Angle-dependent planar thermal Hall effect by quasi-ballistic phonons in black phosphorus

The origin of the phonon thermal Hall effect in insulators is a matter of ongoing debate. The large amplitude of the signal in an elemental non-magnetic solid, such as black phosphorus (BP) calls for a minimal mechanism with no role for spin degree of freedom. Here, we show that a longitudinal heat flow generates a transverse temperature gradient in BP even when the magnetic field, the heat current and the thermal gradient lie in the same plane. The long phonon mean-free-path leaves little room for scattering by point-like symmetry breaking defects. we show that the signal peaks when the magnetic field is oriented along one of the two diagonal orientations of the puckered honeycomb plane and argue that this can be understood as the sum of two distinct contributions each parallel to a mirror plane. This angular dependence as well as the order of magnitude of the observed signal points to the torque exerted by magnetic field on electric dipoles traveling with heat-carrying phonons as the driver of the effect.
Comment: 10 pages, 6 figures, Supplemental Materials included