Fundamental relations for anomalous thermoelectric transport coefficients in the non-linear regime

In a series of recent papers anomalous Hall and Nernst effects have been theoretically discussed in the non-linear regime and have seen some early success in experiments. In this paper, by utilizing the role of Berry curvature dipole, we derive the fundamental mathematical relations between the anomalous electric and thermoelectric transport coefficients in the non-linear regime. The formulae we derive replace the celebrated Wiedemann-Franz law and Mott relation of anomalous thermoelectric transport coefficients defined in the linear response regime. In addition to fundamental and testable new formulae, an important byproduct of this work is the prediction of nonlinear anomalous thermal Hall effect which can be observed in experiments.