Global trends in the interplane penetration depth of layered superconductors

We report on generic trends in the behavior of the interlayer penetration depth $\lambda_c$ of several different classes of quasi two-dimensional superconductors including high-T$_c$ cuprates, Sr$_2$RuO$_4$, transition metal dichalcogenides and organic materials of the $(BEDT-TTF)_2X$ - series. Analysis of these trends reveals two distinct patterns in the scaling between the values of $\lambda_c$ and the magnitude of the c-axis DC conductivity $\sigma_{DC}$: one realized in the systems with a ground state formed out of well defined quasiparticles and the other seen in systems in which the quasiparticles are not well defined. The latter pattern is found primarily in under-doped cuprates and indicates a dramatic enhancement (factor $\simeq 10^2$) of the energy scale $\Omega_C$ associated with the formation of the condensate compared to the data for conventional materials. We discuss the implication of these results on the understanding of superconductivity in high-$T_c$ cuprates.