Temperature dependences of the critical parameters of an inhomogeneous superconducting layer surrounded by non-superconducting layers

The superconducting state of an inhomogeneous in thickness layer, adjacent to non-superconducting layers that influence it, is considered. Within the framework of the Ginzburg–Landau (GL) theory a technique has been formulated that allows one to estimate the critical parameters of the superconducting layer for the described problem. In the expansion of free energy in powers of the order parameter modulus an additional term and more accurate dependences of the expansion coefficients on temperature are taken into account, which allows quantitative estimates to be made over a wider temperature range than the classical GL theory. Using the technique, the temperature dependences of the critical current density and the critical magnetic field of the layer were simulated. It is shown that simultaneous consideration of the inhomogeneity of the superconducting layer in thickness and the influence of adjacent layers on its state in the calculation makes it possible to significantly improve the estimate of the critical current density in comparison with experimental data. In this case, temperature dependence type of the critical current density changes with distance from the critical temperature.