Thermal transport and phonon hydrodynamics in strontium titanate

We present a study of thermal conductivity, $\kappa$, in undoped and doped strontium titanate in a wide temperature range (2-400 K) and detecting different regimes of heat flow. In undoped SrTiO${}_3$, $\kappa$ evolves faster than cubic with temperature below its peak and in a narrow temperature window. Such a behavior, previously observed in a handful of solids, has been attributed to a Poiseuille flow of phonons, expected to arise when momentum-conserving scattering events outweigh momentum-degrading ones. The effect disappears in presence of dopants. In SrTi${}_{1-x}$Nb${}_x$O${}_3$, a significant reduction in lattice thermal conductivity starts below the temperature at which the average interdopant distance and the thermal wavelength of acoustic phonons become comparable. In the high-temperature regime, thermal diffusivity becomes proportional to the inverse of temperature, with a prefactor set by sound velocity and Planckian time (${\tau }_p=\frac{\mathrm{\hslash }}{k_{B}T}$).