Thermodynamics of vortices in layered superconductors and the dependence of T_c on anisotropy

Data on multilayered superconductors such as YBa₂Cu₃O₇{plus 45 degree rule}PrBa₂Cu₃O₇ show a strong dependence of T_c on anisotropy. In particular, the ratio T_c{plus 45 degree rule}τ, where τ is the effective XY coupling constant, is found to vary by much more than the theoretical XY limit of 2.4. Layered superconductors allow for an additional anisotropy due to the core energy E_c of vortices perpendicular to the layers. It is shown that if E_c is large, such that the anisotropy is larger than exp(-E_c{plus 45 degree rule}T_c), T_c is near a fluxon transition which is described by fluctuations of flux loops parallel to the layers. In the latter case T_c{plus 45 degree rule}τ can vary by more than 2.4, accounting for the data.