Pairing, pair-breaking, and their roles in setting the Tc of cuprate high temperature superconductors

The key ingredients in any superconductor are the Cooper pairs, in which two electrons combine to form a composite boson. In all conventional superconductors the pairing strength alone sets the majority of the physical properties including the superconducting transition temperature T${}_c$. In the cuprate high temperature superconductors, no such link has yet been found between the pairing interactions and T${}_c$. Using a new variant of photoelectron spectroscopy we measure both the pair-forming ($\mathrm{\Delta }$) and a self energy/pair-breaking term (${\mathrm{\Gamma }}_s$) as a function of sample type and sample temperature, and we make the measurements over a wide range of doping and temperatures within and outside of the pseudogap/competing order doping regimes. In all cases we find that T${}_c$ is approximately set by a crossover between the pair-forming strength $\mathrm{\Delta }$ and 3 times the self-energy term ${\mathrm{\Gamma }}_s$ - a new paradigm for superconductivity. In addition to departing from conventional superconductivity in which the pairing alone sets T${}_c$, these results indicate the zero-order importance of the near-nodal self-energy effects compared to competing order/pseudogap effects.