Theory of reduced superfluid density in underdoped cuprate superconductors

The critical temperature of an underdoped cuprate superconductor is limited by its phase stiffness ρ. In this paper we argue that the dependence of ρ on doping x should be understood as a consequence of deleterious competition with antiferromagnetism at large electron densities, rather than as evidence for pairing of holes in the $x=0$ Mott insulator state. ρ is suppressed at small x because the correlation energy of a d-wave superconductor has a significant pairing-wave-vector dependence when antiferromagnetic fluctuations are strong.