Heat transport in the cuprate superconductors YBa2Cu3Oy and La2-xSrxCuO4 was measured at low temperatures as a function of doping. A residual linear term kappa(0)/T is observed throughout the superconducting region and it decreases steadily as the Mott insulator is approached from the overdoped regime. The low-energy quasiparticle gap extracted from kappa(0)/T is seen to scale closely with the pseudogap. The ubiquitous presence of nodes and the tracking of the pseudogap shows that the overall gap remains of the pure d-wave form throughout the phase diagram, which excludes the possibility of a complex component (ix) appearing at a putative quantum phase transition and argues against a nonsuperconducting origin to the pseudogap. A comparison with superfluid density measurements reveals that the quasiparticle effective charge is weakly dependent on doping and close to unity.
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