  Thermal transport in the T -> 0 limit was measured as a function of doping in
high-quality single crystals of the cuprate superconductor YBa_2Cu_3O_y. The
residual linear term kappa_0/T is found to decrease as one moves from the
overdoped regime towards the Mott insulator region of the phase diagram. The
doping dependence of the low-energy quasiparticle gap extracted from kappa_0/T
is seen to scale closely with that of the pseudogap, arguing against a
non-superconducting origin for the pseudogap. The presence of a linear term for
all dopings is evidence against the existence of a quantum phase transition to
an order parameter with a complex (ix) component.
