Enhanced anomalous Nernst effect in disordered Dirac and Weyl materials

We analyze the thermoelectric response of Dirac and Weyl semimetals using the semiclassical approach, focusing on the extrinsic contributions due to skew-scattering and side jump. Our results apply to the linear response Nernst effect in ferromagnetic Dirac materials such as ${\mathrm{Fe}}_{3}{\mathrm{Sn}}_{2}$ and Weyl semimetals like ${\mathrm{Co}}_{3}{\mathrm{Sn}}_{2}{\mathrm{S}}_{2}$. In the case of ${\mathrm{Fe}}_{3}{\mathrm{Sn}}_{2}$ we obtain a very good agreement with known experimental anomalous Hall effect measurements, and based on that we predict a large Nernst effect in this material. We also extend the investigation to second-order response, focusing on monolayer graphene on hBN with trigonal warping as an example. Our analysis indicates that the extrinsic contributions can be a significant component of anomalous Nernst response and may be used to explain an enhanced thermoelectric response.