Previous continuum theory of type-II superconductors of various shapes with and without vortex pinning in an applied magnetic field and with transport current is generalized to account for a finite London penetration depth λ. This extension is particularly important at low inductions B, where the transition to the Meissner state is now described correctly, and for films with thickness comparable to or smaller than λ. The finite width of the surface layer with screening currents and the correct dc and ac responses in various geometries follow naturally from an equation of motion for the current density in which the integral kernel now accounts for finite λ. New geometries considered here are thick and thin strips with applied current, and “washers,” i.e. thin-film squares with a slot and central hole, as used for superconducting quantum interference devices.

• Received 14 February 2001

DOI:https://doi.org/10.1103/PhysRevB.64.024505