Superfluid Density in High-$T_c$ Superconductors: Enabled by Holes or Suppressed by Electrons?

The critical temperature of an underdoped cuprate superconductor is limited by its phase stiffness $ρ$. In this Letter 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. Our proposal is based on the observation that the correlation energy of a d-wave superconductor increases in magnitude at finite pairing wavevector when antiferromagnetic fluctuations are strong.

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