Electric field control of third-order nonlinear Hall effect

Jiaju Yang; Jiarui Chen; Jun Du; Lina Chen; Lujun Wei; Wei Niu; Yanghui Li; Yong Pu

REVIEW 3 major objections 4 minor 2 cited by

Electric field control of third-order nonlinear Hall effect

T0 review · 3 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The third-order nonlinear Hall signal in TaIrTe4 reverses sign near 23 K and can be suppressed by up to 65.3% with an in-plane DC electric field.

desk verdict The sign-reversal observation is probably real, but the electric-field control claim is at risk because the paper never excludes DC Joule heating, and its own resistivity data show the expected heating signature. read the letter →

arxiv 2506.10657 v2 pith:BDHKXGZT submitted 2025-06-12 cond-mat.mes-hall cond-mat.mtrl-sci

Jiaju Yang , Lujun Wei , Yanghui Li , Lina Chen , Wei Niu , Jiarui Chen , Jun Du , Yong Pu This is my paper

classification cond-mat.mes-hallcond-mat.mtrl-sci

keywords third-ordernonlinearHalleffectBerry-connectionpolarizabilityTaIrTe4Weylsemimetalelectric-fieldcontrolsignreversalimpurityscatteringtransport

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

The paper claims that in the type-II Weyl semimetal TaIrTe4 the third-order nonlinear Hall response changes sign as temperature is lowered, with a crossover near 23 K. It interprets the high-temperature response as dominated by the Berry-connection polarizability of the bands and the low-temperature response as dominated by impurity scattering, using a scaling-law decomposition. The paper also claims that applying a static in-plane electric field weakens the response, reaching a 65.3% relative change at 4 K and 0.3 kV/cm, and that the field lowers the sign-reversal temperature. A sympathetic reader would care because this makes a band-geometric transport quantity electrically addressable without changing the material, and because it offers a testable recipe for separating geometric from scattering contributions in nonlinear Hall measurements.

What carries the argument

The carrying object is the third-order nonlinear Hall effect, a transverse third-harmonic voltage generated under a longitudinal alternating current, whose coefficient is governed by the Berry-connection polarizability tensor—a band-geometric quantity describing how the Berry connection responds to an electric field. The analytical workhorse is the scaling law $$|E_\$perp^{{3\omega}}$|/(E_\$parallel^{{\omega}}$)^3 = \xi\$sigma^{2}$+\eta,$$ combined with $\sigma\propto\tau$ (scattering time), so the $\xi$ term behaves like $\tau^3$ and the $\eta$ term like $\tau$; the authors read these as Drude-like and BCP-like contributions. Symmetry enters through Eq. (1), the $Pmn2_1$-derived angle dependence used to verify that the signal is intrinsic.

What would settle it

Measure the third-order NLHE in TaIrTe4 samples with deliberately varied disorder (thickness or irradiation) and check whether the sign-reversal temperature tracks the temperature at which resistivity enters the impurity-dominated regime; if the sign flip occurs at a temperature unrelated to that resistivity crossover, or if the data cannot be fitted as two straight lines in Eq. (2) without freely choosing the split, the central mechanism claim is wrong.

Watch

Extended reading notes

Core claim

On the authors' account, the third-order nonlinear Hall voltage $V_\perp^{3\omega}$ in TaIrTe4 is intrinsic and follows $V_\perp^{3\omega}\propto(I^\omega)^3$, with a response strength $V_\perp^{3\omega}/(V_\parallel^{\omega})^3$ whose sign flips near 23 K. Fitting the scaling law $|E_\perp^{3\omega}|/(E_\parallel^{\omega})^3 = \xi\sigma^2+\eta$, where $\sigma$ is longitudinal conductivity, they assign the constant $\eta$ to a Berry-connection-polarizability-like contribution and $\xi$ to a Drude-like impurity-scattering contribution, the two competing across temperature. A DC in-plane field $E_{dc}$ reduces the BCP-like part at high temperature and both parts at low temperature, moving the critical temperature from about 23 K to 17 K at 0.5 kV/cm and producing a maximum relative modulation of 65.3% at 4 K with 0.3 kV/cm. The same electric-field-controlled behaviour is reproduced in a second, thinner device.

Load-bearing premise

The interpretation rests on splitting the data at the observed sign-change temperature and reading the two fitted constants in $|E_\perp^{3\omega}|/(E_\parallel^{\omega})^3 = \xi\sigma^2+\eta$ as separate physical contributions; if that split or assignment is not correct, the mechanism story collapses.

Editorial extensions

If this is right

Temperature alone can reverse the sign of the third-order nonlinear Hall effect in a given material, so transport-based band-geometry probes need to specify temperature rather than assume a fixed sign.
A static in-plane electric field provides a continuous, all-electrical tuning knob for the nonlinear Hall response, complementing strain and gate tuning.
The sign-reversal (critical) temperature moves downward under DC bias, meaning the field shifts the balance between geometric and impurity-scattering contributions rather than merely scaling both.
The 65.3% relative change at low temperature indicates electric-field control is strong enough for electrically programmable nonlinear Hall devices such as tunable rectifiers or vector sensors.

Reading between the lines

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

If the BCP-versus-scattering crossover is generic, the same sign flip should appear in other noncentrosymmetric semimetals when disorder is varied; a controlled impurity-series experiment would test this directly.
The two-constant fit assumes the data split at the sign-change temperature is physically meaningful; a stronger test would measure $\xi$ and $\eta$ at finer temperature steps and check that each regime collapses on a single line without optimizing the split.
The paper does not derive the field-induced lowering of the critical temperature from a microscopic model; a quantum-kinetic or Boltzmann calculation of BCP under DC bias could turn the empirical shift into a quantitative prediction.
Because the effect persists to room temperature and the modulation is DC-driven, pulsed or AC control may be a natural extension for high-speed operation, though the paper does not report time-dependent measurements.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Colleague,

The paper is worth knowing about for the sign-reversal observation: the third-order NLHE in TaIrTe4 flips sign near 23 K, and the authors show it follows the expected symmetry and I^3 scaling. That seems like a new data point, and the angle dependence fits are clean. The second claim, electric-field control, is where I get off. The paper attributes the modulation to a shift in the BCP/impurity balance, but it never rules out the plainest explanation: the DC field is simply heating the sample. Their own Fig. 5a shows the resistivity crossover move from ~24 K to ~19 K when Edc=0.5 kV/cm. That is a textbook Joule-heating signature. The Supplementary Fig. S3 exclusion is about the AC third-harmonic signal being capacitive/thermal, not about the DC bias changing the sample temperature. So the 65.3% modulation at 4 K could be trivial: the field raises T, and the temperature dependence alone does the rest.

The scaling-law analysis does not rescue this. Equation (2) is fitted separately above and below a data-defined cutoff, with no error bars and no independent prediction. The mapping of xi to Drude and eta to BCP comes from previous work, but the two-region split means any heating-induced renormalization is absorbed into the fitted parameters. So the mechanism for the sign reversal is plausible but not proven, and the field-control mechanism is under-supported.

Where the authors deserve credit: the signal is carefully checked for some artifacts, the symmetry-based fit for the angle dependence is good, they show reproducibility in a second device, and they are clear about what they did. The paper is readable. The central observation is probably real.

The soft spot is serious, though. For the claim 'electric field control' to hold, a referee should demand a direct temperature check under DC bias (e.g., a local thermometer, or a comparison with the zero-field curve at the effective elevated temperature). Without that, the title-level claim is not supported. The sign reversal itself may still be a real effect, but the mechanism argument needs more work at minimum.

I think this deserves a serious referee, not a desk reject, because the observation is new and the field is young. But my own verdict would be: must fix the heating issue before publication. I would not cite the field-control claim in my own work yet.

Yours,

Referee Report

3 major / 4 minor

Summary. The paper reports measurements of the third-order nonlinear Hall effect (NLHE) in micro/nano devices of the type-II Weyl semimetal TaIrTe4, both without and with an applied in-plane DC electric field Edc. The authors find a sign reversal of the third-order Hall response V_perp^3omega/(V_parallel^omega)^3 near 23 K as temperature is lowered, and a DC-field modulation of the response that reaches a 65.3% relative change at 4 K and Edc = 0.3 kV/cm, with a 180-degree periodicity in the DC-field angle. Based on the scaling relation |E_perp^3omega|/(E_parallel^omega)^3 = xi*sigma^2 + eta, they attribute the high-temperature response to Berry-connection polarizability (eta) and the low-temperature response to impurity scattering (xi), and argue that the DC electric field weakens both contributions and shifts the crossover temperature. The central microscopic interpretation is that an in-plane DC field controls the BCP/impurity-scattering balance.

Significance. If the nonthermal nature of the DC-field modulation is established, the sign reversal and the 65.3% relative modulation would be of clear interest to the nonlinear-transport community and to proposals for electric-field-tunable quantum devices. The paper contains useful falsifiable observations: the (I^omega)^3 scaling of the third harmonic, the lattice-angle dependence fitted by Eq. (1), the exclusion of some AC capacitive/thermal artifacts, and reproducibility on a second device. However, the mechanistic claims rest on data-defined two-region fits of Eq. (2) and on an unverified assumption that the DC bias does not cause Joule heating; the latter is directly challenged by the paper's own resistivity data. The empirical observations are plausible and worth reporting, but the title-level claim of electric-field control requires an additional thermal control.

major comments (3)

[Electric field control of third-order NLHE; Fig. 5a] The central claim of electric-field control is not yet separated from DC Joule heating. The only thermal check cited (Supplementary Fig. S3) addresses the origin of the AC third-harmonic signal, not the thermal load from Edc. More direct evidence is in Fig. 5a: with Edc = 0.5 kV/cm the onset of the impurity-scattering (residual-resistance) regime shifts from about 24 K to about 19 K, which is exactly what one would expect if the DC bias raises the sample temperature above the bath temperature. If the sample at Edc = 0.3 kV/cm and 4 K is in fact several kelvin warmer, then the 65.3% modulation shown in Fig. 4d is largely a temperature effect (Fig. 2d) rather than an electric-field effect. The authors should provide a control in which the sample temperature is determined from its own resistance or a co-located thermometer under DC bias, or show that the modulation persists when the DC bias is pulsed with variable duty cycle. Without such a control, the title-level claim is not established.
[Mechanism of electric-field control; Eq. (2) and Figs. 5c-5f] The attribution to competing BCP-like (eta) and Drude-like (xi) contributions rests on fitting Eq. (2) separately to data above and below a data-defined crossover temperature (about 23 K, shifted to about 17-19 K under Edc). These fits are reported without error bars or the number of points in each region, and the same data set is used both to define the two regions and to obtain the fitted parameters. Equation (2) is therefore used as a decomposition rather than as a quantitative test: xi and eta are not independently predicted, and any heating-induced renormalization of sigma(T) will be absorbed into the fitted xi and eta. The authors should report fit uncertainties and a stability analysis showing that the xi and eta trajectories in Figs. 5c and 5d are insensitive to small changes of the crossover temperature. As it stands, the mechanism section does not discriminate between a BCP/impurity-scattering crossover and a simpler temperature-shift scenario.
[Angle-dependent modulation; Fig. 4] The 180-degree angle dependence of the modulation is presented as evidence of a directional electric-field effect, but the same dependence is expected from Joule heating alone, because the anisotropic resistivity (Fig. 1e) makes the DC power dissipation depend on the direction of Edc even at fixed |Edc|. The measured quantity V_perp^3omega/(V_parallel^omega)^3 is also sensitive to changes in the longitudinal resistance with Edc direction. A heating control, for example a measurement of the longitudinal resistance at each angle and Edc, is needed to separate the angular modulation of the response from the angular modulation of the dissipated power. This issue is load-bearing for the field-direction claims in Fig. 4.

minor comments (4)

[Throughout] There are several typographical errors that should be corrected: 'TaTrTe4' instead of 'TaIrTe4' in multiple headings, 'sanning' for 'scanning', 'ffeld' for 'field', and 'anning' for 'annealing' throughout the Methods and figure captions.
[Eq. (2) and Fig. 5b] The scaling law is written for electric fields, but the data are plotted as voltage ratios V_perp^3omega/(V_parallel^omega)^3. The conversion factor between electric-field ratio and voltage ratio, including device geometry and any anisotropic resistivity, should be stated explicitly.
[Supplementary Fig. S3] The main text cites Supplementary Fig. S3 as ruling out capacitive and thermal contributions to the third-harmonic signal, but the experimental checks are not described in the main text. A one-sentence summary of what was measured and why it excludes those artifacts would help the reader assess the claim.
[Fig. 3d] The apparent linear dependence of V_perp^3omega/(V_parallel^omega)^3 on Edc at 4 K is stated, but no fit parameters or residuals are given. Given the small number of Edc values shown, the linearity claim should be substantiated with fit statistics.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the sign reversal and electric-field modulation are direct measurements, and the scaling-law decomposition is an external theoretical framework, not a self-referential prediction.

full rationale

The paper's central experimental claims—temperature-induced sign reversal of the third-order NLHE and its modulation by an in-plane DC electric field—are direct transport measurements presented in Figs. 2c-d, 3a-d, and 4. These observations are not derived from the scaling law; rather, the scaling law in Eq. (2) is imported from prior literature (refs [1,11]) and used to interpret the measured temperature dependence in terms of BCP-like (eta) and Drude-like (xi) contributions. This is a post-hoc mechanistic interpretation, not a prediction whose output equals its input. The two-region split at the sign-reversal temperature is data-defined, but the assignment of eta and xi to physical mechanisms comes from external theoretical work (refs [1,2,11,24]), not from the present data alone. No equation in the paper reduces to another by construction, and no load-bearing claim rests on a self-citation chain. The possible Joule-heating artifact under DC bias is an experimental correctness concern, not a circularity. Score 1 reflects a mild caveat that the mechanistic conclusion is inferred from the same fits used to describe the data, while the core observations are independent and falsifiable.

Assumptions & free parameters 2 free parameters · 3 assumptions · 0 invented entities

The central claims rest on a standard scaling law and on a data-split fitting procedure. No new entities are introduced. The free parameters are the fit coefficients used to assign physical meaning.

free parameters (2)

xi (Drude-like coefficient in Eq. 2) = not stated numerically
Fitted separately for high- and low-temperature regions and for each applied dc field; used to attribute response to impurity scattering.
eta (BCP-like coefficient in Eq. 2) = not stated numerically
Fitted in the same procedure; used to attribute response to Berry-connection polarizability.

assumptions (3)

domain assumption The third-order nonlinear Hall response obeys the scaling law |E_perp^3omega|/(E_parallel^omega)^3 = xi*sigma^2 + eta (Eq. 2) over the measured temperature range.
The paper applies this relation from Refs. [1,11] without re-deriving it for TaIrTe4.
domain assumption The measured third harmonic voltage is an intrinsic third-order nonlinear Hall effect after ruling out capacitive and thermal artifacts.
The paper states artifact checks in Supplementary Fig. S3 but does not show quantitative details.
ad hoc to paper The sign of the total response equals the sign of the dominant contribution between BCP-like (eta) and Drude-like (xi) terms, with no significant interference.
The crossover interpretation requires that xi and eta add with a sign that flips at the critical temperature; this is not independently verified.

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Cite this review

Pith. "Pith review of Electric field control of third-order nonlinear Hall effect." pith.science (2026). https://pith.science/paper/BDHKXGZT

@misc{pith2026250610657,
  author       = {Pith},
  title        = {Pith review of: Electric field control of third-order nonlinear Hall effect},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BDHKXGZT}},
  note         = {Machine review of arXiv:2506.10657}
}

read the original abstract

The third-order nonlinear Hall effect (NLHE) serves as a sensitive probe of energy band geometric property, providing a new paradigm for revealing the Berry curvature distribution and topological response of quantum materials. In the Weyl semimetal TaIrTe4, we report for the first time that the sign of the third-order NLHE reverses with decreasing temperature. Through scaling law analysis, we think that the third-order NLHE at high (T > 23 K) and low (T < 23 K) temperatures is dominated by Berry-connection polarizability (BCP) and impurity scattering, respectively. The third-order NLHE response strength can be effectively modulated by an additional applied in-plane constant electric field. At the high temperature region, the BCP reduction induced by the electric field leads to a decrease in the third-order NLHE response strength, while at the low temperature region, the electric field cause both BCP and impurity scattering effects to weaken, resulting in a more significant modulation of the third-order NLHE response strength. At 4 K and an electric field strength of 0.3 kV/cm, the modulated relative response strength could reach up to 65.3%. This work provides a new means to explore the third-order NLHE and a valuable reference for the development of novel electronic devices.

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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Identifying geometric third-order nonlinear transport in disordered materials
cond-mat.mes-hall 2025-10 conditional novelty 6.0 of 10

A catalog of 20 third-order nonlinear-transport mechanisms plus a scaling-law fingerprint table for identifying geometric vs. disorder-dominated responses in experiments.
Electric field controlled second-order anomalous Hall effect in altermagnets
cond-mat.mes-hall 2025-10 conditional novelty 6.0 of 10

A dc field generates a Berry-curvature-dipole-driven second-order anomalous Hall effect in Rashba-coupled hybrid altermagnets, whose magnitude can distinguish dxy from dx2-y2 order at certain dopings.

Reference graph

Works this paper leans on

24 extracted references · 24 canonical work pages · cited by 2 Pith papers

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

Nature Nanotechnology, 2021

Lai, S., et al., Third-order nonlinear Hall effect induced by the Berry-connection polarizability tensor. Nature Nanotechnology, 2021. 16(8): p. 869-873

work page 2021

[2] [2]

Physical Review B, 2022

Liu, H., et al., Berry connection polarizability tensor and third -order Hall effect. Physical Review B, 2022. 105(4)

work page 2022

[3] [3]

Physical Review B, 2022

Ye, X.-G., et al., Orbital polarization and third-order anomalous Hall effect in WTe2. Physical Review B, 2022. 106(4)

work page 2022

[4] [4]

Physical Review Letters, 2025

Liu, X.-Y ., et al., Giant Third-Order Nonlinearity Induced by the Quantum Metric Quadrupole in Few-Layer WTe2. Physical Review Letters, 2025. 134(2)

work page 2025

[5] [5]

Applied Physics Letters, 2023

Li, H., et al., Current induced second-order nonlinear Hall effect in bulk WTe2. Applied Physics Letters, 2023. 123(16)

work page 2023

[6] [6]

Physical Review Letters, 2023

Zhao, T.-Y ., et al., Gate-Tunable Berry Curvature Dipole Polarizability in Dirac Semimetal Cd3As2. Physical Review Letters, 2023. 131(18)

work page 2023

[7] [7]

Physical Review B, 2024

Chen, Z.-H., et al., Charge density wave modulated third-order nonlinear Hall effect in 1T−VSe2 nanosheets. Physical Review B, 2024. 110(23)

work page 2024

[8] [8]

Nature Nanotechnology, 2024

He, P., et al., Third-order nonlinear Hall effect in a quantum Hall system. Nature Nanotechnology, 2024. 19(10): p. 1460-1465

work page 2024