Kosterlitz-Thouless behavior in layered superconductors: The role of the vortex core energy

In layered superconductors (SC) with small interlayer Josephson coupling vortex-antivortex phase fluctuations characteristic of quasi two-dimensional (2D) Kosterlitz-Thouless behavior are expected to be observable at some energy scale T-d. While in the 2D case T-d is uniquely identified by the KT temperature T-KT where the universal value of the superfluid density is reached, we show that in a generic anisotropic 3D system T-d is controlled by the vortex-core energy, and can be significantly larger than the 2D scale T-KT. These results are discussed in relation to recent experiments in cuprates, which represent a typical experimental realization of layered anisotropic SC.