Effect of Antimony, Indium, and Zinc Impurities on the Critical-Field Curve of Tin

Measurements have been made of the superconducting critical field and the residual resistivity of oriented single-crystal tin samples containing In, Sb, and Zn impurities up to 2.2 at.%. The theory of Markowitz and Kadanoff is found to describe the variation of transition temperature with resistivity reasonably well. From the comparison, we obtain a value of 0.020 for the mean squared anisotropy of the superconducting energy gap in tin. Linear variations of $\Delta T_c$, ascribable to impurity-induced variations of the gross parameters of the superconducting system, are determined to be 141, 135, and 58 m °K/μΩ cm for Zn, Sb, and In impurities, respectively. These results are in good agreement with previous measurements on polycrystalline material. It is found that the impurity-induced variation of the critical-field parameters, $\frac{{\mathrm{H}}_0}{T_c}$ and ${\left(\frac{d{H}_c}{\mathrm{dT}}\right)}_{T_c}$, is in accord with Clem's theoretical calculations based on the washing out of gap anisotropy by impurity scattering. Comparison of the data with this theory suggests that the average density of states at the Fermi surface in tin is not seriously altered by the addition of up to 2 at.% impurity. Linear variations of $\Delta H_0$ with ${\rho }_{0\perp }$ are found to be similar to those of $\Delta T_c$. These linear variations of $\Delta H_0$ and $\Delta T_c$ are correlated in a way predicted by BCS.