Microscopic superconducting parameters ofNb3Al: Importance of the band density of states

Critical-field measurements are carried out in low fields on a series of $A15\mathrm{}$ Nb-Al as-deposited films where structural disorder, as characterized by the residual resistivity $\rho \left(T_c\right)$, is introduced by varying the composition in the $A15\mathrm{}$ phase. Analysis of the critical-field slopes near $T_c$ gives relatively low electronic densities of states at Fermi level $N^b\mathrm{}\left(0\right)\mathrm{}$ in agreement with heat-capacity results. The $N^b\mathrm{}\left(0\right)\mathrm{}$'s remain nearly constant over the resistivity range varied. Lacking data in the low resistivity range, our results neither support nor disagree with the resistive lifetime-broadening model of the density of states. Nonetheless, the data unambiguously demonstrate that the conventional model, in which a peak in the band density of states at the Fermi level plays the essential role, is not sufficient to explain the observed systematics in high-$T_c$ ${\mathrm{Nb}}_3$Al. More specifically, changes in $\frac{〈I^2〉}{〈{\omega }^2〉}$ with disorder are found to be responsible for the observed changes in $T_c$, where the increase of $〈{\omega }^2〉$ with disorder has been shown earlier in the tunneling studies. Further consideration of similar data for the other superconductors ${\mathrm{V}}_3$Si, ${\mathrm{Nb}}_3$Sn, and ${\mathrm{Nb}}_3$Ge suggests that important variations in $\frac{〈I^2〉}{〈{\omega }^2〉}$ may be a general feature of the high-$T_c$ $A15\mathrm{}$ superconductors. $\frac{〈I^2〉}{〈{\omega }^2〉}$ increases as one progresses from ${\mathrm{V}}_3$Si through ${\mathrm{Nb}}_3$Sn and ${\mathrm{Nb}}_3$Al to ${\mathrm{Nb}}_3$Ge in correlation with the relative instability of the $A15\mathrm{}$ phase in these materials.