We report systematic, high-precision measurements of the low-$T$ (down to 70 mK) thermal conductivity $\kappa$ of ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_y$, ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$, and ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$. Careful examinations of the Zn- and hole-doping dependences of the residual thermal conductivity ${\kappa }_0/T$, as well as the in-plane anisotropy of ${\kappa }_0/T$ in ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$, indicate a breakdown of the universal thermal conductivity, a notable theoretical prediction for $d$-wave superconductors. Our results point to an important role of electronic inhomogeneities, which are not considered in the standard perturbation theory for thermal conductivity, in the underdoped to optimally doped regime.

• Received 13 September 2005

DOI:https://doi.org/10.1103/PhysRevLett.96.017008