Superconducting properties of tin-copper amorphous thin films

Abstract

The thermodynamic properties of the superconducting state in the amorphous ${\rm Sn_{1-x}Cu_{x}}$ thin films have been characterized. The concentration of copper changes in the range from $0.08$ to $0.41$. The calculations have been conducted in the framework of the strong-coupling formalism, wherein the Eliashberg functions determined in the tunnel experiment (Phys. Rev. B {\bf 51}, 685 (1995)) have been used. The value of the Coulomb pseudopotential equal to $0.1$ has been adopted. It has been found that the critical temperature ($T_{C}$) decreases from $7$ K to $3.9$ K. The ratio of the energy gap to the critical temperature: $R_{\Delta}=2\Delta\left(0\right)/k_{B}T_{C}$, differs significantly from the BCS value: $R_{\Delta}\in\left<4.4,3.95\right>$. Similarly behaves the ratio of the specific heat jump to the specific heat of the normal state: $R_{C}=\Delta C\left(T_{C}\right)/C^{N}\left(T_{C}\right)$, and the parameter: $R_{H}=T_{C}C^{N}\left(T_{C}\right)/H^{2}_{C}\left(0\right)$, where $H_{C}\left(0\right)$ is the thermodynamic critical field. In particular, $R_{C}\in\left<2.2,1.75\right>$ and $R_{H}\in\left<0.141,0.154\right>$.