Microscopic mechanism of the universal phonon thermal Hall effect in nonmagnetic crystals

Develop a microscopic theory that explains the universal phonon thermal Hall effect observed in nonmagnetic single-crystal insulators and semiconductors, including the empirical scaling relation |Kxy| ~ Kxx.

Background

A universal phonon thermal Hall effect with |Kxy| ~ Kxx has been reported in various nonmagnetic insulators and semiconductors. This suggests a common mechanism that does not require exotic excitations.

Identifying the microscopic origin of this universal behavior is crucial for unifying interpretations of phonon-mediated transverse thermal transport and for distinguishing intrinsic lattice effects from extrinsic scattering mechanisms.