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 not invoking the 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 phonon mean-free-path is close to the sample thickness. Therefore, it is unlikely that scattering by point-like symmetry-breaking defects play a major role. We show that the angular dependence of the signal can be mapped to the sum of two sinusoidal components each peaking when the magnetic field is parallel to a high symmetry. We propose that anharmonicity may play a major role and argue that the magnetic field can exert a torque on electric dipolar waves traveling with phonons.