Phonon Hall effect in nonmagnetic insulators

Thermal Hall effect (THE), a phenomena in which the presence of magnetic field causes thermal current perpendicular to the temperature gradient, is a useful probe to detect current of charge-neutral particles in materials: excitation of spin or lattice motion. Recently, mechanisms of THE have been theoretically investigated to reveal how the charge-neutral particles are affected by magnetic moments or magnetic field. THE of phonons has been observed only in magnetic insulators [1], and previous studies have attributed the origin of THE to spin-phonon interaction, such as the Raman interaction [2] and magnon-phonon interaction [3].
In sharp contrast, our study shows that THE of phonon is possible even without magnetic moment. This is due to imperfect screening of magnetic field in crystals: negative charge of electrons and positive one of nuclei do not completely cancel each other when the correction beyond the adiabatic approximation is taken into account. For quantitative estimation, we calculated the THE in lattice models of band insulators.

[1] C. Strohm, et al., PRL 95, 155901 (2005)
[2] L. Sheng, et al., PRL 96, 155901 (2006)
[3] X. Zhang, et al., PRL 123, 167202 (2019)