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.

中文翻译：

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非均匀超导薄膜的 Ginzburg-Landau 计算

提出了一种模拟非均匀薄膜超导状态的方法。通过在薄膜厚度上改变 Ginzburg-Landau (GL) 参数来改变超导特性。使用修正的 GL 自由能泛函的标准最小化来描述非均匀板的超导状态，发现了一个一维方程组。使用所提出的方法，对于超导特性在膜厚度上的不均匀和均匀分布的情况，计算临界电流的磁场依赖性并相互比较。结果表明，随着薄膜不均匀程度的增加，零磁场中的临界电流减小，临界磁场显着增加。作为外部磁场函数的计算的体钉扎力的分析表明，随着不均匀程度的增加，该值的最大值向更强的场移动。检测到板边界处的性质变化更剧烈，因此，中间的均匀性水平越高，临界电流变得明显更大。同时，临界磁场在这种情况下略有变化。