Influence of magnetic field and Pincus states in normal-metal—superconductor tunnel junctions

Abstract

Normal-metal—superconductor tunneling, when applied to metallic superconductors with well-known bulk properties, yields useful information on barrier properties. In particular, it is quite common to observe deviations from the predictions of a homogeneous barrier model, Nb-oxide barriers being the most-investigated example. In discussing these shortcomings, high local nearly metallic transparency instead of a tunneling probability of order 10−8 is an often applied concept. We here present experimental results on Ag/Nb and Ag/Ta tunneling junctions which, in addition to a commonly observed finite zero-bias conductance, show a pronounced, characteristic magnetic field dependence. A theory is developed on the basis of the Bogoliubov-de Gennes equations which takes into account the influence of the shielding current as well as tunneling of quasiparticles with nonperpendicular incidence, typical for inhomogeneous tunneling barriers with high local transparency. The field effect due to quasiparticles with non-normal incidence is nearly antisymmetric with respect to the gap voltage. Below Δe the effect is positive on account of resonant transmission to, the Pincus-type bound states appearing for quasiparticle momenta antiparallel to the shielding current. Above Δe, a compensating negative contribution is obtained. The results are quantitatively discussed with respect to their dependence on barrier transparency and angular spreading of quasiparticle injection. We find good agreement with the experiments for a broad angular distribution of injected quasiparticles, typical for inhomogeneous barriers with high local transparency. Furthermore differences by an order of magnitude between Nb-and Ta-based junctions can be fully accounted for. On the other hand, strong confinement of quasiparticle injection in forward direction which is typical for an ideal, homogeneous barrier, yields marked deviations from experiment. Thus, we can conclude a broad angular distribution of quasiparticle transmission, characteristic for high local transparency.

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