c-axis microwave conductivity of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ in the superconducting state

We measured the surface impedance of ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ single crystals at 10 GHz in two kinds of magnetic-field configurations (${\mathit{H}}_{\mathrm{\omega }}$∥c,${\mathit{H}}_{\mathrm{\omega }}$ ⊥c). We investigated the temperature dependence of the c-axis microwave conductivity ${\mathrm{\sigma }}_1^{\mathit{c}}$ in the superconducting state for a fully oxygenated sample (${\mathit{T}}_{\mathit{c}}$=93 K) and two oxygen-reduced samples (${\mathit{T}}_{\mathit{c}}$=65 K, 63 K). In the fully oxygenated sample, ${\mathrm{\sigma }}_1^{\mathit{c}}$(T) shows a broad peak similar to that of ${\mathrm{\sigma }}_1^{\mathit{ab}}$(T), while in the oxygen-reduced samples ${\mathrm{\sigma }}_1^{\mathit{c}}$(T) shows quite different dependence on temperature from ${\mathrm{\sigma }}_1^{\mathit{ab}}$(T). Namely, ${\mathrm{\sigma }}_1^{\mathit{c}}$(T) in the superconducting state strongly depends on the oxygen content in ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$. The result suggests that the dynamics of the quasiparticles in the oxygen-reduced ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ keeps a strong two-dimensional nature in the superconducting state.