Anisotropic surface impedance of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ single crystals

The anisotropic surface resistance ${\mathit{R}}_{\mathit{s}\mathrm{-}\mathit{ab}}$ and ${\mathit{R}}_{\mathit{s}\mathrm{-}\mathit{c}}$ as well as the penetration depth ${\lambda }_{\mathit{ab}}$ and ${\lambda }_{\mathit{c}}$ of ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ single crystals have been measured at 9.6 GHz. ${\lambda }_{\mathit{c}}$(T) and ${\lambda }_{\mathit{ab}}$(T) are linear in temperature at low temperatures with much different slopes, consistent with the existence of line nodes on a cylindrical Fermi surface. A collapse of the c-axis scattering rate below ${\mathit{T}}_{\mathit{c}}$ is also observed, and the temperature dependence of the ab plane scattering rate is consistent with quasiparticle-quasiparticle scattering. The behavior of ${\lambda }_{\mathit{c}}$(T) is not consistent with proximity-effect models, or with cubic ${\mathit{d}}_{{\mathit{x}}^2+{\mathit{y}}^2\mathrm{-}{\mathit{z}}^2}$ pairing symmetry, but is consistent with a cubic ${\mathit{d}}_{{\mathit{x}}^2\mathrm{-}{\mathit{y}}^2}$ pairing state.