Phonon thermal Hall as a lattice Aharonov-Bohm effect

Abstract: In a growing list of insulators, experiments find that magnetic field induces a misalignment between the heat flux and the thermal gradient vectors. This phenomenon, known as the phonon thermal Hall effect, implies energy flow without entropy production along the orientation perpendicular to the temperature gradient. Experimentally, the thermal Hall angle is maximal at the temperature of peak longitudinal thermal conductivity. At this temperature, $T_{max}$, Normal phonon-phonon collisions dominate over Umklapp and boundary scattering events. In the presence of a magnetic field, Born-Oppenheimer approximated molecular wave functions are known to acquire a phase, due to the difference in the spatial distributions of the positive charge of the nuclei and the negative charge of the electrons. Combined with unavoidable anharmonicity, the field-induced phase of the molecular wave-function gives rise to a geometric [Berry] phase for phonons and modifies three-phonon interference. The rough amplitude of the thermal Hall angle expected in this picture is set by the wavelength, $\lambda_{ph}$, and the crest displacement, $\delta u_m$, of phonons at $T_{max}$. The derived expression is surprisingly close to what has been experimentally found in black phosphorus, germanium and silicon.