Thermal Hall effect induced by phonon skew-scattering via orbital magnetization

Thermal transport acts as a powerful tool for studying the excitations and physical properties of insulators, where a charge gap suppresses electronic conduction. Recently, the thermal Hall effect has been observed across various materials, including insulators and semiconductors, but its fundamental origin remains unclear. Here, I propose a promising mechanism to explain the emergence of the thermal Hall effect in these systems: axial chiral phonon skew scattering mediated by orbital magnetization. Starting from basic principles, I derive the form and magnitude of the orbital magnetization-phonon coupling using the well-established Haldane model. Using this coupling, I calculate the thermal Hall conductivity and Hall angle as functions of temperature, achieving semi-quantitative agreement with experimental findings. This work enhances our understanding of the role of electron-phonon coupling in thermal transport and provides a pathway to tailor thermal properties in a broad range of materials.