Meissner response of a bulk superconductor with an embedded sheet of reduced penetration depth

We calculate the change in susceptibility resulting from a thin sheet with reduced penetration depth embedded perpendicular to the surface of an isotropic superconductor, in a geometry applicable to scanning superconducting quantum interference device microscopy, by numerically solving Maxwell's and London's equations using the finite-element method. The predicted stripes in susceptibility agree well in shape with the observations of Kalisky [Phys. Rev. B 81, 184513 (2010)] of enhanced susceptibility above twin planes in the underdoped pnictide superconductor Ba (Fe_1-x Co_x) ₂As₂. By comparing the predicted stripe amplitudes with experiment and using the London relation between penetration depth and superfluid density, we estimate the enhanced Cooper-pair density on the twin planes, and the barrier force for a vortex to cross a twin plane. Fits to the observed temperature dependence of the stripe amplitude suggest that the twin planes have a higher critical temperature than the bulk, although stripes are not observed above the bulk critical temperature.