Fundamental distinction between intrinsic and extrinsic nonlinear thermal Hall effects

We theoretically investigated the fundamental distinction between the intrinsic and extrinsic nonlinear thermal Hall effects in the presence of disorder at the second-order response to the temperature gradient in terms of the semiclassical Boltzmann equation. We found that, at low temperatures, the intrinsic contribution of the nonlinear thermal Hall conductivity is proportional to the square of temperature, whereas the extrinsic contributions (side jump and skew scattering) are independent of temperature. This distinct dependency on temperature provides an approach to readily distinguish between the intrinsic and extrinsic contributions. Specifically, we analyzed the nonlinear thermal Hall effect for a tilted two-dimensional massive Dirac material. In particular, we showed that when the Fermi energy is located at the Dirac point, the signal is solely from the intrinsic mechanism; when the Fermi energy is higher, the extrinsic contributions are dominant, which are two to three orders of magnitude larger than the intrinsic contribution.