Superconductivity from incoherent Cooper pairs in strong-coupling regime

We propose a scenario for superconductivity at strong electron-electron attractive interaction, in the situation when the increase of interaction strength promotes the nucleation of the local Cooper pairs and forms a state with a spatially phase incoherent Cooper pair order parameter. We show that this state can be characterized by a pseudogap and a scattering rate, which are determined by the self-energy due to electron scattering on phase fluctuations. At low temperatures, however, long-range correlations between the regions with different phases become important and establish global phase coherence hence superconductivity in the system. We develop a mean-field theory to describe a phase transition between the preformed Cooper pair and superconducting states. This scenario of superconductivity applies not only to conductors with parabolic bands but also to the flat-band systems in which flat and dispersive bands coexist and responsible for the Cooper pair formation as well as their phase synchronization.