Enhanced Thermal Hall Effect in Nearly Ferroelectric Insulators

In the context of recent experimental observations of an unexpectedly large thermal Hall conductivity, ${\kappa }_H$, in insulating ${\mathrm{La}}_2{\mathrm{CuO}}_4$ (LCO) and ${\mathrm{SrTiO}}_3$ (STO), we theoretically explore conditions under which acoustic phonons can give rise to such a large ${\kappa }_H$. Both the intrinsic and extrinsic contributions to ${\kappa }_H$ are large in proportion to the dielectric constant, $\epsilon$, and the “flexoelectric” coupling, $F$. While the intrinsic contribution is still orders of magnitude smaller than the observed effect, an extrinsic contribution proportional to the phonon mean-free path appears likely to account for the observations, at least in STO. We predict a larger intrinsic ${\kappa }_H$ in certain insulating perovskites.