Anomalous Thermal Diffusivity in Bad Metals*

Local measurements of thermal diffusivity are used to analyze the transport of heat in the bad metallic regime of several strongly correlated materials. Thermal diffusivity was measured for several curate systems in their so-called bad metal regime. For underdoped YBCO, we find that the thermal anisotropy is comparable to reported values of the electrical resistivity anisotropy and drops sharply below the charge order transition, suggesting that both anisotropies have the same origin. For some electron-doped cuprates the inverse diffusivity is found to be proportional to temperature, again similar to the behavior of the electrical resistivity. We interpret our results through a strong electron-phonon scattering picture where both electron and lattice system saturates a quantum scattering time bound of ~h/k_BT. Our results suggest that neither well-defined electron nor phonon quasiparticles might be present in these systems, and that thermal transport is carried out by a collective ”soup” of strongly coupled electrons and phonons.