On the contribution of the superconductor to the resistance of a superconductor-normal metal system

The problem of dc current flow through a superconductor-normal metal interface near the critical temperature T _c is considered. The equations for the Green's functions integrated with respect to the variable ζ = v(p−p₀) are used to calcuate the resistance of the pure and dirty superconductor S. It is shown that the electric field E decays exponentially over a length % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% acbaGaa8xmamaaBaaaleaacaWFIbaabeaakiabg2da9iaacIcadaWc% gaqaaiaa-reacqaHepaDdaWgaaWcbaGaa8xzaaqabaacbiGccaGF0a% Gaa8hvaaqaaiabec8aWjabgs5aejaa-LcadaahaaWcbeqaamaaliaa% baGaa8xmaaqaaiaa-jdaaaaaaaaaaaa!49B4!\[1_b = ({{D\tau _e 4T} \mathord{\left/ {\vphantom {{D\tau _e 4T} {\pi \Delta )^{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$2$}}} }}} \right. \kern-\nulldelimiterspace} {\pi \Delta )^{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$2$}}} }}\] within the superconductor and at the S-N interface there is a jump of E [strictly speaking, E varies over the correlation length ζ(T)]; here D is the diffusion coefficient, and Τ _e is the energy relaxation time. The magnitude of the jump of E is of the order of or less than the value of E at the boundary of the S region. In the case of a pure superconductor this jump is caused by the Andreev reflection of quasiparticles at the S-N interface.