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 $T^{\ast }$ line, which shows a sharp reduction towards $T^{\ast }\sim 0$ at a mildly overdoped critical concentration $x_c$. This model explains anomalous doping and temperature dependences of $n_s\mathrm{/}{m}^{\ast }$ (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.