Absence of Residual Quasiparticle Conductivity in the Underdoped CuprateYBa2Cu4O8

We report measurements of the in-plane thermal conductivity $\kappa$ of the stoichiometric underdoped cuprate ${\mathrm{YBa}}_2{\mathrm{Cu}}_4{\mathrm{O}}_8$ (Y124) below 1 K. $\kappa \left(T\right)$ is shown to follow a simple phononic $T^3$ dependence at the lowest temperature $T$ for both current directions, with a negligible linear quasiparticle contribution. This observation is in marked contrast with behavior reported in optimally doped cuprates, and implies that extended zero-energy (or low-energy) quasiparticles are absent in Y124.