Fundamental relations for anomalous thermoelectric transport coefficients in the nonlinear regime

In a series of recent papers anomalous Hall and Nernst effects have been\ntheoretically discussed in the non-linear regime and have seen some early\nsuccess in experiments. In this paper, by utilizing the role of Berry curvature\ndipole, we derive the fundamental mathematical relations between the anomalous\nelectric and thermoelectric transport coefficients in the non-linear regime.\nThe formulae we derive replace the celebrated Wiedemann-Franz law and Mott\nrelation of anomalous thermoelectric transport coefficients defined in the\nlinear response regime. In addition to fundamental and testable new formulae,\nan important byproduct of this work is the prediction of nonlinear anomalous\nthermal Hall effect which can be observed in experiments.\n