Influence of the 3D-2D crossover on the critical current of Nb/Cu multilayers

We report the experimental observation of the Josephson critical current across layers, ${\mathit{I}}_{\mathit{c}}^{\mathrm{\perp }}$, for Nb/Cu multilayers. Unique samples with a small cross section (20 μm in diameter) consisting of ten Nb/Cu junctions were fabricated for such measurements. A strong influence of the dimensional 3D-2D crossover on the ${\mathit{I}}_{\mathit{c}}^{\mathrm{\perp }}$ was observed. Thus, as the temperature becomes smaller than ${\mathit{T}}_{2\mathrm{D}}$, hysteresis in the current-voltage characteristic appears and the behavior of the temperature dependence of the ${\mathit{I}}_{\mathit{c}}^{\mathrm{\perp }}$ changes. For T>${\mathit{T}}_{2\mathrm{D}}$ the diminishing of the hysteresis is caused by a sharp decrease of the junction capacitance in the 3D regime when the sample becomes uniform across layers. Calculation of the critical-current temperature dependence ${\mathit{I}}_{\mathit{c}}^{\mathrm{\perp }}$(T) for our multilayers was made. An agreement between experimental and theoretical dependencies ${\mathit{I}}_{\mathit{c}}^{\mathrm{\perp }}$(T) was found. From the theoretical simulations, we have obtained the dependence of the crossover and the critical temperatures of multilayers on the layer thicknesses, the boundary transparency, and layer conductivity.