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 . 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. 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,  in  the  slightly  overdoped  region  of  the  phase diagram  where  the  superfluid  pair  density  and  correlation energy   are   both   maximal. Here   we   show,   by   tracking the   restoration   of   the   normal-state   magnetoresistance   in overdoped La_2−xSr_xCuO₄,  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,  a  characteristic  of both underdoped and overdoped cuprates . The formation of the pseudogap, by inference, is therefore both independent of and distinct from superconductivity.

DOI: 10.1038/nphys1945