The I-V Curves of Superconducting Microconstrictions.

Although the I-V curve properties of classic (high barrier) tunnel junctions have long been understood in great detail, the properties of metallic (no barrier) junctions have been studied only more recently and in less detail, and the transitional case (small barrier) has received practically no attention at all. Here we present a new unified treatment which is sufficiently general to embrace both limits, as well as the intermediate regime. In addition, by suitably joining two normal-superconducting (N-S) interfaces together as a model for the S-S interface, we have discovered a physically plausible explanation for the subharmonic energy gap structure that has been observed in the I-V curves of a wide variety of microconstrictions. The key to our theory is a generalized Andreev reflection model, where the properties of electron transport have been elucidated by studying the Bogoliubov equations. These equations have been solved for a simple, 1-dimensional N-S interface, where the interface contains a barrier of adjustable strength. Smooth variation in the strength of this potential is the basis for the smooth transition from microbridge to tunnel junction. The 1-dimensional calculations are then extended to 3 dimensions and to non-zero temperatures and voltages. A variety of I-V curve shapes, showing the crossover from metallic to tunnel-junction behavior, are presented as a function of barrier height and temperature. Quantitative results for the excess current and the zero voltage conductivity are compared to the predictions of other workers. We then report on a study of Cu-Nb point contacts as a model experimental system. For T << T(,c), and over a wide range of contact resistances, we find excellent quantitative confirmation of our N-S theory. The experimental problem is critically examined, with attention focussed on computer-aided measurement techniques, as well as the limits to our knowledge of the "actual" (as opposed to idealized) point contact geometry. Finally, predictions for the occurrence of subharmonic energy gap structure in S-S microconstriction I-V curves are presented. Our model, based on multiple Andreev reflections in the neck of the S-S device, correctly predicts the position of the peak structure, even when the two superconductors have different gaps.