Thermal Hall effect and the Wiedemann-Franz law in Chern insulator

Thermal Hall effect, where a transverse temperature difference is generated by implementing a longitudinal temperature gradient and an external magnetic field in the perpendicular direction to systems, is a useful tool to reveal transport properties of quantum materials. A systematic study of the thermal Hall effect in a Chern insulator is still lacking. Here, using the Landauer-Buttiker formula, we investigated the thermal Hall transport of the Harper-Hofstadter model with flux phi = 1/2 and its generalizations. We demonstrated that the Wiedemann-Franz law, which states that the thermal Hall conductivity is linearly proportional to the quantum Hall conductivity in the low temperature limit, is still valid in this Chern insulator, and that the thermal Hall conductivity can be used to characterize the topological properties of quantum materials.