  We report here measurements of the in-plane thermal conductivity K(T) of the
underdoped cuprate YBa2Cu4O8 (Y124) below 1K. K(T) is shown to follow a simple,
phononic T^3 dependence at the lowest temperatures 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) low-energy quasiparticles are absent
in YBa2Cu4O8 at low temperatures.
