Asymmetric Scattering Drives Large Nonlinear Nernst and Seebeck Effects

TL;DR

This work develops a unified semiclassical kinetic theory for nonlinear Nernst and Seebeck effects in non-magnetic systems by incorporating disorder-induced asymmetric scattering via side-jump and skew-scattering channels. It identifies six second-order thermoelectric conductivities, derives their explicit forms, and provides a symmetry classification showing which channels survive under parity and time-reversal constraints; crucially, four extrinsic channels tie their band-geometric origin to the Berry curvature. The ABA-stacked trilayer graphene case demonstrates that extrinsic skew scattering can dominate the nonlinear responses, with results aligning with recent experiments and yielding sizable, field-free nonlinear voltages near the band-structure hotspots. The findings offer design principles for high-efficiency nonlinear thermoelectric devices and clarify how disorder and geometry together govern nonlinear caloritronic transport in nearly ${\cal C}_3$-symmetric systems.

Abstract

The nonlinear Nernst and Seebeck effects (NNE and NSE) offer promising routes for thermoelectric energy conversion in non-magnetic systems. While intrinsic mechanisms such as the nonlinear Drude and Berry-curvature-dipole terms are well established, extrinsic contributions to thermoelectric responses arising from disorder-induced asymmetric scattering remain comparatively less explored, despite growing experimental evidence of their dominance. Here, we develop a unified semiclassical theory of NNE and NSE that incorporates skew scattering and side-jump processes, identifying four distinct extrinsic contributions to NNE and two for NSE. A systematic symmetry analysis shows that these responses are allowed in time-reversal-symmetric non-magnets, PT-symmetric antiferromagnets, and non-centrosymmetric magnetic systems such as altermagnets. As a case study, we demonstrate that ABA-stacked trilayer graphene hosts large nonlinear Nernst and Seebeck responses dominated by extrinsic scattering, in excellent agreement with recent experiments. Our results establish the microscopic origin of these effects and provide guiding principles for designing high-efficiency nonlinear thermoelectric devices.

Figures (6)

• Figure 1: Schematic illustration of extrinsic nonlinear Nernst and Seebeck effects. The upper panel depicts the NNE and NSE scaling quadratically with the applied temperature gradient [$\propto~(\nabla T)^2$]. Under a thermal bias, Bloch electrons scatter asymmetrically from ${\bm k}$ to ${\bm k}'$ due to impurities (lower panel), generating transverse (Nernst) and longitudinal (Seebeck) nonlinear currents. For clarity, the conventional linear Seebeck current is not shown explicitly.
• Figure 2: Lattice structure, electronic properties and Berry curvature of ABA-staked trilayer graphene (TLG). (a) Crystal structure of ABA TLG with intra- and interlayer hopping parameters listed in the bottom panel. (b) Full band structure from $-10$ to $10$ eV, with the first conduction band projected onto the $k_x$–$k_y$ plane. The high-symmetry points ($\Gamma$, $K$, $K'$) and the first Brillouin zone are marked in black. (c) Band dispersion along high-symmetry lines, highlighting low-energy crossings near the Dirac points ($K$, $K'$). (d) Zoomed view near the $K$ point with Berry curvature projected onto the bands, showing pronounced hotspots near the charge-neutrality point. The right panel shows the corresponding density of states (DOS) as a function of energy. In all plots, we use the onsite potential ($\delta$) and the layer potential due to the applied vertical electric field as ($\Delta_1, ~ \Delta_2$) as $[\delta, \Delta_1, \Delta_2] = [0.046,\ 0.1,\ 0]$ eV.
• Figure 3: Momentum-space distribution of the Berry curvature and side-jump velocity for ABA-TLG. a) Berry curvature around the $K$ valley for the first conduction (c1) and valence (v1) bands, shown in the left and right panels, respectively. (b-c) The same plotting scheme is used for the $x$ and $y$ components of the side-jump velocity around the $K$ valley. Energy contours are drawn at $0.01$ and $0.02$ eV in the conduction band, and at $-0.005$ and $-0.02$ eV in the valence band. In all plots, the Hamiltonian parameters are identical to those in Fig. \ref{['fig2']}.
• Figure 4: Nonlinear Nernst and Seebeck conductivities in ABA trilayer graphene. (a–d) Chemical-potential ($\mu$) dependence of the nonlinear Nernst ($\alpha_{yxx}$, left panel) and Seebeck ($\alpha_{yyy}$, right panel) conductivities, expressed in units of ${\rm \mu A~nm/K^2}$. Calculations are performed at $T = 20$ K with symmetric scattering time $\tau = 0.1$ ps, impurity concentration $n_i \approx 10^{10} ~{\rm cm^{-2}}$, $V_0 = 6.2 \times 10^{-13}~{\rm eV ~cm^2}$ and $V_1 = 0.5 V_0$. All remaining parameters are the same as in Fig. \ref{['fig2']}.
• Figure 5: Electric field due to the nonlinear Nernst current. (a) Different components of nonlinear Nernst conductivity are plotted as a function of $\mu$ at a system temperature of 5 K. (b) Variation of the electric field arising due to the nonlinear Nernst current with the electron density ($n$). In computing this, we consider a temperature gradient across the sample of 0.1 K/${\rm \mu m }$ order, while the other system parameters are the same as in the Fig. \ref{['fig3']}.