The phonon thermal Hall angle in black phosphorus

The origin of phonon thermal Hall Effect observed in a variety of insulators is yet to be identified. Black phosphorus (BP) is a non-magnetic elemental insulator, displaying a thermal Hall conductivity larger than what has been previously observed in any insulator. Thelongitudinal  and the transverse thermal conductivities peak at the same temperature and at this peak temperature, the thermal Hall angle at ~10 T is of the order of a few parts in thousand.  Both these features are shared by other insulators displaying THE, despite an

absolute amplitude spreading over three orders of magnitude. Thus there is no correlation between  the thermal Hall angle and the phonon mean-free-path. In this particular system,theoretical phon spectrum has a striking feature, which may play a role.  A longitudinal and a transverse acoustic phonon mode anti-cross, facilitating wave-like transport across modes¹. 

1) Xioakang Li et al., Nature Communications, 14:1027 (2023)