Relationship between the density of states and the superconducting transition temperature inA-15 compounds

Data by Wiesmann et al. on the temperature coefficient of the upper critical field, $\frac{d{H}_{c2\mathrm{}}\mathrm{}\left(T\right)\mathrm{}}{\mathrm{dT}}$, and the normal-state resistivity ${\rho }_0$ near the superconducting transition temperature $T_c$ are analyzed to estimate the bare density of states $N\left(E_F\right)$ as a function of structural disorder and $T_c$ in various $\alpha$-particle irradiated samples of $A$-15 ${\mathrm{Nb}}_3$Ge and ${\mathrm{Nb}}_3$Sn. By taking into account the change in the electron-phonon coupling strength with $T_c$ and the effect of mass enhancement arising from the electron-phonon interaction, the results of the new analysis indicate that (i) the drop in $N\left(E_F\right)$ for ${\mathrm{Nb}}_3$Ge is relatively small as $T_c$ changes from ∼ 21 to ∼ 4 K, in agreement with a recent low-temperature specific-heat measurement; (ii) the value of $N\left(E_F\right)$ in ${\mathrm{Nb}}_3$Sn decreases by a factor of ∼ 4 as $T_c$ varies from ∼ 18 to ∼ 3 K. The implication of these findings is discussed in terms of the origin of high-$T_c$ superconductivity in $A$-15 compounds.