Superfluid density of high-Tc cuprate systems: implication on condensation mechanisms, heterogeneity and phase diagram

Extensive muon spin relaxation (μSR) measurements have been performed to determine the magnetic field penetration depth λ in high Tc cuprate superconductors with simple hole doping, Zn-doping, overdoping, and formation of static SDW nano-islands. System dependence of ns/m∗ (superconducting carrier density/effective mass) reveals universal correlations between Tc and ns/m∗ in all these cases with/without perturbation. Evidence for spontaneous and microscopic phase separation into normal and superconducting regions was obtained in the cases with strong perturbation, i.e. Zn-doping (swiss cheese model), overdoping, and coexisting magnetic and superconducting states (SDW nano-islands). The length scale of this heterogeneity is shown to be comparable to the in-plane coherence length. We discuss implication of these results on condensation mechanisms of HTSC systems, resorting to an analogy with pure 4He and 4He/3He mixture films on regular and porous media, reminding essential features of Bose–Einstein, BCS and Kosterlitz–Thouless condensation/transition in 3-d and 2-d systems, and comparing models of BE–BCS crossover and phase fluctuations. Combining the μSR results on ns/m∗ and the pseudo-gap behavior, we propose a new phase diagram for HTSC, characterized by: (1) the T∗ line that represents pair formation; (2) disappearance of this line above the critical hole concentration x=xc; (3) in the underdoped region between Tc and T∗, there exists another line Tdyn which corresponds to the onset of dynamic superconductivity with superconducting phase fluctuations; and (4) the overdoped region being phase separated between hole-poor superfluid and hole-rich normal fermion metal regions. Finally, we elucidate anomalous reduction of superfluid spectral weight in the crossover from superconducting to metallic ground states found not only in overdoped HTSC cuprates but also in pressurized organic BEDT and A3C60 fulleride superconductors.