Inhomogeneous magnetic flux focusing in superconducting josephson networks

The bending effects of a transverse magnetic field on planar superconducting structures in the Meissner state are investigated. Systematic measurements are performed on arrays made of four and six small Josephson junctions connected in parallel by superconducting films. By applying an external uniform magnetic field H, we measure the Josephson critical current (Formula presented) which is sensitive to the local magnetic-field distribution, as a function of H. We find that the experimental data cannot be accounted for by the external magnetic field, and a strong focusing effect is present. Moreover, only by using a nonuniform magnetic-field distribution with a maximum in the center of the array are we able to fit the experimental data by numerical simulations. We show that, in the absence of self-field effects resulting from the Josephson currents, the nonuniform magnetic-field distribution is caused by the diamagnetic shielding produced by Meissner currents flowing in the superconducting electrodes. Three-dimensional finite element numerical calculations are performed on several planar geometries in a transverse external magnetic field to compute the magnetic-field distribution and the screening current patterns. In this way, we find a quantitative agreement with the observed inhomogeneous field distribution. The multiloop geometry has also been compared with equivalent networks, which considerably reduce the numerical calculations and substantially give the same inhomogeneous flux focusing. © 1999 The American Physical Society.