Vortex Rings and Phase Transition in Layered-Lattice Superconductors

The phase transition temperature of a layered-lattice superconductor (Josephson-junction array) is shown to have a finite limit T c 0 for arbitrarily small interlayer coupling. T c 0 is a temperature of a phase transition in the absence of Josephson coupling between layers. In contrast to a single layer for which phase transition (in a strict sense of the word) is smeared due to screening of long-range vortex-vortex interaction, in layered systems the interaction of layers via magnetic field restores the Berezinskii-Kosterlitz-Thouless transition. We show also that phase transition in layered superconductors cannot be associated with proliferation of vortex rings of the most favourable orientation ( i.e. lying between the layers) as was recently suggested by Friedel. The temperature of the hypothetical phase transition in the subsystem of such vortex rings turns out to be much higher than T c 0 . The results obtained are also applicable for layered planar magnets. We expect them to be qualitatively valid to all layered superconductors, e.g. , high- T c crystals.