Resistance of superconducting-normal interfaces

Abstract

The temperature dependence of the electrical resistance in two mixed superconducting-normal (SN) systems has been investigated by means of a Clarke 'Slug'. In both the intermediate state of superconducting tin and various SNS sandwiches (e.g. Pb-Cu-Pb) the resistance rises as the transition temperature is approached from below. The main effect takes place above 0.8$T_{c}$, where the energy gap is comparable with $k_{B}T$, and is therefore attributed to the penetration of excitations above the gap from S into N and vice versa. The resistance rise is particularly large in SNS sandwiches employing alloy superconductors. The transport equation for the excitations is solved for a simplified one-dimensional model incorporating elastic and inelastic scattering as well as partial reflexion (Andreev) at the SN boundary. The solution demands a potential step, proportional to the current, at the boundary, and this is the mechanism of the observed additional resistance. Its magnitude is proportional to the distance, measured in terms of free paths, that an excitation travels into the superconductor before being destroyed by an inelastic process. In the intermediate state the only important factor is Andreev reflexion, and the theoretical expression, which involves no arbitrary parameters, agrees well with the data. SNS sandwiches may have, in addition, considerable elastic scattering at the boundary between different metals and this shows up in the experiments as a temperature-independent resistance in excess of what is expected from the measured resistivity of the normal metal. It is conjectured that at a temperature below the lowest used (0.35 K) the extra resistance may disappear when the excitations in the normal metal are unable to reach the junction. The temperature-variation of the resistance just below $T_{\text{c}}$ is well accounted for by the theory when a reasonable choice is made of the one unknown parameter involved.