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Cuprate superconductors have long been known to exhibit an energy gap thatpersists high above the superconducting transition temperature ($T_c$). Debatehas continued now for decades as to whether it is a precursor superconductinggap or a pseudogap arising from some competing correlation. Failure to resolvethis has arguably delayed explaining the origins of superconductivity in thesehighly complex materials. Here we effectively settle the question bycalculating a variety of thermodynamic and spectroscopic properties, exploringthe effect of a temperature-dependent pair-breaking term in the self-energy inthe presence of pairing interactions that persist well above $T_c$. We start byfitting the detailed temperature-dependence of the electronic specific heat andimmediately can explain its hitherto puzzling field dependence. Taking thissame combination of pairing temperature and pair-breaking scattering we arethen able to simultaneously describe in detail the unusual temperature andfield dependence of the superfluid density, tunneling, Raman and opticalspectra, which otherwise defy explanation in terms a superconducting gap thatcloses conventionally at $T_c$. These findings demonstrate that the gap above$T_c$ in the overdoped regime likely originates from incoherent superconductingcorrelations, and is distinct from the competing-order "pseudogap" that appearsat lower doping.

Incoherent superconductivity well above $T_c$ in high-$T_c$ cuprates - harmonizing the spectroscopic and thermodynamic data