Damping mechanism of the strongly renormalized c-axis plasma frequency in high-T_c cuprates

We study the charge dynamics of high-T_c superconductors with the electric field perpendicular to the planes, using polarized oblique-incidence reflectometry for thin films of Tl₂Ba₂Ca₂Cu₃O₁₀ and normal incidence reflectometry for single crystals of La_1.85Sr_0.15CuO₄. In Tl₂Ba₂Ca₂Cu₃O₁₀ we observe no c-axis optical plasmon either above or below T_c. For E//c in La_2-xSr_xCuO₄, no plasmon is observed in the normal state, but as soon as T drops below T_c, a plasma edge in the reflectivity occurs, which moves up to about 2k_BT_c for T→0. The electronic contribution to σ(ω)≈7ω^-1 cm^-1 is independent of frequency up to several hundred cm^-1, which implies that the optical scattering rate (τ_c^-1) is large compared to the c-axis plasma frequency (ω_pc). We prove experimentally that h {combining short stroke overlay}/τ_c h {combining short stroke overlay}ω_pc≫ 3.5k_ET_c, hence the c-axis response is in a universality class different from the dirty (Mattis-Bardeen) limit, and the absence of a plasma edge in the normal state is due to overdamping. Recent experimental data of various groups show that this is a generic feature of high-T_c cuprates. There is no need to assume a large many-body reduction of the ab initio LDA-RPA plasma frequency along the c-axis. Yet the overdamping of the plasmon could be a many-body effect. The 'confinement' to the planes as was proposed by Anderson is therefore due to a strong scattering in the c-direction. In the dirty limit only the relatively small amount of oscillator strength in the below-gap region is transferred to the pair-response (the δ-function at zero frequency). As a result the plasma edge in the superconducting state occurs at about 3.4(k_BT_c h {combining short stroke overlay}/τ)^0.5 ω_pc≪3.5k_BT_c ≪ h {combining short stroke overlay}ω_pc.