Superconductivity from a pseudogapped normal state: a mode coupling approach to precursor superconductivity

We derive a phase diagram for the pseudogap onset temperature $T^*$ (associated with the breakdown of the Fermi liquid state, due to strong pairing correlations) and the superconducting instability, $T_c$, as a function of variable pairing strength. Our diagrammatic approach to the BCS - Bose-Einstein cross-over problem self consistently treats the coupling between the single particle and pair propagators, and leads to a continuous evolution of these propagators into the standard $T<T_c$ counterparts. A rich structure is found in $T_c$ which reflects the way in which the superconducting instability at $T_c$ is affected by the pseudogap $\Delta_{pg}$. An important consequence of Cooper-pair- induced pseudogaps is that the magnitude of $T_c$ is sustained, even when $\Delta_{pg}>T_c$.