Analytical model of the response of a superconducting film to line currents

We theoretically investigate the response of a superconducting film to line currents flowing in linear wires placed above the film, and we present analytic expressions for the magnetic-field and current distributions based on the critical state model. The behavior of the superconducting film is characterized by the sheet-current density Kz, whose magnitude cannot exceed the critical value jcd, where jc is the critical current density and d is the thickness of the film. When the transport current I₀ flowing in the wire is small enough, Kz is smaller than jcd and the magnetic field is shielded below the film. When I₀ exceeds a threshold value Ic0∝jcd, on the other hand, Kz reaches jcd and the magnetic field penetrates below the film. We also calculate the ac response of the film when an ac transport current flows in the linear wires.