Phase-fluctuating superconductivity in overdoped La _2-x Sr _x CuO ₄

In underdoped cuprate superconductors, phase stiffness is low and long-range superconducting order is destroyed readily by thermally generated vortices (and anti-vortices), giving rise to a broad temperature regime above the zero-resistive state in which the superconducting phase is incoherent ^1-4 . It has often been suggested that these vortex-like excitations are related to the normal-state pseudogap or some interaction between the pseudogap state and the superconducting state ^5-10 . However, to elucidate the precise relationship between the pseudogap and superconductivity, it is important to establish whether this broad phase-fluctuation regime vanishes, along with the pseudogap ¹¹ , in the slightly overdoped region of the phase diagram where the superfluid pair density and correlation energy are both maximal ¹² . Here we show, by tracking the restoration of the normal-state magnetoresistance in overdoped La _2-x Sr _x CuO ₄ , that the phase-fluctuation regime remains broad across the entire superconducting composition range. The universal low phase stiffness is shown to be correlated with a low superfluid density ¹ , a characteristic of both underdoped and overdoped cuprates ^12-14 . The formation of the pseudogap, by inference, is therefore both independent of and distinct from superconductivity.