Numerical investigation of critical states in superposed superconducting films

While offering enhanced or new functionalities, three-dimensional superconducting structures have
a richer magnetic response than planar devices. A particular class of three-dimensional structures is obtained by stacking nanostructured superconducting layers, resulting in systems where the planar subcomponents are magnetically coupled with one another, thereby opening the possibilities of new magnetic flux penetration processes. In thin superconducting films, abrupt changes in the direction of shielding currents are manifested in the form of discontinuity lines (d-lines), which vortices cannot cross. For instance, in a square film, d-lines appear along the diagonals, while in a rectangular film, they follow a double Y shape. Such structures can be observed through magneto-optical imaging (MOI). When a rectangular superconducting thin strip is superimposed to a superconducting square film, the resulting d-lines do not correspond to a simple superposition of the d-lines of each individual film, additional d-lines appear [1].
In this work, we investigate the d-lines of bi-layered superconducting thin films numerically. We use a finite element H-phi formulation, where shell-transformations [2] are used in the far-field region outside the films, so that boundary conditions are applied at an infinite distance from the conductors. We show the key role of the magnetic field dependence of the critical current density jc(B), which is modelled with Kim’s law jc(B) = jc0/(1+|B|/ B0), in the apparition of the additional d-lines. We demonstrate the modification in the shape of the d-lines with respect to the magnitude of the applied magnetic field, while it is increased and then decreased back to the remanent state. The influence of the spacing between both films, B0, jc0 on the geometrical characteristics of the additional d-lines is also investigated.