Sign structure of thermal Hall conductivity for in-plane field polarized Kitaev magnets

The half-quantized thermal Hall conductivity measured in α-RuCl3 in the presence of in-plane magnetic fields has been taken as evidence for Kitaev spin liquid. Apart from the quantization, the sign structure of the thermal Hall conductivity is also consistent with theoretical predictions. When the field is perpendicular to one of the nearest neighbour bonds on the honeycomb lattice, the thermal Hall conductivity changes sign when the field direction is reversed, while it is nearly zero when the field is applied along the bond direction. We demonstrate that this sign structure is a generic property of the polarized state in the presence of in-plane magnetic fields. Here, the thermal Hall effect arises from topological magnons with finite Chern numbers, and the sign structure follows from the symmetries of the momentum space Berry curvature. We show that the magnitude of the thermal Hall conductivity can be comparable to that observed in the experiments. Thus, the sign structure alone cannot make a strong case for Kitaev spin liquid. The quantization at very low temperatures, however, will be a decisive test as the magnon contribution vanishes in the zero temperature limit. [arXiv:2008.12788]