Microscopic phase separation in the overdoped region of high-Tc cuprate superconductors

We propose a phenomenological model for high-$T_{c}$ superconductors (HTSC) assuming: (1) a microscopic phase separation between superconducting and normal-metal areas in the overdoped region; and (2) existence of a homogeneous superconducting phase only below the pseudo-gap $T^{*}$ line, which shows a sharp reduction towards $T^{*}\sim 0$ at a mildly overdoped critical concentration $x_{c}$. This model explains anomalous doping and temperature dependences of $n_{s}/m^{*}$ (superconducting carrier density / effective mass) observed in several overdoped HTSC systems. We point out an analogy to superfluid $^{4}$He/$^{3}$He films, and discuss an energetic origin of microscopic phase separation.