Specific Heat of Superconducting Transition Metals Containing Nonmagnetic Impurities at Low Temperatures

Green's-function theory is used for the calculation of the specific heat of superconducting transition metals containing nonmagnetic impurities at low temperatures, $T$ ≳ $0$. It is found that in this temperature region, the $s$-band specific heat is lowered by the presence of the nonmagnetic impurities. The logarithm of the $s$-band specific heat obeys the following relation: $\ln C_s=\ln C_s^{\mathrm{}\left(0\right)\mathrm{}}-\frac{\Gamma }{k_{B}T}$ for $T\gtrsim 0$, where $C_s^{\mathrm{}\left(0\right)\mathrm{}}$ is the $s$-band specific heat for a pure two-band superconductor, and $\Gamma$ is proportional to the density of impurities, the density of states at the $d$-band Fermi surface, and the strength of the interband impurity scattering. This relation agrees very well with the low-temperature experimental data of Shen, Senozan, and Phillips.