Relationship between the pseudo- and superconducting gaps: Effects of residual pairing correlations belowTc

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 $T<\mathrm{}{T}_c$ and reproduces Leggett’s results in the $T=0\mathrm{}$ limit. We explore the resulting experimental implications.