Superfluid and normal-fluid density in the cuprate superconductors

As carriers are introduced into the cuprates (by doping the insulating "parent" compounds) spectral weight appears in the optical spectrum at photon energies below the charge-transfer gap. This spectral weight increases as the doping level increases. Magnetic 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 allow independent determination of the total doping-induced spectral weight and the superfluid density. These measurements, made on cuprates with transition temperatures from 40 to 110 K, find 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.