Superconducting slab in contact with thin superconducting layer at higher critical temperature

Within the framework of nonlinear time dependent Ginzburg–Landau equations (TDGL) we study the properties of a mesoscopic superconducting film with both surfaces in contact with a thin superconducting layer at a higher critical temperature. The properties of the layer are taken into account by the de Gennes boundary conditions via the extrapolation length b. We assume that the magnetic field is parallel to the multilayer interfaces. We obtain magnetization curves and calculate the spatial distribution of the superconducting electron density using a numerical method based on the technique of gauge invariant variables. This work tests both the rectangular cross-section size and b limit for the occurrence of vortices in a mesoscopic sample of area d_xxd_y where d_y = 80ξ(0) and dx varies discretely from 20ξ(0) to 3ξ(0). Our data also show a linear behavior of the magnetization curve and a power-law of order parameter modulus in limit b → 0_-.