Signatures of Kosterlitz-Thouless behavior in the superfluid density of anisotropic layered superconductors

In quasi-two-dimensional (2D) systems, as thin films of $^4$He or of superconductors, the superfluid transition is expected to be driven by phase fluctuations, according to the Kosterlitz and Thouless (KT) theory. However, signatures of KT vortex-antivortex phase fluctuations should be observable, at some energy scale $T_d$, also in strongly anisotropic layered superconductors, where quasi-2D behavior arises due to a small Josephson coupling between neighboring planes. While in the 2D case $T_d$ is uniquely identified by the KT temperature $T_{KT}$ where the universal jump of the superfluid density is observed, in the layered case such universality is lost. Here we show this effect by means of a renormalization-group analysis of a layered version of the sine-Gordon model, appropriate to describe the occurrence of KT physics in layered superconductors. We find that in the presence of a finite interlayer coupling $T_d$ is controlled by the vortex-core energy, and can be significantly larger than the 2D scale $T_{KT}$. When applied to the superfluid-density behavior in cuprate superconductors these results allows us to determine a non-trivial behavior of the vortex-core energy in these systems. L.Benfatto, C.Castellani and T.Giamarchi, Phys. Rev. Lett. 98, 117008 (2007)