Fundamental Relations as the Leading Order in Nonlinear Thermoelectric Responses with Time-Reversal Symmetry

TL;DR

This paper develops a theoretical framework for understanding second-order nonlinear thermoelectric transport in quantum materials with time-reversal symmetry, highlighting disorder effects and fundamental relations like the Mott relation and Wiedemann-Franz law.

Contribution

It introduces a semi-classical wave packet approach to calculate disorder-induced second-order transport coefficients and explores their relationships in topological insulators.

Findings

Quantitative characterization of second-order coefficients in topological insulators.

Establishment of second-order Mott relation and Wiedemann-Franz law.

Explicit inclusion of Coulomb impurity effects on transport coefficients.

Abstract

In recent years, nonlinear transport phenomena have garnered significant interest in both theoretical explorations and experiments. In this work, we utilize the semi-classical wave packet theory to calculate disorder-induced second-order transport coefficients: second-order electrical ($\sigma$), thermoelectric ($\alpha$), and thermal ($\kappa$) coefficients, capturing the interplay between side-jump and skew-scattering contributions in systems with time-reversal symmetry. Using a topological insulator model, we quantitatively characterize the Fermi-level dependence of these second-order transport coefficients by explicitly including Coulomb impurity potentials. Furthermore, we elucidate the relationships between these coefficients, establishing the second-order Mott relation and the Wiedemann-Franz law induced by disorder. This study develops a comprehensive theoretical framework elucidating the nonlinear thermoelectric transport mechanisms in quantum material systems.