Phonon thermal Hall effect in undoped and doped strontium titanate*

We present a study of thermal Hall conductivity in strontium titanate, a non-magnetic insulator  known to be a quantum paralectric. A sizeable thermal Hall effect is detectable and iits phononic origin appears obvious. Upon substitituation with Ca and syabilization of a ferroelectric ground state, the effect is drastically damped. On the other hand, introduction of oxygen vacancies, which makes the sytem a metal greatly enhaces the signal. The analysis of the latter case points to a phonon-electron mutual drag  mecahnism, generating a novel contribution in addition to the phononic and electronic terms. The combination of the  phonon dominance in energy transport with the large Hall angle of electrons and frequent momentum exchange between electrons and phonons generates a trasnverse thermal gradient , larger than what electrons and phonons alone can produce.