The critical temperature of an underdoped cuprate superconductor is limited by its phase stiffness $\rho$. In this paper we argue that the dependence of $\rho$ 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. $\rho$ 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.

• Received 6 May 2008

DOI:https://doi.org/10.1103/PhysRevB.77.214518