Strongly reduced superfluid density in the inhomogeneoushigh-Tc cuprates: far-infrared study

The superfluid density is estimated from the in-plane optical spectra for various high-Tc cuprates. The estimate from the missing area in σ1(ω) almost coincides with that from the slope of σ2(ω) vs 1/ω, which indicates the Ferrell-Glover-Tinkham sum rule is almost valid within an infrared range. The superfluid density is radically suppressed by underdoping and/or by impurity pair-breaking, deviating from the linear relation with Tc. The origin of the reduced superfluid density is discussed in relation with the accompanied residual conductivity at low ω below Tc.