Coherence and Superconductivity in Coupled One-Dimensional Chains: A Case Study ofYBa2Cu3Oy

We report the infrared (IR) response of Cu-O chains in the high-$T_c$ superconductor ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_y$ over the doping range spanning $y=6.28–6.75$. We find evidence for a power law scaling at mid-IR frequencies consistent with predictions for Tomonaga-Luttinger liquid, thus supporting the notion of one-dimensional transport in the chains. We analyze the role of coupling to the ${\mathrm{CuO}}_2$ planes in establishing metallicity and superconductivity in disordered chain fragments.