Pairing, Pair-Breaking, and the Critical Temperature in the Cuprate Superconductors

In conventional superconductors, the pairing strength sets the majority of the physical properties including the superconducting transition temperature, T$_{\mathrm{C}}$. However, the cuprates show no such link between the pairing interactions and T$_{\mathrm{C}}$. Using a new variant of photoelectron spectroscopy, we measure both the pair-forming ($\Delta )$ and pair-breaking ($\Gamma_{\mathrm{S}})$ processes with greatly improved accuracy over a wide range of doping and temperatures. We find that, across the phase diagram, $\Delta $ directly scales with the temperature marking the onset of pairing, T$_{\mathrm{Pair}}$, rather than those for the onsets of superconductivity, T$_{\mathrm{C}}$, or the pseudogap, T*. Instead, T$_{\mathrm{C}}$ is set by a simple ratio of $\Delta $(T$_{\mathrm{C}})$ and $\Gamma_{\mathrm{s}}$(T$_{\mathrm{C}})$, in contrast to conventional superconductivity in which the pairing alone, $\Delta $(T$=$0), sets T$_{\mathrm{C}}$. This finding shows the pair-breaking processes are a critical limiting factor for superconductivity in the cuprates. Finally, we will discuss the merits of the potential candidates for the origin of $\Gamma_{\mathrm{s}}$.