Superconducting phase coherence in the presence of a pseudogap: Relation to specific heat, tunneling, and vortex core spectroscopies - art. no. 184519

In this paper we demonstrate how, using a natural generalization of,BCS the ory, superconducting phase coherence manifests itself in phase-insensitive measurements-when there is a smooch evolution of the excitation gap Delta f rom above to below T-c. In this context, we address the underdoped cuprates , Our premise is that just as Fermi-liquid theory fails above T-c, BCS theo ry fails below. The order parameter Delta (sc) is different from the excita tion gap Delta. Equivalently there is a (pseudo)gap in the excitation spect rum above T-c which is also present in the underlying normal state of the s uperconducting phase. A central emphasis of our paper is that the latter ga p is most directly inferred from specific heal and vortex core experiments. At the same time there are indications that fermionic quasiparticles exist below T-c so that many features of BCS theory are clearly present. A natur al reconciliation of these observations is to modify BCS theory slightly wi thout abandoning it altogether. Here we review such a modification based on a BCS-like ground-state wave function. A central parameter of our extended BCS theory is Delta (2)-Delta (2)(sc) which is a measure of the number of bosonic pair excitations which have a nonzero net momentum. These bosons ar e present in addition to the usual fermionic quasiparticles. Applying this theory we find that the Bose condensation of Cooper pairs, which is reflect ed in Delta (sc), leads to sharp peaks in the spectral function once T less than or equal toT(c). These are manifested in angle-resolved photoemission spectra as well as in specific heat jumps, which become more like the beha vior in a lambda transition as the pseudogap develops. We end with a discus sion of tunneling experiments and condensation energy issues. The compariso n between theoretical and experimental plots of C-v, tunneling, vortex core spectroscopy measurements is good.