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REVIEW 3 major objections 4 minor 46 references

Nonlinear planar Hall effect from superconducting vortex motion

T0 review · 3 major / 4 minor · reviewed 2026-08-04 · deepseek-v4-flash

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Pith's one-line read A centrosymmetric FeSe film shows a nonreciprocal transverse voltage under an in-plane field parallel to the current, which the authors trace to thermally excited vortex-antivortex pairs.

desk verdict First convincing observation of nonreciprocal transverse resistance in a centrosymmetric 2D superconductor under H||I, with a plausible but unverified vortex-Hall mechanism that needs the missing SM and a film-specific Hall-angle measurement. read the letter →

arxiv 2509.06313 v1 pith:CD5GKM2Q submitted 2025-09-08 cond-mat.supr-con

Mio Hashimoto , Takako Konoike , Tomoki Kobayashi , Shintaro Hoshino , Takuya Kawada , Tomoyuki Yokouchi , Shinya Uji , Atsutaka Maeda
show 1 more author
Yuki Shiomi
This is my paper · ORCID
classification cond-mat.supr-con PACS 74.25.F74.25.Wx
keywords nonreciprocaltransportnonlinearHalleffectvortexratchetvortex-antivortexpairsFeSethinfilmtwo-dimensionalsuperconductorcentrosymmetric
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 direction-dependent (nonreciprocal) charge transport in both the longitudinal and transverse directions of a superconducting FeSe film, with the transverse signal appearing when the in-plane magnetic field is parallel to the current. Because the FeSe crystal is centrosymmetric, the symmetry breaking must come from the film surfaces, and the current-parallel-field configuration is one where ordinary field-induced vortices should feel no driving force. The authors attribute the effect to thermally excited vortex-antivortex pairs: these pairs have out-of-plane flux and are driven by the current, while the in-plane field and interface asymmetry bias their motion and produce a Hall-like voltage. If correct, this is the first experimental demonstration of a nonreciprocal transverse response in a centrosymmetric two-dimensional superconductor under current-parallel field.

What carries the argument

The carrier of the effect is the thermally excited vortex-antivortex pair: two oppositely circulating phase whirlpools whose out-of-plane magnetic flux responds to in-plane current even when the applied field is parallel to the current. The two ingredients that turn these pairs into a rectifier are the vortex Hall effect (a large Hall angle, about 0.5, reported in FeSe crystals, so vortex velocity is not parallel to the driving force) and mirror-symmetry breaking along the field direction, supplied by the in-plane field acting on the intrinsically asymmetric FeSe/LaAlO3 and FeSe/Si interfaces. The supporting model calculation adds Rashba spin-orbit coupling to the Ginzburg-Landau free energy

What would settle it

Measure ΔR_yx under current-parallel field in FeSe films with thickness spanning the two-dimensional-to-three-dimensional crossover: if thermally excited (anti)vortices are the cause, the transverse nonreciprocal signal should collapse as two-dimensional vortex fluctuations weaken, whereas a surface-barrier ratchet would persist.

Watch

Extended reading notes

Core claim

The central claim is that, in the vortex-flow regime of a 23-nm FeSe film below Tc ≈ 2.8 K, the current-nonlinear longitudinal resistance ΔR_xx appears for an in-plane field perpendicular to current, while a nonreciprocal transverse resistance ΔR_yx appears for field parallel to current—the geometry in which the Lorentz force on field-induced vortices vanishes. The signal is absent above Tc and at zero field, grows and then shrinks with current, and obeys the angular symmetry expected for a polar two-dimensional system, which the authors use to rule out vortex Nernst artifacts. They propose that thermally excited vortex-antivortex pairs—whose flux points out of the film plane—are driven by t

Load-bearing premise

The explanation assumes that thermally excited vortex-antivortex pairs are numerous enough in the two-dimensional FeSe film to produce the measured voltage, and that the in-plane field makes their sideways motion asymmetric; the paper itself calls this attribution tentative, and the quantitative model calculation is placed in a Supplemental Material not included in this preprint.

Editorial extensions

If this is right

  • Nonreciprocal Hall voltages become accessible in ordinary centrosymmetric films, with only the interfaces providing the symmetry breaking.
  • The measured ΔR_xx/ΔR_yx ratio of 2–4, close to the predicted 3, supports a common (anti)vortex-ratchet origin for both nonreciprocal signals.
  • The H-parallel-I geometry is not inert: thermally excited pairs with out-of-plane flux can still produce a transverse rectified voltage even though field-induced vortices feel no Lorentz force.
  • The mechanism is not specific to FeSe, so similar nonreciprocal transverse responses should appear in other two-dimensional superconductors.
  • Surface and interface symmetry breaking, rather than bulk crystal symmetry, is sufficient to generate vortex-based rectification.

Reading between the lines

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

  • If the mechanism holds, ΔR_yx under current-parallel field could serve as a quantitative electrical readout of the thermally excited vortex-antivortex density, letting transport measurements track Berezinskii-Kosterlitz-Thouless-type fluctuations without noise or susceptibility probes.
  • Thickness dependence provides a clean discriminator: as FeSe films cross from two-dimensional to three-dimensional superconducting behavior, the transverse nonreciprocal signal should fade or vanish, while a purely surface-barrier ratchet would be less thickness-sensitive.
  • The predicted ratio ΔR_xx/ΔR_yx ≈ 3 could be used as a diagnostic; deviations in samples with stronger pinning may reveal a separate contribution to ΔR_xx from magnetic-field-induced vortices.
  • Because uniform field-induced vortices are immobile in the H-parallel-I configuration, any nonzero ΔR_yx isolates thermal and fluctuating vortex effects, which may help separate intrinsic nonlinear Hall signals from heating artifacts in other materials.
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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 / 4 minor

Summary. The manuscript reports nonreciprocal transport measurements in 23-nm-thick FeSe films in the vortex-flow regime. The authors observe a nonreciprocal longitudinal resistance ΔR_xx for in-plane field perpendicular to the current (H⊥I) and a nonreciprocal transverse (Hall) resistance ΔR_yx for in-plane field parallel to the current (H∥I). Since bulk FeSe is centrosymmetric, the inversion breaking is attributed to the FeSe/LaAlO3 and FeSe/Si interfaces. The paper proposes that thermally excited vortex-antivortex pairs, which arise from the 2D character of superconductivity in the film, move asymmetrically along x when the vortex Hall effect is combined with mirror-symmetry breaking by the in-plane field, producing a transverse nonlinear voltage. A model calculation, reportedly detailed in the Supplemental Material, yields a predicted ratio ΔR_xx/ΔR_yx ≈ 3, which the authors compare with measured values of 2–4.

Significance. If the proposed vortex-antivortex mechanism is correct, this would be the first experimental demonstration of a nonreciprocal Hall response in a centrosymmetric 2D superconductor under H∥I, a regime where conventional vortex motion is expected to vanish. The paper contains several genuine strengths: careful symmetry checks (field reversal, three different rotation planes), a geometric argument that rules out a simple vortex Nernst artifact, an evaluation of the 2D nature of the film via the angular dependence of H_c2, and a falsifiable quantitative prediction (the 3:1 ratio) that is compared to data. The observation itself appears robust and interesting. However, the central mechanistic claim is presented as tentative and rests on two load-bearing elements that are not fully verifiable in the present version: the model calculation is relegated to a Supplemental Material that is not available in the arXiv preprint, and the magnitude of the effect relies on a vortex Hall angle imported from bulk FeSe crystals rather than measured in the 23-nm film under study.

major comments (3)
  1. [Model calculation (p. 4–5, SM [31])] The central derivation of the nonlinear force–velocity relation and the predicted ratio ΔR_xx/ΔR_yx ≈ 3 are contained entirely in the Supplemental Material, which is not included in the version under review. The main text also refers to the SM for the temperature dependence of the nonreciprocal signals and for the zero-field control. As a consequence, the connection between the proposed (anti)vortex mechanism and the observed magnitude cannot be independently checked. The authors should provide the SM in the revision or reproduce the key steps of the calculation in the main text, including any assumptions about the vortex Hall angle and the origin of the 3:1 ratio.
  2. [Vortex Hall effect assumption (p. 4, Refs. [45,46])] The proposed transverse signal is stated to be proportional to the vortex Hall angle, and the manuscript imports a large Hall angle (~0.5) from FeSe single crystals. The vortex Hall angle of the 23-nm film used in this work is never measured. Since disorder, pinning, and interface scattering in a thin film can suppress or even reverse the Hall angle, the magnitude and sign of the predicted transverse response rest on an unmeasured parameter. The measured ratio ΔR_xx/ΔR_yx of 2–4 versus the predicted value of 3 therefore does not yet constitute a quantitative test of the mechanism unless the film's Hall angle is known. A direct measurement of the flux-flow Hall angle in the same film, or at least an explicit estimate based on the film's parameters, is needed.
  3. [Methods, definition of ΔV_i (p. 2)] The nonreciprocal voltage is defined as ΔV_i = {V_i(+I) + V_i(−I)}/2. If taken literally, this is the symmetric (average) voltage, not the nonreciprocal difference; the surrounding text says 'difference', so the '+' is presumably a typo for '−'. Because this quantity defines all subsequent data (ΔR_xx and ΔR_yx), the equation must be corrected to ΔV_i = {V_i(+I) − V_i(−I)}/2. This is not just cosmetic: as written, the formula cannot produce the reported nonzero signals from a purely nonreciprocal component.
minor comments (4)
  1. [Fig. 3 caption and text] The text refers to 'α-scan in Fig. 3(a), β-scan in Fig. 3(b), and γ-scan in Fig. 3(c)', but the caption assigns the α scan to panel (b), β scan to (c), and γ scan to (d). The panel references should be corrected.
  2. [Fig. 2 caption] The caption labels panels as H∥I and H⊥I, while the text distinguishes H∥−x, H∥+x, and H∥y. Since the sign of H matters for the nonreciprocal transverse signal, the caption should explicitly state the field direction (e.g., H along −x) to avoid ambiguity.
  3. [Typos throughout] Several typographical errors should be corrected: 'V ortices' (p. 2), 'inplane' used in place of 'in-plane' in multiple places, and 'T c' should be 'T_c'.
  4. [Vortex Nernst discussion (p. 3)] The argument against a vortex Nernst artifact uses the ratio of ΔR_xx to ΔR_yx (≈3) versus the geometric ratio of sample dimensions (1.7/1.2). This is reasonable, but it would be more direct to state explicitly that a Nernst contribution would have a different symmetry under current reversal and would not appear in the antisymmetric-in-I combination used here. A sentence clarifying this would strengthen the exclusion.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the nonreciprocal transverse signal is a new measurement, and the model comparison is a post-hoc consistency check, though the model relies on prior theory by co-author Hoshino and the derivation is relegated to unavailable Supplemental Material.

full rationale

The central claim is an experimental observation of nonreciprocal transverse resistance in FeSe films under H||I. The measurement is new and not constructed from the model. The proposed thermal-(anti)vortex mechanism is explicitly tentative ('We tentatively attribute...'). The model calculation is based on prior GL theory [25] by co-author Hoshino; this is a self-citation, but [25] is a published, parameter-free theory with stated assumptions and is externally checkable, so it is independent support. The theory's prediction that ΔR_xx/ΔR_yx ≈ 3 (for nearly equal width and length) is compared with measured peak ratios of 2–4; no parameter is fitted to the nonreciprocal data to force agreement. The bulk vortex Hall angle of ~0.5 imported from FeSe crystals [45,46] is an unverified assumption for the 23-nm film, but it is not fitted to the present data and the ratio prediction does not depend on its magnitude; this is a correctness risk, not a circularity. The model derivation is confined to SM [31], not available in the arXiv preprint, so it cannot be independently checked; this is an omitted proof, not a demonstrated circular step. Self-citations appear, but none is load-bearing in the sense of reducing the result to its own inputs.

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

The paper introduces no new entities or free parameters in the main text. The central explanatory mechanism relies on known physics: thermally excited vortices and antivortices, vortex Hall effect, and surface-induced inversion breaking. The model calculation presumably uses Rashba SOC parameters, but these are not disclosed in the available text. The 2D nature of the film is a key input that is itself derived from a fit to data.

assumptions (4)
  • domain assumption FeSe is centrosymmetric in bulk, so inversion symmetry is broken only at the film interfaces.
    The authors rely on this to explain why nonreciprocal signals appear at all, citing the crystal structure of FeSe (Ref. [36]).
  • domain assumption The FeSe film behaves as a 2D superconductor with thermally excited vortex-antivortex pairs.
    This is inferred from the angular dependence of H_c2, which fits a 2D model better than a 3D model. The fit is shown in Fig. 4(a), but the details and robustness are partly in the SM.
  • domain assumption An in-plane magnetic field parallel to the current breaks mirror symmetry with respect to the xz plane, enabling a nonreciprocal transverse response.
    This is a symmetry argument used to justify the allowed form of the response, stated in the introduction and in the proposed mechanism section.
  • standard math Ginzburg-Landau theory with Rashba spin-orbit coupling describes the vortex dynamics and yields the nonlinear force terms.
    The model calculation is said to follow Ref. [25], but the equations are not shown in the main text; they are in the SM.

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Cite this review

Pith. "Pith review of Nonlinear planar Hall effect from superconducting vortex motion." pith.science (2026). https://pith.science/paper/CD5GKM2Q

@misc{pith2026250906313,
  author       = {Pith},
  title        = {Pith review of: Nonlinear planar Hall effect from superconducting vortex motion},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CD5GKM2Q}},
  note         = {Machine review of arXiv:2509.06313}
}
read the original abstract

We report the nonreciprocal charge transport along the longitudinal and transverse directions in the vortex flow regime of FeSe superconducting films. Clear nonreciprocal signals under an inplane magnetic field reveals symmetry breaking at the film surfaces since the crystal structure of FeSe is centrosymmetric. Although the symmetry in such polar superconductors allows the nonreciprocal transverse response under a magnetic field parallel to the electric current, its observation is physically counterintuitive because vortex motion is not expected in this configuration. We propose that thermally excited (anti)vortices due to the two-dimensional nature of FeSe give rise to the nonreciprocal transverse signals when the mirror symmetry is broken by the inplane magnetic field.

Figures

Figures reproduced from arXiv: 2509.06313 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Sample and measurement setup. (b) Temperature ( [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Definitions of magnetic field angles [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. FIG. 4. (a) (b) [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

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