Type II superconductors with applied current and magnetic field:effects of geometry and London depth

Abstract

It is shown how the previous continuum theory of type II superconductorswith and without vortex pinning, of various shapes and in an applied magneticfield, is generalized to account for an applied transport current and a finiteLondon penetration depth λ. This extension is particularly importantat low inductions B, where the transition to the Meissner state is nowdescribed correctly, and for films with thickness comparable to or smallerthan λ. The finite width of the surface layer with screening currentsand the correct dc and ac responses in various geometries follow naturallyfrom an equation of motion for the current density in which the integralkernel now accounts for finite λ. Also considered is the geometry of`washers', i.e. thin-film squares with a slot and central hole as used forSQUIDs.