Josephson tunneling and the proximity effect

Abstract

Josephson junctions containing one or two proximity systems (e.g., $S_{\alpha }-M_{\beta }-I-S_{\gamma }$, $S_{\alpha }-M_{\beta }-I-M_{\gamma }-S_{\delta }$; $M_{\beta \left(\gamma \right)}$ is a normal metal or superconductor) are studied. An analysis of the thickness and temperature dependences of the maximum dc Josephson current $I_M$ is carried out. The curvature of the function $I_M\left(L_{\beta }\right)$ is found to depend strongly on the ratio of energy gaps $\frac{{\epsilon }_{\gamma }}{{\epsilon }_{\alpha }}$ and on the temperature. The analysis is based on the thermodynamic Green's-function method, and the effect of strong coupling is also taken into account. If the proximity system contains two superconductors $S_{\alpha }$ and $S_{\beta }$ then it appears that the electron-phonon interaction described by the constant ${\lambda }_{\beta }$ contributes noticeably even if $T>\mathrm{}{T}_{c\beta }$.