Hole Localization in Underdoped Superconducting Cuprates Near 1/8th Doping

Measurements of thermal conductivity versus temperature over a broad range of doping in YBa${}_2$Cu${}_3$O${}_{6+x}$ and HgBa${}_2$Ca${}_{n-1}$Cu${}_n$O${}_{2n+2+\delta }$ ($n$=1,2,3) suggest that small domains of localized holes develop for hole concentrations near $p$=1/8. The data imply a mechanism for localization that is intrinsic to the CuO${}_2$-planes and is enhanced via pinning associated with oxygen-vacancy clusters.