Thermal Hall resistivity and transverse entropy production in a phonon gas

Most theories of the phonon thermal Hall effect ignore phonon-phonon interactions. Here, by recalling the Senftleben-Beenakker effect in molecular gases, we argue that a magnetic field, by influencing collisions between neutral non-chiral [quasi-]particles, can induce a Hall response. Our study of two insulators with distinct crystal structures, layered honeycomb WS$_2$ and ferroelectric perovskite LiNbO$_3$, finds that $κ_{xx}$ and $κ_{xy}$ peak at nearly the same temperature in both materials, as reported in other insulators. We show that the amplitude of transverse thermal \emph{resistivity} in clean and simple insulators is of the order of $|W_\perp/B|\simeq \frac{e}{k_B u}$, where $e$ and $k_B$ are fundamental constants and $u$ is the binding energy density of the crystal. In complex and dirty insulators, $|W_\perp/B|$ is much larger and has a significant temperature dependence. Nevertheless, the peak thermal Hall \textit{angle} in all insulators remains roughly the same.