What can we learn from comparison between cuprates and He films ? : phase separation and fluctuating superfluidity

In the underdoped, overdoped, Zn-doped or stripe-forming regions of high-$T_c$ cuprate superconductors (HTSC), the superfluid density $n_s\mathrm{/}{m}^{\ast }$ at $T\to 0$ shows universal correlations with $T_c$. Similar strong correlations exist between 2-dimensional superfluid density and superfluid transition temperature in thin films of ${}^4$He in non-porous or porous media, and ${}^4$He/${}^3$He film adsorbed on porous media. Based on analogy between HTSC and He film systems, we propose a model for cuprates where: (1) the overdoped region is characterized by a phase separation similar to ${}^4$He/${}^3$He; and (2) pair (boson) formation and fluctuating superconductivity occur at separate temperatures above $T_c$ in the underdoped region.