It is shown that a vortex trapped in one of the banks of a planar edge-type Josephson junction in a narrow thin-film superconducting strip can change drastically the field dependence of the junction critical current $I_c(H)$. When the vortex is trapp
ed at certain positions in the strip middle, the pattern $I_c(H)$ has zero at $H=0$ instead of the traditional maximum of 0-type junctions. The number of these positions is equal to the number of vortices trapped at the same location. When the junction-vortex separation exceeds approximately $2W$, $I_c(H)$ is no longer sensitive to the vortex presence.
We argue that cutoff in the London model cannot be settled without use of the microscopic theory.
We discuss the Meissner response to a known field source of superconductors having inhomogeneities in their penetration depth. We simplify the general problem by assuming that the perturbations of the fields by the penetration depth inhomogeneities a
re small. We present expressions for inhomogeneities in several geometries, but concentrate for comparison with experiment on planar defects, perpendicular to the sample surfaces, with superfluid densities different from the rest of the samples. These calculations are relevant for magnetic microscopies, such as Scanning Superconducting Quantum Interference Device (SQUID) and Magnetic Force Microscope, which image the local diamagnetic susceptibility of a sample.
We study the field dependence of the maximum supercurrent in narrow edge-type thin-film Josephson junctions. It is assumed that the junction extends across thin-film strip of width W that is much less than the Pearl length; the film thickness is much
less than the London penetration depth. We calculate the maximum supercurrent within nonlocal Josephson electrodynamics, which takes into account the stray fields affecting tunneling currents. In the case when W is much less than the thin-film Josephson length, the phase difference along the junction depends only on the junction geometry and the applied field, but is independent of the Josephson critical current density, i.e., it is universal. Zeros of the maximum supercurrent are equidistant only in large fields (unlike the case of junctions with bulk banks); they are spaced by a field that is much smaller than the one of bulk junctions. Peaks of the maximum supercurrent decrease inversely proportional to the square root of the applied field, i.e., slower than 1/H for the bulk.
