Inductance effects and dimensionality crossover in hybrid superconducting arrays

We report measurements made on hybrid arrays consisting of superconducting wires along one direction of a square geometry and Josephson junctions along the perpendicular direction. The differential resistance ${\mathit{R}}_{\mathit{d}}$ across the array as a function of normalized applied flux per plaquette f=Φ/${\mathrm{\Phi }}_0$ exhibits two distinct types of behavior. When the ratio β≡${\mathit{L}}_{\mathit{g}}$/${\mathit{L}}_{\mathit{J}}$ of the geometric inductance of an array plaquette to the Josephson-junction inductance is much less than unity, we observe oscillations in ${\mathit{R}}_{\mathit{d}}$ characteristic of a one-dimensional (1D) N-junction interferometer. However, as β approaches 1, the simultaneous suppression of interferometer oscillations and emergence of local minima in ${\mathit{R}}_{\mathit{d}}$ at commensurate fields f=p/q (where p and q are integers) signal a crossover to behavior typical of 2D superconducting arrays. To model the experimental system, we have performed simulations of 2D arrays of Josephson junctions made anisotropic by incorporating different coupling in the two perpendicular directions (i.e., anisotropic XY model). In the limit of large anisotropy we find 1D interferometer behavior; as the anisotropy is reduced, we see a crossover to the 2D behavior familiar in isotropic arrays.