Thin superconductors and SQUIDs in perpendicular magnetic field
  It is shown how the static and dynamic electromagnetic properties can be calculated for thin flat superconducting films of any shape and size, also multiply connected as used for SQUIDs, and for any value of the effective magnetic London penetration depth Lambda. As examples, the distributions of sheet current and magnetic field are obtained for rectangular and circular films without and with slits and holes, in response to an applied perpendicular magnetic field and to magnetic vortices moving in the film. The self energy and interaction of vortices with each other and with an applied magnetic field and/or transport current are given. Due to the long ranging magnetic stray field, these energies depend on the size and shape of the film and on the vortex position even in large films, in contrast to the situation in large bulk superconductors. The focussing of magnetic flux into the central hole of square films without and with a radial slit is compared. 
Ernst Helmut Brandt