Damping mechanism for the strongly renormalized $c$-axis charge transport in high-$T_c$ cuprate superconductors

We analyze the $c$-axis infrared reflectivity of La$_{1.85}$Sr$_{0.15}$CuO$_4$ single crystals. The plasma edge near 6 meV, observed below $T_c$, is due to Cooper-pair tunneling. This low value of the plasma edge is consistent with the $c$-axis plasma frequency ($\nu_p$) obtained from LDA calculations ($>0.1$ eV) if we take into account that the single-particle charge transport along the $c$ axis is strongly incoherent both above and below $T_c$. We find no evidence for a reduction of the $c$-axis scattering rate ($\gamma$) below $T_c$. Our investigation suggests $h\gamma>h\nu_{p}\gg 3.5k_BT_c$, which is exactly opposite to the clean limit. VSGD.94.6.1