Why the superfluid density tracks $T_{\rm c}$ in cuprate superconductors?

One of the first finding concerning the superconducting (SC) density $n_{\rm sc}$ in cuprates was their small magnitudes that revealed the importance of phase fluctuations. More recently, measurements in a variety of overdoped cuprates indicate that it is also much smaller than expected from BCS theories and falls smoothly to zero as doping is increased. We explain these observations by an electronic phase separation theory with a Ginzburg-Landau potential $V_{\rm GL}$ that produces alternating charge domains whose fluctuations lead to localized SC order parameters that are connected by Josephson coupling $E_{\rm J}$. The average ${\left <E_{\rm J}( p,T)\right>}$ is proportional to the local superfluid phase stiffness $ρ_{\rm sc} \propto n_{\rm sc}$. The fraction of condensed carriers decreases in the overdoped region due to the weakening of $V_{\rm GL}$. The results agreed with $ρ_{\rm sc}(p)$ vs. $T_{\rm c}(p)$ and the Drude-like peak measurements.

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