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 use scanning SQUID microscopy to investigate the behavior of vortices in the presence of twin boundaries in the pnictide superconductor Ba(Fe1-xCox)2As2. We show that the vortices avoid pinning on twin boundaries. Individual vortices move in a pre
ferential way when manipulated with the SQUID: they tend to not cross a twin boundary, but rather to move parallel to it. This behavior can be explained by the observation of enhanced superfluid density on twin boundaries in Ba(Fe1-xCox)2As2. The observed repulsion from twin boundaries may be a mechanism for enhanced critical currents observed in twinned samples in pnictides and other superconductors.
It is widely believed that the perovskite Sr$_2$RuO$_4$ is an unconventional superconductor with broken time reversal symmetry. It has been predicted that superconductors with broken time reversal symmetry should have spontaneously generated supercur
rents at edges and domain walls. We have done careful imaging of the magnetic fields above Sr$_2$RuO$_4$ single crystals using scanning Hall bar and SQUID microscopies, and see no evidence for such spontaneously generated supercurrents. We use the results from our magnetic imaging to place upper limits on the spontaneously generated supercurrents at edges and domain walls as a function of domain size. For a single domain, this upper limit is below the predicted signal by two orders of magnitude. We speculate on the causes and implications of the lack of large spontaneous supercurrents in this very interesting superconducting system.
