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 $n_{s}/m^{*}$ 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.