Determinining the Critical Condition for Superconductivity in Bi$_{2}$Sr$_{2}$CaCuO$_{8+\delta }$

Using the tomographic density of states (TDoS) ARPES-based technique we present a detailed study of the temperature and doping dependences of the pair-forming, represented by the gap magnitude ($\Delta )$, and pair-breaking, represented by the scattering rate ($\Gamma )$, ~processes in BSCCO.~ We find that $\Delta $ is finite through the superconducting transition, T$_{C}$, and ceases only at the higher temperature T$_{Pair}$, which corresponds with the T$_{Onset}$~from Nernst experiments rather than the T* tied to the antinodal pseudogap.~ Furthermore, we find $\Gamma $ is large and strongly temperature dependent and T$_{C}$~is strongly correlated with the ratio of $\Delta $/$\Gamma $.~ Consequently, the presence of pairs is not sufficient for superconductivity: the pair-breaking processes must also be diminished to the point that pairs have a long enough lifetime to develop long range coherence.~