Superfluid density in cuprate high-T_c superconductors: A new paradigm

We show that the Uemura relation, namely T_c proportional to superfluid density ρ_s, is not generally satisfied in high-T_c superconductors. Instead, a modified plot of T_c/Δ₀ versus ρ_s where Δ₀ 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_cρ_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.