The thermal conductivity к of underdoped YBa2Cu3Oy was measured in the T→0 limit as a function of hole concentration p across the uperconducting critical point at psc=5.0 %. The evolution of bosonic and fermionic contributions to к was tracked as the doping level evolved continuously in each of our samples. For p≤psc, we observe a T3 component in к which we attribute to the boson excitations of a phase with long-range spin or charge order. Fermionic transport, observed as a T-linear term in к which persists unaltered through psc, violates the Wiedemann-Franz law,since the electrical resistivity varies as log(1/T) and grows with decreasing p.

The in-plane resistivity ρ and thermal conductivity к of a single crystal of NaxCoO2 (x = 0.7) were measured down to 40 mK. Verification of the Wiedemann-Franz law, к/T = L0/ρ as T→0, and observation of a T2 dependence of ρ at low temperature, △ρ= AT2, establish the existence of a well-defined Fermi-liquid state. The measured value of coefficient A reveals enormous electronelectron scattering, characterized by the largest Kadowaki-Woods ratio A/γ 2 encountered in any material. The rapid suppression of A with magnetic field suggests a possible proximity to a magnetic quantum critical point. We also speculate on the possible role of magnetic frustration and proximity to a Mott insulator.