Effect of pseudogap formation on the superconducting gap in underdoped cuprates

Abstract

Many anomalous properties of the normal and superconducting state of underdoped cuprates can be understood qualitatively within a resonating valence bond spin liquid model which incorporates pseudogap formation below a quantum-critical point. It also contains band narrowing, and reduction in coherence, both effects captured through Gutzwiller factors. The superconducting state is treated phenomenologically within the usual BCS model with a $d$-wave superconducting gap. Here we solve a generalized gap equation which explicitly incorporates the emergence of a pseudogap in the electronic structure. The magnitude of the pairing potential is found to still be increasing as the bottom underdoped edge of the superconducting dome is approached. Consequently, it is the Mott physics with implied reduction in metallicity which drives the superconducting critical temperature ${T}_{c}$ to zero. The superconducting gap contains many higher harmonics, is nonmonotonic as the magnetic coherence length increases, although its amplitude remains finite everywhere on the Fermi contour even in the antinodal direction where the pseudogap is largest. The superconducting gap to critical temperature ratio increases strongly with decreasing doping.