Infrared Probe of Transition from Superconductor to Nonmetal in ${\mathrm{YBa}}_2({\mathrm{Cu}}_{1-\mathit{x}}{\mathrm{Zn}}_{\mathit{x}}{)}_4{O}_8$

We report on a study of the optical conductivity of single crystals of the high- $T_c$ superconductor ${\mathrm{YBa}}_2{\mathrm{Cu}}_4{\mathrm{O}}_8$ in which superconductivity is suppressed by random substitution of Cu with Zn. The $a$-axis infrared spectrum, which is a direct measure of the charge dynamics in the ${\mathrm{CuO}}_2$ planes, is dominated by a bound state at $\approx 120{\mathrm{cm}}^{-1\mathrm{}}$. This indicates that the low-energy electronic states are on the verge of localization driven by the Zn impurities.