Dissociation of vortex stacks into fractional-flux vortices

We discuss the superconducting phase transition in a finite system of magnetically coupled superconducting layers. Transverse screening is modified by the presence of other layers resulting in topological excitations with fractional flux. The presence of additional layers leads to drastic modifivations in the potential between individual vortices in the same layer. Vortex stacks trapping a full flux and present at any finite temperature undergo a dissociation transition which corresponds to the depairing of fractional-flux vortices in individual layers. We propose an experiment with a bi-layer system allowing to identify the dissociation of bound vortex molecules.