Superconducting properties of tin-copper amorphous thin films

TL;DR

This study investigates the thermodynamic properties of amorphous tin-copper thin films across various copper concentrations, revealing deviations from BCS theory predictions and how critical temperature decreases with increased copper content.

Contribution

The paper provides a detailed theoretical analysis of the superconducting state in amorphous Sn-Cu films using strong-coupling formalism and experimental Eliashberg functions, highlighting deviations from BCS ratios.

Findings

Critical temperature decreases from 7 K to 3.9 K with copper doping.

Energy gap to critical temperature ratio exceeds BCS value, ranging from 3.95 to 4.4.

Specific heat jump and thermodynamic critical field ratios also deviate from BCS predictions.

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 $R_{H}\in\left<0.141,0.154\right>$.