Anomalous thermal diffusivity in underdoped YBa2Cu3O6+x

Significance Transport in the so-called “bad metallic” regime of strongly correlated electron systems with no well-defined electronic quasiparticles has been a long-standing challenge in theoretical physics. This challenge has motivated collection of an ample amount of data on bad metals. However, so far, emphasis has been given to the charge sector, with the host crystal lattice treated as a well-defined phonon background. In this paper, we show that, for cuprates in the bad metallic regime where resistivity exceeds the “Mott–Ioffe–Regel” limit, phonon excitations are also not well-defined. The data lead to a thermal transport scenario where entropy is carried by an overdamped diffusive fluid of electrons and phonons characterized by a unique velocity and a quantum-limited relaxation time ℏ/kBT. The thermal diffusivity in the ab plane of underdoped YBCO crystals is measured by means of a local optical technique in the temperature range of 25–300 K. The phase delay between a point heat source and a set of detection points around it allows for high-resolution measurement of the thermal diffusivity and its in-plane anisotropy. Although the magnitude of the diffusivity may suggest that it originates from phonons, its anisotropy is comparable with reported values of the electrical resistivity anisotropy. Furthermore, the anisotropy drops sharply below the charge order transition, again similar to the electrical resistivity anisotropy. Both of these observations suggest that the thermal diffusivity has pronounced electronic as well as phononic character. At the same time, the small electrical and thermal conductivities at high temperatures imply that neither well-defined electron nor phonon quasiparticles are present in this material. We interpret our results through a strongly interacting incoherent electron–phonon “soup” picture characterized by a diffusion constant D∼vB2τ, where vB is the soup velocity, and scattering of both electrons and phonons saturates a quantum thermal relaxation time τ∼ℏ/kBT.