Superfluid density in cuprate high-Tcsuperconductors: A new paradigm

We show that the Uemura relation, namely ${T}_{c}$ proportional to superfluid density ${\ensuremath{\rho}}_{s},$ is not generally satisfied in high-${T}_{c}$ superconductors. Instead, a modified plot of ${T}_{c}/{\ensuremath{\Delta}}_{0}$ versus ${\ensuremath{\rho}}_{s}$ where ${\ensuremath{\Delta}}_{0}$ is the maximum d-wave gap at $T=0,$ exhibits universal features that point to an alternative interpretation of the underlying physics. In the underdoped region this plot exhibits the canonical n