Wiedemann-Franz law and Mott relation for transport coefficients in the non-linear regime

In contrast to their counterparts in the linear regime, the non-linear anomalous Hall, Nernst, and thermal Hall effects can survive in time-reversal symmetric system in the presence of inversion symmetry breaking. Within the framework of semiclassical Boltzmann theory, we calculate the analytical expressions for the non-linear anomalous transport coefficients, namely, the non-linear anomalous Hall, Nernst, and thermal Hall coefficients. With these expressions, we predict the fundamental relations between the non-linear anomalous electric and thermo-electric transport coefficients, which are the analog of the Wiedemann-Franz law and the Mott relation in the non-linear regime. We also make several experimental predictions for non-linear anomalous Nernst Hall effect in bilayer WTe2 and for non-linear anomalous thermal Hall effect for monolayer transition metal dichalcogenide which can be verified in experiments.

References:
[1] C. Zeng, S. Nandy, A. Taraphder, and S. Tewari, “Non-linear Nernst effect in bilayer WTe2,” arXiv e-prints, p. arXiv:1905.09814, May 2019.
[2] C. Zeng, S. Nandy, and S. Tewari, “Wiedemann-Franz law and Mott relation for non-linear anomalous transport phenomena,” arXiv e-prints, p. arXiv: 1909.03047, Sep 2019.