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Heat transport in the cuprate superconductors YBa$_2$Cu$_3$O$_{y}$ andLa$_{2-x}$Sr$_x$CuO$_4$ was measured at low temperatures as a function ofdoping. A residual linear term kappa_{0}/T is observed throughout thesuperconducting region and it decreases steadily as the Mott insulator isapproached from the overdoped regime. The low-energy quasiparticle gapextracted from kappa_{0}/T is seen to scale closely with the pseudogap. Theubiquitous presence of nodes and the tracking of the pseudogap shows that theoverall gap remains of the pure d-wave form throughout the phase diagram, whichexcludes the possibility of a complex component (ix) appearing at a putativequantum phase transition and argues against a non-superconducting origin to thepseudogap. A comparison with superfluid density measurements reveals that thequasiparticle effective charge is weakly dependent on doping and close tounity.Comment: 12 pages, 9 figure

Thermal conductivity across the phase diagram of cuprates: Low-energy quasiparticles and doping dependence of the superconducting gap