Optical study of c-axis charge dynamics in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">YBa</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Cu</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">y</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>: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\ensuremath{\Vert}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 ${\mathrm{\ensuremath{\sigma}}}_{\mathrm{c}}$(\ensuremath{\omega}) show a completely metallic T and \ensuremath{\omega} dependence, which can be analyzed by an extended Drude model. However, the obtained quasiparticle scattering rate ${\ensuremath{\gamma}}_{\mathrm{c}}$ 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-\ensuremath{\omega} conductivity changes from a metallic to a semiconducting one, being consistent with the T dependence of the dc resistivity ${\mathrm{\ensuremath{\rho}}}_{\mathrm{c}}$. The conductivity for the underdoped crystals with d${\mathrm{\ensuremath{\rho}}}_{\mathrm{c}}$(T)/dT0 are characterized by a suppression of the conductivity below ${\mathrm{\ensuremath{\omega}}}_{\mathrm{suppression}}$(\ensuremath{\approx}500--${800\mathrm{n}\mathrm{c}\mathrm{m}}^{\mathrm{\ensuremath{-}}1}$). This doping dependence of ${\mathrm{\ensuremath{\sigma}}}_{\mathrm{c}}$(\ensuremath{\omega},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.

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