The phonon thermal Hall angle in black phosphorus

TL;DR

This study reports the observation of a significant phonon thermal Hall effect in black phosphorus, revealing insights into phonon transport and constraints for theoretical explanations of THE in insulators.

Contribution

It provides the first measurement of thermal Hall conductivity in a non-magnetic insulator, highlighting the role of phonon mode interactions and anisotropic charge distributions.

Findings

Thermal Hall conductivity peaks at the same temperature as longitudinal conductivity.

The thermal Hall angle shows no correlation with phonon mean-free-path.

Wave-like phonon transport is facilitated by mode anti-crossing and anisotropic charge distribution.

Abstract

The origin of phonon thermal Hall Effect (THE) observed in a variety of insulators is yet to be identified. Here, we report on the observation of a thermal Hall conductivity in a non-magnetic elemental insulator, with an amplitude exceeding what has been previously observed. In black phosphorus (BP), the longitudinal ($\kappa_{ii}$), and the transverse, $\kappa_{ij}$, thermal conductivities peak at the same temperature and at this peak temperature, the $\kappa_{ij}/\kappa_{jj}/B $ is $\approx 10^{-4}$-$10^{-3}$ T$^{-1}$. Both these features are shared by other insulators displaying THE, despite an absolute amplitude spreading over three orders of magnitude. The absence of correlation between the thermal Hall angle and the phonon mean-free-path imposes a severe constraint for theoretical scenarios of THE. We show that in BP a longitudinal and a transverse acoustic phonon mode anti-cross, facilitating wave-like transport across modes and the anisotropic charge distribution surrounding atomic bonds, paving the way for coupling with magnetic field.