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

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 ($σ$), thermoelectric ($α$), and thermal ($κ$) 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.

Figures (2)

• Figure 1: (a) Illustration of the intrinsic and two other extrinsic mechanisms that can give rise to nonlinear response. (b) Diagrams of transverse and longitudinal electric, thermal and thermoelectric effects, where the electric field or temperature gradient is along the direction of $x$.
• Figure 2: (a) Crystal structure of the surface of the topological insulator X$_2$Y$_3$. The hexagonal lattice is projected along the (001) direction. (b) Variation of the second-order Hall coefficient $\sigma_{xxy}^{\text{sk/sj}}$ with Fermi energy $\varepsilon_F$ under different $\lambda$. (c) Fermi energy $\varepsilon_F$ dependence of the second-order thermal coefficient $\kappa^{\text{sk/sj}}_{xxy}$ for different $\lambda$. (d) Calculated ratio $\alpha^{\text{sk/sj}}_{xxy}/\sigma^{\text{sk/sj}}_{xxy}$ in unit of $L$ as a function of $q_s$. The gray dot line in (b)-(d) is shown for visual guidance. Parameters used: $v=3.291$ eVÅ, $\lambda=80$ eVÅ$^3$, $250$ eVÅ$^3$, $\tau$ = $0.1$$\text{ps}$.