Evidence for three dimensional superconductivity in the cuprates oxides

Abstract

We review the empirical scenario emerging from the measured doping dependence of the transition temperature and the anisotropy parameter $% γ$ $=ξ_{ab}/ξ_{c}$, defined as the ratio of the correlation lengths parallel and perpendicular to the ab-planes. It suggests that two dimensional models cannot explain the occurrence of superconductivity in the cuprates. This conclusion is confirmed and extended in terms of a novel scaling relation. It involves the transition temperature, the aerial superfluid density in the ground state, $γ$ and the dynamic critical exponent of the quantum superconductor to insulator transition. The important implication there is that a non vanishing superfluid density in the ground state of the cuprates is unalterably linked to an anisotropic but 3D condensation mechanism.