Superconducting-plasma resonance along thecaxis in various copper oxide superconductors

Superconducting plasma along the c axis in the far-infrared region are observed in various high-${\mathit{T}}_{\mathit{c}}$ cuprates including electron-doped and Bi cuprates. It is shown that the sphere resonance of the powder samples occurs near the frequency where the plasma along the c axis exists, since it is only sensitive to the c-axis dielectric constant in the far-infrared region due to the metal-like property in the ab plane. This method provides an alternative to the reflectivity measurement of single crystals for investigating the plasma along the c axis. By measuring down to 7.5 ${\mathrm{cm}}^{\mathrm{-}1}$, the resonance is observed in ${\mathrm{Bi}}_{1.85}$ ${\mathrm{Pb}}_{0.35}$ ${\mathrm{Sr}}_2$ ${\mathrm{Ca}}_2$ ${\mathrm{Cu}}_{3.1}$ ${\mathrm{O}}_{\mathit{y}}$, ${\mathrm{La}}_{1.82}$ ${\mathrm{Ca}}_{1.18}$ ${\mathrm{Cu}}_2$ ${\mathrm{O}}_{6+\mathrm{\delta }}$, (${\mathrm{Nd}}_{0.66}$ ${\mathrm{Sr}}_{0.205}$ ${\mathrm{Ce}}_{0.135}$ ${)}_2$ ${\mathrm{CuO}}_4$ (${\mathit{T}}^{\mathrm{*}}$ phase), (${\mathrm{Ba}}_{0.56}$ ${\mathrm{Sr}}_{0.44}$ ${)}_2$ ${\mathrm{Cu}}_{1.1}$ ${\mathrm{O}}_{2.2+\mathrm{\delta }}$(${\mathrm{CO}}_3$ ${)}_{0.9}$, ${\mathrm{Pr}}_{1.85}$ ${\mathrm{Ce}}_{0.15}$ ${\mathrm{CuO}}_4$, and ${\mathrm{Nd}}_2$ ${\mathrm{CuO}}_{4\mathrm{-}\mathit{x}}$