Optical study of c-axis charge dynamics in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{\mathrm{y}}$:nnCarrier self-confinement in the normal and the superconducting states

The optical conductivity spectra of ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{\mathrm{y}}$ crystals have been investigated with polarization E‖c over a wide doping range from the heavily underdoped to the overdoped regime, focusing on the charge dynamics in the c direction. For overdoped crystals, the conductivity spectra ${\mathrm{\sigma }}_{\mathrm{c}}$(ω) show a completely metallic T and ω dependence, which can be analyzed by an extended Drude model. However, the obtained quasiparticle scattering rate ${\gamma }_{\mathrm{c}}$ is one order larger than the in-plane value, which is quite different from the case of a conventional low-dimensional material with a strong mass anisotropy. It is evidence for a non-Fermi-liquid state in high-${\mathrm{T}}_{\mathrm{c}}$ cuprates and suggests unconventional charge dynamics along the c axis such as incoherent hopping. With decreasing oxygen content y, temperature dependence of the low-ω conductivity changes from a metallic to a semiconducting one, being consistent with the T dependence of the dc resistivity ${\mathrm{\rho }}_{\mathrm{c}}$. The conductivity for the underdoped crystals with d${\mathrm{\rho }}_{\mathrm{c}}$(T)/dT<0 are characterized by a suppression of the conductivity below ${\mathrm{\omega }}_{\mathrm{suppression}}$(≈500–${800\mathrm{n}\mathrm{c}\mathrm{m}}^{\mathrm{-}1}$). This doping dependence of ${\mathrm{\sigma }}_{\mathrm{c}}$(ω,T) indicates a change from a strongly confined regime for low doping to a weakly confined regime for high doping, and suggests that the mechanism of carrier confinement is closely related to strong electron correlation. The carrier-confined state which is symbolized by a large scattering rate leads to a dirty limit behavior for the c direction in the superconducting state, whereas it is in a clean limit in the plane direction. There are a couple of experimental facts which suggest a d-wave gap. A huge amount of unpaired carriers and no decrease of maximum gap amplitude were found for the overdoped crystals, which does not support the mean-field theory for explanation of the ${\mathrm{T}}_{\mathrm{c}}$ drop in the overdoped regime.