Measurements of heat and charge transport at very low temperature were used to investigate the ground state of high-purity single crystals of the cuprate YBa2Cu3Oy as a function of doping. Samples were investigated on either side of the superconducting phase boundary, in both zero and applied magnetic field. We find that from optimal doping to a doping near the onset of superconductivity the elementary electronic excitations are understood to be nodal quasiparticles, whose excitation spectrum is governed by the energy scale of the pseudogap. In a magnetic field, these quasiparticles behave unexpectedly in our purest samples---conventional transport theory cannot account for their field and temperature dependence in either the unitary or Born scattering limits. At very low dopings, such that the hole concentration in the CuO2 planes is slightly less than the critical doping needed for the onset of superconducting order, we observe delocalized fermionic excitations at zero energy. This reveals that the ground state of clean underdoped cuprates is metallic, in contrast to the insulating ground state observed in underdoped La2- xSrxCuO 4. The ratio of heat to charge transport in this metallic state violates the Wiedemann-Franz law, the first such observation in underdoped cuprates.
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