Superfluid density in cuprate high-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>superconductors: 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 negative curvature expected when a ground-state correlation competes with superconductivity (SC) by opening up a gap (the pseudogap) in the normal-state density of states. Moreover we observe simple linear relations between ${T}_{c}{\ensuremath{\rho}}_{s},$ the electronic entropy at ${T}_{c},$ and the critical impurity concentration for suppressing SC. These relations confirm that the pseudogap persists to $T=0,$ strongly modifying the SC ground state.

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