Current states in superconducting films: numerical results

Abstract

We present numerical solutions of Aslamazov–Lempitskiy (AL) equations for distributions of the transport current density in thin superconducting films in the absence of external magnetic field, in both the Meissner and the vortex states. These solutions describe smooth transition between the regimes of a wide film and a narrow channel and enable us to find critical currents and current-voltage characteristics within a wide range of the film width and temperature. The normalized critical currents and the electric field were found to be universal functions of the relation between the film width and the magnetic field penetration depth. We calculate the fitting constants of the AL theory and propose approximating formulas for the current density distributions and critical currents.