In a series of recent papers, anomalous Hall and Nernst effects have been theoretically discussed in the nonlinear 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 nonlinear regime. The formulas 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 formulas, an important by-product of this work is the prediction of nonlinear anomalous thermal Hall effect which can be observed in experiments.

中文翻译：

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非线性条件下热电输运系数的基本关系

在最近的一系列论文中，已经在非线性机制中对异常霍尔和能斯特效应进行了理论讨论，并在实验中取得了一些早期成功。在本文中，通过利用Berry曲率偶极子的作用，我们推导了非线性条件下反常的电和热电输运系数之间的基本数学关系。我们得出的公式取代了著名的Wiedemann-Franz定律和线性响应范围中定义的异常热电输运系数的Mott关系。除了基本的和可检验的新公式外，这项工作的重要副产品是可在实验中观察到的非线性异常热霍尔效应的预测。