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Room-temperature intrinsic nonlinear planar Hall effect in TaIrTe$_4$

T0 review · 3 major / 3 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read The paper reports the first experimental observation of the intrinsic nonlinear planar Hall effect in the topological semimetal TaIrTe$_4$, where a second-harmonic Hall voltage quadratic in the driving current and linear in an in-plane…

desk verdict First credible intrinsic NPHE claim with strong scaling checks; the load-bearing intercept needs more supporting data before it is fully trusted. read the letter →

arxiv 2506.17730 v1 pith:BLIAFYVS submitted 2025-06-21 cond-mat.mes-hall cond-mat.mtrl-sci

Chang Jiang , Fan Yang , Jinshan Yang , Peng Yu , Huiying Liu , Yuda Zhang , Zehao Jia , Xiangyu Cao
show 7 more authors
Jingyi Yan Zheng Liu Xian-Lei Sheng Cong Xiao Shengyuan A. Yang Shaoming Dong Faxian Xiu
This is my paper · ORCID
classification cond-mat.mes-hallcond-mat.mtrl-sci
keywords nonlinearplanarHalleffectBerry-connectionpolarizabilityBCPdipolesusceptibilityTaIrTe4topologicalsemimetalorbitalmagneticmomentsecond-harmonictransportquantumgeometry
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 tries to establish that the topological semimetal TaIrTe$_4$ shows an intrinsic nonlinear planar Hall effect: a Hall voltage that scales with the square of the driving current and linearly with an in-plane magnetic field, with the coefficient set by a band-geometric quantity, the Berry-connection polarizability dipole susceptibility, rather than by scattering. The signal persists at room temperature, reaching about $10^{-4}\ \mathrm{m\,T^{-1}\,V^{-2}}$, roughly two orders of magnitude above the extrinsic signals reported earlier. By fitting the conductivity to $\chi = \xi\sigma + \eta$ over a temperature sweep, the authors separate a temperature-linear extrinsic term from a temperature-independent intercept $\eta$ and show that its two independent components match first-principles values ($2.40\times10^{-4}$ and $-1.73\times10^{-4}\ \mathrm{m\,T^{-1}\,V^{-2}}$) in magnitude and sign. The calculations also identify a previously unnoticed orbital-moment coupling to the magnetic field that dominates the response and does not require spin-orbit coupling.

What carries the argument

The load-bearing object is the Berry-connection polarizability (BCP) dipole susceptibility, a fourth-rank tensor $\Upsilon_{abcd}$ defined by $\mathfrak{D}_{abc} = \Upsilon_{abcd} B_d$, where $\mathfrak{D}$ is the Fermi-surface integral of the BCP dipole and the BCP tensor itself is $G_{ab} = 2\,\mathrm{Re}\sum_{n\neq m} v_a^{mn}v_b^{nm}/(\varepsilon_m-\varepsilon_n)^3$. It converts an in-plane magnetic field into a field-induced BCP dipole, and the resulting second-order current is $j_a^{(2)} = \Upsilon_{abcd} E_b E_c B_d$. On the experimental side, the linear scaling $\chi = \xi\sigma + \eta$ is the tool that separates the intrinsic intercept $\eta$, identified with $\Upsilon$, from the extrinsic slope $\xi$.

What would settle it

Measure the same second-harmonic Hall response on TaIrTe4 flakes of different thicknesses (e.g., 30 nm vs 10 nm) and with different surface terminations: a bulk intrinsic intercept $\eta$ must remain constant, while a surface or contact artifact would vary with the surface-to-volume ratio.

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Extended reading notes

Core claim

The central discovery is the first observation of the intrinsic nonlinear planar Hall effect in a nonmagnetic crystal. In TaIrTe$_4$, the second-harmonic transverse voltage obeys $j_a^{(2)} = \Upsilon_{abcd} E_b E_c B_d$, with $\Upsilon$ the BCP dipole susceptibility, and shows the angular dependence dictated by $C_{2v}$ symmetry: the signal's phase $\beta$ differs from the current angle $\theta$, the amplitude peaks when current is along the $y$ axis, and both magnetic-field and current scalings are linear as required. The temperature sweep produces an almost perfect linear scaling $\chi = \xi\sigma + \eta$, and the intercepts $\eta_1 = 2.8\times10^{-4}$ and $\eta_2 = -1.6\times10^{-4}\ \mathrm{m\,T^{-1}\,V^{-2}}$ agree with the first-principles components $\chi_1^{\mathrm{int}} = 2.40\times10^{-4}$ and $\chi_2^{\mathrm{int}} = -1.73\times10^{-4}$, including the opposite signs. A further claim is that the orbital moment of Bloch electrons, not just the spin Zeeman coupling, generates most of $\Upsilon$ — for one component the orbital part is an order of magnitude larger — and this orbital channel works even without spin-orbit coupling.

Load-bearing premise

The intercept $\eta$ in the empirical scaling $\chi = \xi\sigma + \eta$ is assumed to contain only the intrinsic BCP-dipole-susceptibility contribution; any temperature-independent artifact, such as contact asymmetry, surface background, thermoelectric offset, or electrode misalignment, that survives the background subtraction would be mistaken for the intrinsic effect.

Editorial extensions

If this is right

  • The intrinsic NPHE is a material property, so any TaIrTe$_4$ crystal with the same band structure should reproduce the intercept $\eta$ regardless of device geometry or contact quality.
  • Because all polar and chiral crystal classes support the intrinsic NPHE, the measurement protocol transfers to high-symmetry point groups such as $C_{6v}$, $D_6$, $T$, and $O$, where other second- and third-order nonlinear Hall effects are symmetry-forbidden.
  • The dominant orbital mechanism operates without spin-orbit coupling, so sizable intrinsic NPHE should appear in light-element polar and chiral materials.
  • The room-temperature magnitude of $\chi_1 \sim 10^{-4}\ \mathrm{m\,T^{-1}\,V^{-2}}$ supports nonlinear device functions such as wireless rectification and energy harvesting at ambient conditions.

Reading between the lines

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

  • The authors do not test this, but their $\chi$–$\sigma$ intercept protocol could be applied to existing NPHE data in Bi$_2$Se$_3$, SrIrO$_3$, and Te: a nonzero temperature-independent intercept there would reveal an intrinsic component hidden under the dominant extrinsic $\sim\tau^2$ response.
  • A thickness-dependence experiment would settle the surface-artifact question: if $\eta$ is the bulk BCP susceptibility, it should be identical in 30-nm and 40-nm flakes and after different surface treatments, whereas any surface background would scale with surface-to-volume ratio.
  • Because the orbital channel needs no spin-orbit coupling, two-dimensional polar materials made of light atoms are natural testbeds; a null intercept in such a material, despite a symmetry-allowed tensor, would force a re-examination of the orbital mechanism.
  • Searching for correlations between the intercept and Fermi-level position, for example by chemical doping or electrostatic gating in a material where the carrier density is tunable, would test the k-space localization of $\Upsilon$ near small-gap regions.
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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 experimental discovery of a nonlinear planar Hall effect (NPHE) in the type-II Weyl semimetal TaIrTe4, with a Hall current scaling as E^2 B and an angular dependence consistent with the C2v crystal symmetry. The effect persists up to room temperature. By measuring the NPHE conductivity as a function of longitudinal conductivity over 100–300 K, the authors observe an approximately linear scaling chi = xi sigma + eta and identify the zero-conductivity intercept eta with the intrinsic Berry-connection polarizability (BCP) dipole susceptibility. First-principles calculations yield Upsilon_yxxy = 2.40e-4 and Upsilon_yxxx = -1.73e-4 m T^-1 V^-2, matching the experimental intercepts (eta_1 = 2.8e-4, eta_2 = -1.6e-4) in sign and magnitude. The calculations also show a dominant orbital contribution to the BCP dipole susceptibility, beyond the conventional spin Zeeman mechanism.

Significance. If the identification of the intercept eta with the intrinsic BCP dipole susceptibility is correct, this is the first observation of intrinsic NPHE and the first experimental probe of the BCP dipole susceptibility, achieving room-temperature operation. The paper is strengthened by its frequency-independence tests (Supplemental Note 3), out-of-plane field checks (Supplemental Note 4), multiple device geometries (Hall bar and circular disk), consistency across three devices (Table S1), and parameter-free DFT calculations that reproduce the signs and approximate magnitudes of both independent tensor components. The claims would be transformative for nonlinear transport in polar/chiral semimetals. However, the central claim rests on a scaling intercept that is assumed to be temperature-independent and purely intrinsic, which is not yet fully established, as detailed in the major comments.

major comments (3)
  1. [Fig. 4 and Eq. (4)] The identification of the zero-conductivity intercept eta with the intrinsic BCP dipole susceptibility assumes that chi = xi sigma + eta holds with a temperature-independent eta over the entire 100–300 K range. The intrinsic susceptibility defined in Eq. (1) contains the Fermi-Dirac derivative f0', so in a semimetal with small-gap regions near the Fermi level it can itself vary substantially with temperature. The paper does not compute Upsilon(T) over 100–300 K nor provide an argument for its constancy. If Upsilon varies with temperature, the fitted intercept is a weighted average over the temperature window, and the agreement with zero-temperature DFT (chi1^int = 2.40e-4, chi2^int = -1.73e-4) could be coincidental. Please provide the temperature dependence of the calculated Upsilon, or an explicit theoretical justification that it is constant, and show how the experimental intercept relates to the zero-temperature value.
  2. [Fig. 4(c,d) and Eq. (4)] The 'almost perfect linear scaling' is not supported by statistical evidence: the figures show no error bars, residuals, or the number of independent temperature points, and the statement in the text that uncertainties are smaller than the symbol size is not a substitute for a quantitative fit. The extrapolation to sigma = 0 is a two-parameter linear fit over a limited temperature range; any small curvature (e.g., a term proportional to sigma^2) would bias the intercept. Please report the raw data, the fit parameters with uncertainties, and a statistical test comparing the linear form with an alternative functional form (for example, chi = xi sigma + eta + gamma sigma^2).
  3. [Eq. (4) and angular dependence section] The extraction of eta as an intrinsic contribution assumes that all temperature-independent second-harmonic artifacts are either absent or completely removed. The paper subtracts a magnetic-field-independent background and rules out electrode misalignment and some geometric effects through temperature-dependent measurements (Supplemental Notes 5 and 9), but it does not quantitatively exclude temperature-independent contributions from contact asymmetry, thermoelectric voltages, or magnetic-field-dependent contact resistances. Because the intercept is the sole evidence for the intrinsic claim, a control experiment (e.g., reversing current and voltage contacts, or measuring a centrosymmetric reference sample with identical contact geometry) is needed to confirm that no such artifact contributes to eta.
minor comments (3)
  1. [Eq. (1)] The indices in the definition of the BCP dipole appear inconsistent: the integrand is written with v_y G_xy and v_y G_yy, but the component D_yxx should involve G_xx or a combination that is not clearly defined. Please check the index structure and ensure the notation matches the derivation in the Supplemental Material.
  2. [Fig. 3(c)] The fit of beta versus theta depends on the resistivity anisotropy ratio r (determined to be about 0.24), but the sensitivity of the extracted chi_1 and chi_2 to the uncertainty in r is not discussed. Please provide an estimate of how errors in r propagate to the NPHE conductivity values.
  3. [Conclusion] The conclusion states that the measurements 'allow us to probe the BCP dipole susceptibility,' but the experimental access is indirect (through the scaling intercept). Consider softening this wording to reflect the model-dependent identification.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the measured intercept and the first-principles BCP dipole susceptibility are independently determined.

full rationale

The paper's derivation chain is: (1) define the intrinsic NPHE current in terms of the BCP dipole susceptibility Υ (Eqs. 1-2, following prior theory); (2) measure the second-harmonic Hall voltage and extract the nonlinear conductivity components χ1 and χ2 from the angular dependence (Eq. 3); (3) observe the linear scaling χ = ξσ + η (Eq. 4) and fit the intercepts η1 and η2; (4) compute Υ from first principles for TaIrTe4 and compare with η. No step reduces to its own input by construction. The intercept η is an empirical fit parameter, while the DFT values χ1^int = 2.40×10^-4 and χ2^int = -1.73×10^-4 are independent parameter-free calculations; the paper gives no indication that these values were adjusted or refitted to match the experimental intercepts. The self-citations (Refs. [4], [14], [29], [32]) supply the theoretical framework for BCP dipole susceptibility and the scaling-law discussion, but they are published theoretical results and the experiment plus DFT constitute an independent test of that framework rather than a circular reliance on it. The identification of the zero-conductivity intercept with the intrinsic contribution rests on the assumption that other temperature-independent second-harmonic artifacts are absent; this is a physical assumption that could be challenged on correctness grounds, but it is not a definitional or statistical circularity. Therefore the analysis is self-contained with respect to circularity, and the score is 0.

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

The central claim depends on the theoretical framework of BCP dipole susceptibility, the empirical decomposition χ = ξσ + η, the accuracy of DFT band structure, and the absence of artifacts in the second-harmonic measurement. No invented entities are needed. The two experimental intercepts are fitted values that carry the entire intrinsic claim.

free parameters (3)
  • η1 = 2.8e-4 m T^-1 V^-2
    Zero-conductivity intercept of the linear fit in Fig. 4(c), identified as the intrinsic χ1^int.
  • η2 = -1.6e-4 m T^-1 V^-2
    Zero-conductivity intercept of the linear fit in Fig. 4(d), identified as the intrinsic χ2^int.
  • Resistivity anisotropy ratio r = 0.24
    Fitted from first-harmonic angular resistance data and used in Eq. (3) to convert the measured voltage into the NPHE conductivity components.
assumptions (4)
  • domain assumption The BCP dipole susceptibility Υ is the intrinsic band geometric coefficient governing j_i = Υ_ijkl E_j E_k B_l (Eq. 2).
    The central claim is interpreted through this theoretical framework provided by Ref. [14], which has overlapping authorship with the present paper.
  • ad hoc to paper The measured NPHE conductivity decomposes as χ = ξσ + η with a temperature-independent intercept η that is the intrinsic contribution.
    The decomposition is an empirical modeling choice used in Eq. (4); it is not derived from a microscopic theory, and any temperature-independent artifact would also enter η.
  • domain assumption DFT-PBE band structure and Wannier interpolation accurately describe the small-gap regions of TaIrTe4 relevant to the BCP dipole susceptibility.
    The quantitative comparison between theory and experiment depends on the fidelity of the first-principles band structure near the Fermi level.
  • domain assumption The measured second-harmonic voltage, after subtracting a B-independent background, arises from the electronic NPHE rather than capacitive, thermal, or contact artifacts.
    The authors provide frequency-independence and out-of-plane rotation checks, but the exclusion of all temperature-independent artifacts is not exhaustive.

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Pith. "Pith review of Room-temperature intrinsic nonlinear planar Hall effect in TaIrTe$_4$." pith.science (2026). https://pith.science/paper/BLIAFYVS

@misc{pith2026250617730,
  author       = {Pith},
  title        = {Pith review of: Room-temperature intrinsic nonlinear planar Hall effect in TaIrTe$_4$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BLIAFYVS}},
  note         = {Machine review of arXiv:2506.17730}
}
abstract

Intrinsic responses are of paramount importance in physics research, as they represent the inherent properties of materials, independent of extrinsic factors that vary from sample to sample, and often reveal the intriguing quantum geometry of the band structure. Here, we report the experimental discovery of a new intrinsic response in charge transport, specifically the intrinsic nonlinear planar Hall effect (NPHE), in the topological semimetal TaIrTe$_4$. This effect is characterized by an induced Hall current that is quadratic in the driving electric field and linear in the in-plane magnetic field. The response coefficient is determined by the susceptibility tensor of Berry-connection polarizability dipole, which is an intrinsic band geometric quantity. Remarkably, the signal persists up to room temperature. Our theoretical calculations show excellent agreement with the experimental results and further elucidate the significance of a previously unknown orbital mechanism in intrinsic NPHE. This finding not only establishes a novel intrinsic material property but also opens a new route toward innovative nonlinear devices capable of operating at room temperature.

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