Suppression of Superfluid Density in Underdoped Cuprates

A key challenge for theories of high-T$_{c}$ cuprates is to explain why the superfluid density vanishes as the antiferromagnetic insulator state is approached. Viewing a cuprate as a doped Mott insulator gives a natural explanation of this property, but one that is not obviously compatible with the fact that superconductivity always vanishes at finite doping. We propose another possible explanation, starting from weak-coupling conventional d-wave BCS theory and calculating the correlation contribution to the superfluid density. We show that triplet fluctuations of the d-wave superconducting order parameter are canonically conjugate to antiferromagnetic fluctuations, and that this causes the correlation energy to increase in magnitude when superconductivity is weakened by a phase gradient. In our theory the inelastic neutron scattering resonance has the character of a magnetic plasmon rather than the character of an exciton.