Quantum fluctuations, pseudogap, and theT=0superfluid density in strongly correlatedd-wave superconductors

Abstract

I study the effect of Coulomb interaction on superconducting order in a $d$-wave lattice superconductor at $T=0$ by considering the superconducting saddle point in the two-dimensional $t\text{\ensuremath{-}}J\text{\ensuremath{-}}U$ model with a repulsion $U$. The theory of low-energy superconducting phase fluctuations around this saddle point is derived in terms of the effective hard-core bosons (representing the density of spin-up electrons and the phase of the order parameter), interacting with the fluctuating density of spin-down electrons. Whereas the saddle-point value of the superconducting gap is found to continuously increase towards half filling, the phase stiffness at $T=0$ has a maximum, and then decreases with further underdoping. Right at half filling the phase stiffness vanishes for large $U$. This argues that the pseudogap phenomenon of the type observed in cuprates is in principle possible without a development of any competing order, purely as a result of growing correlations in the superconducting state. Implications for the finite temperature superconducting transition and the effects of static disorder are discussed qualitatively.