Ginzburg–Landau Calculations for Inhomogeneous Superconducting Films

A method for modeling the superconducting state of an inhomogeneous film is proposed. The superconducting properties are changed by varying Ginzburg–Landau (GL) parameters over the film thickness. A system of 1-D equations was found using the standard minimization of the modified GL-free energy functional to describe the superconducting state of the inhomogeneous plate. Using the proposed method, the magnetic field dependencies of the critical current were calculated and compared with each other for the cases of inhomogeneous and homogeneous distributions of the superconducting properties over the film thickness. It was shown that the critical current in the zero magnetic field decreases and the critical magnetic field increases significantly when the degree of inhomogeneity of the film increases. Analysis of the calculated bulk pinning force as a function of the external magnetic field shows a shift of the maximum of this value toward stronger fields with increasing degree of inhomogeneity. It was detected the sharper change in properties at the boundaries of the plate and, consequently, the greater level of homogeneity in the middle, the critical current becomes noticeable larger. At the same time, the critical magnetic field changes slightly in this case.