Technique for calculating the critical current of inhomogeneous superconducting films

A method for calculating the critical current of an inhomogeneous superconducting film (plate) in different external magnetic fields has been proposed. The superconducting properties are changed by varying the coherence length and London penetration depth over the thickness. The coherence length is maximum at the center of the plate and decreases upon approaching its boundaries and the London depth, on the contrary, is minimum at the center of the plate and increases toward its boundaries. Using the proposed approach, the magnetic field dependences of the critical current on the external magnetic field for the cases of nonuniform and uniform distributions of the superconducting properties over the film thickness have been calculated and compared. It has been established that at the nonuniform distribution of the superconducting properties the critical current of the plate is higher than at the uniform distribution at the same external magnetic fields. This is due to the fact that the order parameter is redistributed over the inhomogeneous plate thickness in such a way that the superconducting state becomes more stable against the current and magnetic field. It has been shown that the vortex-free Meissner state in inhomogeneous films is maintained at higher fields than in homogeneous films. The greater the film nonuniformity, the higher the stability of the Meissner state against an external magnetic field.