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

TL;DR

This paper derives fundamental relations between anomalous electric and thermoelectric transport coefficients in the non-linear regime, replacing classical laws and predicting a nonlinear thermal Hall effect observable in experiments.

Contribution

It introduces new mathematical relations for non-linear anomalous transport coefficients using Berry curvature dipole, extending beyond linear response laws.

Findings

Derived fundamental relations for non-linear anomalous transport coefficients.

Replaced Wiedemann-Franz law and Mott relation in the non-linear regime.

Predicted the nonlinear anomalous thermal Hall effect for experimental observation.

Abstract

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.