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In-plane optical spectra of Y$_{1-x}$Ca$_{x}$Ba$_{2}$Cu$_{3}$O$_{7-δ}$: Overdoping and disorder effect on residual conductivity

We measured the temperature dependence of the in-plane polarized reflectivity spectra of twin-free Y$_{1-x}$Ca$_{x}$Ba$_{2}$Cu$_{3}$O$_{7-δ}$ single crystals with different Ca-concentrations (x=0,0.11 and 0.16) from optimally doped to heavily overdoped region. Low energy optical conductivity spectra showed a Drude-like residual conductivity at temperatures far below the superconducting transition temperature, which indicates the presence of unpaired-normal carriers in the superconducting state. Comparing the spectra at a fixed Ca-content or at a fixed doping level, we have revealed that the carrier overdoping increases unpaired carriers in addition to those induced by the Ca-disorder. We also found the superconducting behavior of the one-dimensional CuO chains for the Ca-free samples.