Anomalous Hall coefficients of interacting fermions

We investigate the impact of electron-electron interactions on the anomalous Hall coefficients of 2D massive Dirac fermions. In a fully gapped system in the limit of zero temperature, we find that first-order corrections to the electrical Hall effect vanish, confirming the absence of perturbative corrections to the topological Hall conductivity. At finite temperature or chemical potential, we find that interactions make the Hall response decay faster than in the noninteracting case. We also examine the impact of interactions on the anomalous thermal conductivity, testing the robustness of the Wiedemann-Franz law, and on the Nernst coefficient. Our findings are relevant to interacting 2D Chern insulators and surfaces of 3D topological insulators, and highlight the importance of electron-electron interactions for anomalous Hall transport.