Meissner-London Currents in Superconductors with Rectangular Cross Section

Exact analytic solutions are presented for the magnetic moment and screening currents in the Meissner state of superconductor strips with rectangular cross section in a perpendicular magnetic field and/or with transport current. The extension to finite London penetration is achieved by an elegant numerical method which works also for disks. The surface current in the specimen corners diverges as $l^{-1\mathrm{}/3}$ where l is the distance from the corner. This enhancement reduces the barrier for vortex penetration and should increase the nonlinear Meissner effect in $d$-wave superconductors.