Thermal Transport and Phonon Hydrodynamics in Strontium Titanate

We present a study of thermal conductivity, κ, 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}, κ evolves faster than cubic with temperature below its peak and in a narrow temperature window. Such 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 the 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 inter-dopant 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 (τ_{p}=(ℏ/k_{B}T)).