Interaction driven transverse thermal resistivity in a phonon gas

TL;DR

This paper proposes that phonon-phonon interactions, influenced by magnetic fields and Berry forces, are responsible for the transverse thermal resistivity observed in insulators, challenging non-interacting models.

Contribution

It introduces a new interaction-based framework to explain the phonon thermal Hall effect, emphasizing the role of magnetic field-modified phonon interactions.

Findings

Transverse thermal resistivity in insulators can be explained by phonon interactions influenced by magnetic fields.

The proposed model accounts for experimental measurements across seven different crystalline insulators.

A Berry force on phonon drift velocity provides a plausible mechanism for the observed effects.

Abstract

The amplitude of the Hall response of electrons can be understood without invoking interactions. Most theories of the phonon thermal Hall effect have likewise opted for a non-interacting picture. Here, we challenge this approach. Our study of WS$_2$, a transition metal dichalcogenide (TMD) insulator, finds that longitudinal, $\kappa_{xx}$, and transverse, $\kappa_{xy}$, thermal conductivities peak at almost the same temperature. Their ratio obeys an upper bound, as in other insulators. We then compare transverse thermal transport in a phonon gas and in a molecular gas. In the latter, the Senftleben-Beenakker effect is driven by the competition between molecular collisions and applied magnetic field in setting the distribution of molecular angular momenta. An off-diagonal transport response arises thanks to interactions between non-spherical particles, which do not need to be chiral. By analogy, we argue that in a phonon gas, magnetic field will influence phonon-phonon interactions, and generates a transverse thermal \emph{resistivity}, whose order of magnitude can be accounted for by invoking a Berry force on the drift velocity of the nuclei in the presence of a finite heat. This simple picture gives a reasonable account of the experimentally measured transverse thermal resistivity of seven different crystalline insulators.