Persistence of superconducting condensate far above the critical temperature in YBa${}_2$(Cu,Zn)${}_3$O${}_y$ revealed by $c$-axis optical conductivity measurements for several Zn concentrations and carrier doping levels

The superconductivity precursor phenomena in high temperature cuprate superconductors was studied by direct measurements of superconducting condensate with the use of the $c$-axis optical conductivity of YBa${}_2$(Cu${}_{1-x}$Zn${}_x$)${}_3$O${}_y$ for several doping levels ($p$) as well as for several Zn-concentrations. Both of the real and imaginary part of the optical conductivity clearly showed that the superconducting carriers persist up to the high temperatures $T$${}_p$ that is higher than the critical temperature $T$${}_c$ but lower than the pseudogap temperature $T$${}^{\ast }$. $T$${}_p$ increases with reducing doping level like $T$${}^{\ast }$, but decreases with Zn-substitution unlike $T$${}^{\ast }$.