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Observation of room temperature intrinsic nonlinear thermoelectric effects in low-dimensional semimetals

T0 review · 3 major / 3 minor · reviewed 2026-08-01 · deepseek-v4-flash

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Pith's one-line read This paper reports the first observation of intrinsic nonlinear thermoelectric effects—nonlinear Seebeck, nonlinear Nernst, and nonlinear mixed-directional—in zero magnetic field in thin WTe2 and TaIrTe4, persisting to room temperature.

desk verdict Genuinely new — first room-temperature intrinsic nonlinear thermoelectric effects with all three symmetry-allowed tensor components — but the NLN signal is a model-subtracted residual and the symmetrization is the load-bearing seam. read the letter →

arxiv 2607.21808 v1 pith:RSERIKZI submitted 2026-07-23 cond-mat.mes-hall cond-mat.mtrl-sciquant-ph

Kurea Nakagawa , Krishnaraajan Sundararajan , Cédric A. Cordero-Silis , Bart J. van Wees , Marcos H.D. Guimarães This is my paper · ORCID
classification cond-mat.mes-hallcond-mat.mtrl-sciquant-ph
keywords nonlinearthermoelectriceffectsSeebeckeffectNernstsecond-ordertensorBerrycurvaturedipoleskewscatteringWTe2TaIrTe4
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper reports that intrinsic nonlinear thermoelectric effects—responses that do not reverse when the driving temperature gradient is reversed—can arise purely from low crystal symmetry and persist to room temperature. In thin flakes of the type-II Weyl semimetals WTe2 and TaIrTe4, where only a single mirror plane remains, all three symmetry-allowed components of the second-order thermoelectric tensor are observed at zero magnetic field: the nonlinear Seebeck, nonlinear Nernst, and nonlinear mixed-directional effects. The key is a heater-reversal symmetrization that separates the intrinsic fourth-harmonic signal from the far larger temperature-dependent linear Seebeck background. Temperature- and conductivity-scaling analysis indicates skew scattering dominates the nonlinear Seebeck effect, while the nonlinear Nernst effect contains both Berry-curvature-dipole and skew-scattering contributions. If correct, this establishes nonlinear thermoelectricity as a symmetry-governed, material-intrinsic route to thermal-to-electrical rectification beyond engineered structures.

What carries the argument

The central object is the third-rank second-order thermoelectric tensor S^(2)_ijk linking electric field to products of temperature-gradient components. The carrying mechanism is harmonic detection: Joule heating at frequency ω creates a temperature gradient at 2ω, so linear thermoelectric responses appear at 2ω and intrinsic nonlinear ones at 4ω. The essential trick is symmetrizing the 4ω response under swapping the active heater (reversing the in-plane gradient), which removes the much larger contribution from the temperature dependence of the linear Seebeck coefficient and of the heater resistance. A scaling relation S^(2)=Aσ²+C, with σ the longitudinal conductivity, separates skew-scatte

What would settle it

Measure the actual in-plane temperature profile in the device, for example with scanning thermal microscopy or local resistive thermometers patterned along the flake, and check that the temperature difference between the two heater configurations is antisymmetric to within the claimed precision; a measured asymmetric component would directly contaminate the symmetrized 4ω signal. Alternatively, a control measurement on a centrosymmetric material with identical heater geometry should show a vanishing symmetrized 4ω response.

Watch

Extended reading notes

Core claim

The paper claims that in exfoliated thin flakes of T_d-WTe2 and TaIrTe4 the effective space group is Pm, with only the bc mirror plane. Under this symmetry, the in-plane second-order thermoelectric tensor has exactly three nonzero independent components: S^(2)_bbb, S^(2)_baa, and S^(2)_aab. Using dual-heater devices and lock-in detection, the authors observe all three at zero magnetic field, with clear |∇T|^2 scaling in the symmetrized fourth-harmonic voltage, and no detectable response in symmetry-forbidden orientations. The coefficients remain on the order of 10^-6 µV K^-2 cm up to room temperature. The authors further argue that the NLS coefficient scales as σ^2 with vanishing intercept,

Load-bearing premise

The result depends on the assumption that the two heaters create identical temperature patterns except for the direction of the heat flow, so swapping which heater is on cleanly cancels the large ordinary thermoelectric background; no measurement of the actual temperature profile inside the sample is reported.

Editorial extensions

If this is right

  • If confirmed, nonlinear thermoelectric rectification becomes an intrinsic property of low-symmetry crystals, so it should appear in any material where inversion is broken and only a mirror plane survives.
  • The observed room-temperature magnitudes in simple exfoliated flakes suggest practical thermal sensors and energy harvesters that require no magnetic field or engineered asymmetry.
  • Because the nonlinear Seebeck effect is dominated by skew scattering, controlling disorder and scattering processes becomes a direct lever on its magnitude.
  • The nonlinear Nernst effect shares a symmetry origin with the nonlinear Hall effect, allowing thermoelectric and electrical nonlinear responses to be compared quantitatively in the same materials.
  • The method extends naturally to higher-order thermoelectric tensors, since deviations from the quadratic-in-∇T response appear at increased heater power.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • An immediate testable extension would be gated devices: if the Berry-curvature-dipole term is present, tuning the Fermi level should change the intercept C of the σ² scaling while leaving the skew-scattering slope largely unchanged.
  • Because the temperature-dependent linear Seebeck background is roughly 40 times larger than the intrinsic signal, any fourth-harmonic thermoelectric measurement that does not report a simultaneous second-harmonic trace and heater-swap symmetrization should be treated with caution; this paper makes that point for its own data, but the implication extends to reinterpreting earlier reports.
  • If the intrinsic origin holds, the same symmetry rules predict vanishing nonlinear response in centrosymmetric controls and characteristic anisotropy patterns in other low-symmetry materials, offering a fast material-screening criterion.
  • The reported sign ambiguity of the coefficients under reversal of crystal axes could be resolved by combining polarized-Raman orientation with electrical Hall or piezoelectric response measurements, enabling quantitative sign comparison with theory.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 3 minor

Summary. The paper reports the observation of intrinsic second-order thermoelectric responses in exfoliated thin T_d-WTe2 and TaIrTe4 using harmonic detection. A 2ω linear Seebeck/Nernst response and a 4ω response quadratic in |∇T| are measured in three device geometries corresponding to the three symmetry-allowed components: nonlinear Seebeck S^(2)_bbb, nonlinear Nernst S^(2)_baa, and nonlinear mixed-directional S^(2)_aab. The 4ω response is symmetrized with respect to reversing the thermal gradient by swapping the active heater electrode. The authors also report the temperature dependence, a scaling analysis S^(2)=Aσ²+C to assign skew-scattering vs Berry-curvature contributions, null tests in one forbidden orientation, and frequency/DC-offset/capacitive-coupling controls. The central claim is that intrinsic nonlinear thermoelectricity persists to room temperature in zero magnetic field.

Significance. If established, this is a significant advance: it extends nonlinear Hall physics to thermal transport and shows that reduced crystal symmetry alone can produce nonreciprocal thermoelectric response at room temperature. The paper's strengths include the clear |∇T|² scaling of the 4ω signals, a null result in a forbidden configuration, an unusually transparent SI that quantifies the temperature-dependent linear background, and a broad set of control experiments (frequency dependence, dc-offset exclusion, harmonic-content checks). The main risk is the extraction of S^(2)_baa in the NLN configuration, where the symmetrization normalization channel does not track the gradient that drives the intrinsic response; this issue is flagged in the SI itself and needs an independent calibration before the 'all symmetry-allowed components' claim is fully secure.

major comments (3)
  1. [SI Sec. VI B; Fig. S7] In the NLN geometry, the symmetrization of SI Sec. VI B does not satisfy its own precondition. The 2ω normalization signal (Fig. S7c) is V_b=-S^(1)_bb L∇bT, a parasitic longitudinal Seebeck that does not reverse on heater swap; it calibrates only |∇bT|, not the |∇aT| that drives S^(2)_baa or the ΔT difference between heaters. The raw 4ω also does not reverse (Fig. S7d), the case the SI states cannot be unambiguously attributed to intrinsic nonlinearity. The subsequent defense (∇aT≈10∇bT; distinct T-dependence) is an estimate. With the temperature-induced background ~40× larger than the intrinsic signal (Fig. S6e,f), a few-percent heater asymmetry yields a residual of the size of the reported S^(2)_baa. An independent in-plane temperature profile or a phase-shift dual-heater measurement is required.
  2. [Main text 'Results and Discussion'; SI Sec. VII] The main text states that no detectable response is found in symmetry-forbidden configurations, but SI Sec. VII shows a null result only for the S^(2)_abb orientation; for S^(2)_bab the geometry is contaminated by allowed NLS/NLN terms and a pronounced 4ω response is observed (Eq. S19, Fig. S11). The wording should be qualified to avoid overstating the set of forbidden components experimentally tested.
  3. [Main text scaling analysis; SI Sec. XI] The microscopic assignment of the NLS/NLN coefficients from S^(2)_ijj = Aσ²_ii + C is underdetermined by the data shown. SI Sec. XI admits that a linear-in-σ scaling also gives a reasonable description, and the linear term is excluded by invoking theory (Ref. [25]) that intrinsic τ-linear terms cannot contribute to the NLS. With the limited low-temperature window and two-parameter fits, this does not uniquely 'demonstrate' the skew-scattering/Berry-curvature decomposition; the abstract and conclusions should be softened to 'consistent with' unless additional data or an independent mechanism test is provided.
minor comments (3)
  1. [SI Sec. VI B] The sentence introducing the Nernst calibration (V_b = ν_ba B_c L∇aT) is confusing because the NLN measurements are at zero field; clarify whether this is a separate finite-field calibration and how it is used to determine the zero-field ∇aT.
  2. [Fig. S6 caption] The caption says 'second-harmonic voltage (c) and the fourth-harmonic voltage (f)'; panel (f) is the symmetrized fourth-harmonic, so the raw fourth-harmonic is likely panel (d). Please correct the panel callouts.
  3. [SI headings and text] There are several typographical issues in the SI, e.g., 'T emperature', 'Frquency', 'dunction', 'resitance'. These should be corrected.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: 4ω signals are measured, the linear background is removed by gradient reversal, and the thermal calibration is independent; remaining caveats are experimental robustness issues, not definitional loops.

full rationale

The derivation chain is not circular. The nonlinear coefficients S^(2)_bbb, S^(2)_baa, and S^(2)_aab are extracted from measured 4ω lock-in voltages with fixed harmonic prefactors (SI Sec. II), converted to coefficients using temperature gradients from a finite-element simulation calibrated to the measured Pt-heater R(T) and cross-checked against WTe2 resistance versus I^2 (SI Sec. XII). Main-text Eq. 3 writes the 4ω signal as a temperature-dependent linear term proportional to ∂S^(1)/∂T·ΔT·∇T plus the intrinsic S^(2)(∇T)^2 term; the former is odd under heater swap while the latter is even, so the symmetrization cancels the former rather than fitting the latter. In the NLS geometry the 2ω normalization is a valid sign-reversing linear Seebeck calibration. The NLN geometry is weaker: the paper itself states that the 2ω and 4ω responses do not reverse with heater swap and that V4ω alone would not allow unambiguous attribution (SI Sec. VI.B, Fig. S7), then corrects for the parasitic ∇bT contribution using estimates that ∇aT ≈ 10×∇bT and distinct temperature dependencies. That is a model-based correction and a potential systematic error, not a definitional equivalence: the reported coefficient is not defined as the residual, and the correction is not fitted to the target. The self-citations for the Pm symmetry reduction of thin flakes (SI Refs. 1–4) refer to independent published measurements, including work by other groups, and are not an unverified uniqueness theorem. The BCD-versus-scattering assignment comes from a post-hoc scaling fit S^(2)_ijj = Aσ² + C after the coefficients were already measured; it is an interpretation, not part of the observation. Thus the central observation is self-contained against measurement and simulation, and the score is 1 rather than 0 only because the symmetry premise leans partly on prior work by the same group and the NLN background subtraction is not directly verified; these are correctness risks, not circularity.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The paper's central observation rests on the symmetry reduction assumption, the Boltzmann/BCD-scattering interpretive framework, and simulation-derived temperature gradients. No new entities are introduced. The only fitted quantities are the slopes/intercepts of the scaling analysis used for mechanism attribution, not for the existence of the effect.

free parameters (3)
  • A (slope in S^(2) = A σ^2 + C) = Not stated numerically; extracted from fits in Fig. 3 insets
    Fitted to low-T (<55 K) data; attributed to skew-scattering contribution.
  • C (intercept in S^(2) = A σ^2 + C) = Not stated numerically; extracted from fits in Fig. 3 insets
    Fitted; attributed to Berry-curvature-dipole contribution. Used to claim BCD contribution to the NLN effect.
  • low-temperature fit window = 55 K
    Hand-chosen cutoff for the scaling analysis, justified by validity of the Mott-Boltzmann framework; data above 55 K excluded.
assumptions (4)
  • domain assumption Thin flakes of WTe2 and TaIrTe4 have Pm symmetry with only the mirror plane σ(bc); bulk Pmn21 screw/glide symmetries are broken.
    Invoked in SI Sec. I A; based on prior electronic/magnonic transport studies (SI Refs 1-3) and comparable thicknesses, but not directly verified on the measured flakes.
  • domain assumption Semiclassical Boltzmann framework: σ_ii ∝ τ_i, so σ_ii^2 scaling corresponds to skew scattering and a constant term corresponds to Berry-curvature-dipole / intrinsic contributions.
    Used in SI Sec. XI to interpret fits; the authors note Mott-Boltzmann assumptions break down above 55 K.
  • domain assumption Temperature gradient in the flake is accurately given by COMSOL finite-element simulation calibrated to Pt heater resistance rise, and out-of-plane gradients are negligible.
    SI Sec. XII; authors state the inferred coefficients should be regarded as lower bounds because the simulation overestimates ΔT and ∇T.
  • standard math Harmonic detection lock-in relations (V4 ∝ I^4 R4 with numerical prefactors as in SI Eq. 14) and the absence of parasitic capacitive/dc-offset contributions.
    SI Secs. II, VIII, IX.

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Pith. "Pith review of Observation of room temperature intrinsic nonlinear thermoelectric effects in low-dimensional semimetals." pith.science (2026). https://pith.science/paper/RSERIKZI

@misc{pith2026260721808,
  author       = {Pith},
  title        = {Pith review of: Observation of room temperature intrinsic nonlinear thermoelectric effects in low-dimensional semimetals},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RSERIKZI}},
  note         = {Machine review of arXiv:2607.21808}
}
abstract

Nonreciprocal control of thermoelectric responses offers a promising strategy for next-generation thermal-management and energy-conversion. While nonlinear electrical transport has recently emerged as an intrinsic property of low-symmetry quantum materials, their thermoelectric counterparts have not been demonstrated. Here, exploiting harmonic detection with gradient-reversal techniques, we report intrinsic nonlinear thermoelectric responses up to room temperature in the low-symmetry type-II Weyl semimetals $T_\mathrm{d}$-WTe$_2$ and TaIrTe$_4$ in the absence of magnetic fields or magnetic materials. We resolve all symmetry-allowed components of the second-order thermoelectric tensor, including the nonlinear Seebeck, nonlinear Nernst, and nonlinear mixed-directional thermoelectric effects and demonstrate that both Berry-curvature-related and scattering-induced contributions govern the different nonlinear thermoelectric responses. Our results show that nonlinear thermoelectricity arises intrinsically from reduced crystal symmetry and that engineering effects related to scattering in these materials provides a versatile platform for exploring higher-order heat-to-charge current conversion beyond the linear response.

Figures

Figures reproduced from arXiv: 2607.21808 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. We observe that each of the symmetry-allowed [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (1 more)
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png]

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