The critical state of superconducting multilayered structures

Abstract

We propose a new method for calculating the dependence of the critical current on an external magnetic field, and the distribution of this current over the layers in superconducting multilayered structures. The method is based on a numerical solution of a system of nonlinear Ginzburg–Landau equations that describe the behavior of a superconducting plate carrying a transport current in a magnetic field, provided that it does not contain Abrikosov vortices. The way in which boundary conditions in the Ginzburg–Landau theory influence the critical state of superconducting layered structures is also considered. From a mathematical point of view, application of a general boundary condition to the system of Ginzburg–Landau equations leads to a change in the order parameter along the thickness of the thin superconducting plates. The physical nature of this phenomenon is explained by the proximity effect at the superconductor–normal metal (SN) interface, which leads to the suppression of the order parameter near the SN interface. The resulting calculated dependences of the plates’ critical current on the magnetic field strength applied parallel to the layers are used to determine the critical current of multilayer structures. It is assumed that the mutual influence of superconducting layers occurs only via the magnetic field that they create.