Relationship between the pseudo- and superconducting gaps:: effects of residual pairing correlations below Tc

The existence of a normal-state spectral gap in underdoped cuprates raises important questions about the associated superconducting phase. For example, how does this pseudogap evolve into its below T-c counterpart? In this paper we characterize this unusual superconductor by investigating the nature of the "residual" pseudogap below T-c, and find that it leads to an important distinction between the superconducting excitation gap and order parameter. Our approach is based on a conserving diagrammatic BCS Bose-Einstein crossover theory which yields the precise BCS result in weak coupling at any T < T-c and reproduces Leggett's results in the T = 0 limit. We explore the resulting experimental implications.