Lateral proximity effect and long-range energy-gap gradients in Ta/Al and Nb/Al superconducting tunnel junctions

We present the results of current-voltage characterizations of $\mathrm{N}\mathrm{b}/\mathrm{A}\mathrm{l}$ and $\mathrm{T}\mathrm{a}/\mathrm{A}\mathrm{l}$ superconducting tunnel junctions, which reveal a dependence of the measured energy gap on the size of the junction. This implies a geometrical dependence of the energy gap, which suggests that the effective local energy gap has a lateral spatial variation on a scale of several \ensuremath{\mu}m. An extended version of the theory of the proximity effect could explain this phenomenon when lateral coherence lengths are introduced, which are of the order of the bulk coherence length in Al. One of the consequences of this theory is that the coherence length in a thin film cannot be taken to be isotropic. Another is that the effective lateral coherence length, which features in the lateral Usadel equation, actually depends on the quasiparticle energy.