On the role of the boundary conditions in the Ginzburg-Landau theory

The effect of the boundary conditions for solutions on the Ginzburg-Landau (GL) equations for superconducting plates in the vortex-free limit is studied by numerical methods. Based on the self-consistent solution of the system of GL equations, the dependence of the critical current I _c on the external magnetic field and the distribution of the order parameter over the plate thickness are determined. When solving the equations with general boundary conditions, it was found that the critical temperature and critical current density decreased in comparison with those obtained by solving equations with ordinary boundary conditions. According to the results of this study, the use of general boundary conditions leads to a number of interesting results which were not observed when using ordinary boundary conditions. The range of the applicability of the vortex-free limit for the films of thickness of the order of the coherence length ξ are discussed. The effect of boundary conditions on the applicability of this limit is analyzed.