Discovery of universal phonon thermal Hall effect in crystals

Thermal Hall effect (THE) in insulator is a remarkable phenomenon that arises from the motion of chargeless quasi-particles under a magnetic field. While magnons or exotic spin excitations were considered as the origin of THE in some magnetic materials, there are more and more evidences suggesting that phonons play a significant role. However, the mechanism behind phonon THE is still unknown. Here we report the observation of THE, including planar THE, in a broad range of non-magnetic insulators and semiconductors: SrTiO3, SiO2 (quartz), MgO, MgAl2O4, Si and Ge. While the presence of antiferrodistortive domains in SrTiO3 and chiral phonons in SiO2 may complicate the interpretation of THE, the striking observations of THE in trivial insulators MgO and MgAl2O4, as well as in high-purity intrinsic semiconductors Si and Ge, demonstrate that phonon THE is a universal property of crystals. Without other effects on phonons such as from magnons, this universal phonon THE is characterized by a scaling law of |\k{appa}_xy| ~ \k{appa}_xx^2. Our results experimentally discover a fundamental physics of phonons in magnetic field, which should come from the direct coupling between atom vibrations and the field. Starting from this universal phonon THE in crystals, all previous interpretations of THE in magnetic or non-magnetic materials need to be reconsidered.