Thermal conductivity of strontium titanate: signatures of phonon hydrodynamics*

Temperature dependence of thermal conductivity in strontium titanate reveals four different regimes of heat flow between 2K and 400 K. At high temperature, in the kinetic regime, phonons are scattered off each other by Umklapp processes and thermal conductivity is inversely proportional to temperature. At low temperature, their mean-free-path is set by domain boundaries. This is the ballistic regime. Between these two limits, one can detect the Ziman regime where Umklapp events are rare. The hybridization of soft optical phonon with acoustic phonons enhance Normal (momentum-conseving) collisions and leads to a faster-than cubic temperature dependence of thermal conductivity in a narrow tempearture window. This is a hallmark of Poiseuille flow of phonons previously observed in a handful of solids.