Coupling Effects on the Critical-Magnetic-Field Curve of Elemental Superconductors

An empirical method of separating strong-coupling effects from anisotropy effects in critical-magnetic-field curves of elemental superconductors is presented. Using Clem's critical-field expressions for a weak-coupling anisotropic superconductor, together with an empirical scaling of the superconducting energy gap, a set of relations is derived which allows an independent determination of the mean-squared energy-gap anisotropy parameter $〈a^2〉$ and a strong-coupling scaling parameter $\delta$. These parameters depend on the experimental determination of two quantities, $2\pi \gamma {\left(\frac{T_0}{H_0}\right)}^2$ and ${\left(\frac{\mathrm{dh}}{\mathrm{dt}}\right)}_{t=1\mathrm{}}$, where $T_0$ is the zero-field superconducting transition temperature, $H_0$ is the zero-temperature critical magnetic field, $\gamma$ is the temperature coefficient of the normal electronic specific heat, and ${\left(\frac{\mathrm{dh}}{\mathrm{dt}}\right)}_{t=1\mathrm{}}$ is the initial slope of the critical-field curve expressed in reduced variables. Values of $〈a^2〉$ are calculated using published critical-field data and are compared with those values obtained by independent means.