Superfluid and normal-fluid densities in the high-T_c superconductors

In clean metallic superconductors, 100% of the mobile carriers participate in the condensate, so that the London penetration depth (which measures the electromagnetic screening by the superconductor) indicates charge densities comparable to those inferred from the free-carrier plasma frequency. In the cuprates, this is not the case, even though penetration depth measurements have shown a good correlation between superfluid density and superconducting transition temperature in the underdoped-to-optimally-doped part of the phase diagram. Optical measurements, which permit independent determination of the total doping-induced spectral weight and the superfluid density, show that in optimally doped materials only about 20% of the doping-induced spectral weight joins the superfluid. The rest remains in finite-frequency, midinfrared absorption. In underdoped materials, the superfluid fraction is even smaller. This result implies extremely strong coupling for these superconductors.