Puddle formation and persistent gaps across the non-mean-field breakdown of superconductivity in overdoped (Pb,Bi) 2 Sr 2 CuO 6+δ .

The cuprate high-temperature superconductors exhibit many unexplained electronic phases, but the superconductivity at high doping is often believed to be governed by conventional mean-field Bardeen-Cooper-Schrieffer theory 1 . However, it was shown that the superfluid density vanishes when the transition temperature goes to zero 2,3 , in contradiction to expectations from Bardeen-Cooper-Schrieffer theory. Our scanning tunnelling spectroscopy measurements in the overdoped regime of the (Pb,Bi) 2 Sr 2 CuO 6+δ high-temperature superconductor show that this is due to the emergence of nanoscale superconducting puddles in a metallic matrix 4,5 . Our measurements further reveal that this puddling is driven by gap filling instead of gap closing. The important implication is that it is not a diminishing pairing interaction that causes the breakdown of superconductivity. Unexpectedly, the measured gap-to-filling correlation also reveals that pair breaking by disorder does not play a dominant role and that the mechanism of superconductivity in overdoped cuprate superconductors is qualitatively different from conventional mean-field theory.