{"id":"b4c1c384-cfd1-4e9b-b540-fee8bdf73f2d","arxiv_id":"2509.06313","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Nonreciprocal transverse resistance is observed for H||I in superconducting FeSe films and is attributed to asymmetric (anti)vortex motion in 2D superconductivity.","lead":"FeSe films show a counterintuitive nonlinear Hall-like signal when the current and magnetic field are parallel, in the vortex-flow superconducting state. The authors attribute this to thermally excited vortex-antivortex pairs moving asymmetrically because the film's surfaces break inversion symmetry.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Proposed ΔR_yx mechanism hinges on a vortex Hall angle ~0.5 taken from bulk FeSe crystals, but the 23-nm film's actual flux-flow Hall angle is never measured; if it is small, the thermal-(anti)vortex mechanism cannot yield the observed transverse signal.","rationale":"I read the paper in good faith. The experimental observation of a nonreciprocal transverse signal for H||I in the vortex-flow regime appears genuinely novel; the symmetry checks (Figs. 3a, 3c) and the absence of a longitudinal counterpart for H||x argue against trivial contact mixing. The vortex-Nernst argument based on the x/y sample size ratio is a reasonable exclusion of a sole thermal origin. However, the proposed microscopic mechanism is explicitly tentative ('We tentatively attribute'), and its two pillars—the large vortex Hall angle and the model calculation—are not established for this sample or publicly available. The most load-bearing assumption is that the vortex Hall angle in the film is large enough to convert the y-directed Lorentz force into a net x-drift of the thermally excited vortex-antivortex ensemble, and that the H_x-induced asymmetry breaks the exact cancellation of transverse voltages from vortices and antivortices. This hinges on an unmeasured film-specific parameter. The reader's weakest_assumption already identified the missing SM and the inferred Hall angle; I sharpen it by emphasizing that a direct flux-flow Hall measurement in the same film is the decisive experiment. Because the observation itself is not at stake and the mechanism is already framed as tentative, the conditional verdict remains appropriate. I do not propose to reject the paper; the concern motivates a public SM and a Hall-angle measurement.","tokens_in":9362,"tokens_out":18069,"duration_ms":204733,"concrete_test":"Measure the flux-flow Hall resistance in the same 23-nm FeSe film under a small perpendicular field H||z (e.g., 0.1–0.5 T) at 2.1 K, in the same current range (2–20 mA) where the nonreciprocal signals appear. After subtracting the normal-state Hall contribution, extract the vortex Hall angle tanθ_H = R_yx^flux-flow / R_xx^flux-flow. If tanθ_H is substantially smaller than the assumed ~0.5 (say <0.1), or has opposite sign, the proposed thermal-(anti)vortex mechanism cannot produce the observed ΔR_yx magnitude or sign, and the interpretation would need revision. Also check whether the sign and temperature dependence of the measured Hall angle track the sign and temperature dependence of ΔR_yx.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that ΔR_yx under H||I arises from thermally excited (anti)vortices requires a net x-velocity for both vortices and antivortices, provided by the vortex Hall effect, with H_x breaking the mirror symmetry so their transverse voltages do not cancel. The paper explicitly imports a large vortex Hall angle (~0.5) from FeSe single crystals (refs. 45,46), but never measures the flux-flow Hall angle in the 23-nm film used here. In a thin film with FeSe/LAO and FeSe/Si interfaces, strong pinning, and possible disorder, the dirty-limit Hall angle can be suppressed by orders of magnitude or change sign. Without a direct measurement, the magnitude (or even the sign) of the effect that the model relies on is unverified. The model calculation that derives the cancellation-breaking terms is confined to the Supplemental Material, which is not available in the arXiv preprint (SM ref. 31). Thus the key step from 'vortex motion is possible' to 'a net transverse voltage of the observed magnitude appears' rests on an unmeasured parameter and an unavailable derivation. This is the load-bearing weak point of the proposed mechanism.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":9677,"tokens_out":8332,"duration_ms":91789,"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":[{"comment":"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.","section":"Model calculation (p. 4–5, SM [31])"},{"comment":"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.","section":"Vortex Hall effect assumption (p. 4, Refs. [45,46])"},{"comment":"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.","section":"Methods, definition of ΔV_i (p. 2)"}],"minor_comments":[{"comment":"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.","section":"Fig. 3 caption and text"},{"comment":"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.","section":"Fig. 2 caption"},{"comment":"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'.","section":"Typos throughout"},{"comment":"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.","section":"Vortex Nernst discussion (p. 3)"}],"recommendation":"major_revision","confidential_remarks":"The observation of a nonreciprocal transverse signal in this centrosymmetric 2D superconductor is potentially significant and likely to interest the community. However, the main mechanism is not fully testable in the present form: the key calculation is in an unavailable Supplemental Material, and the magnitude of the effect depends on an unmeasured vortex Hall angle. I recommend asking the authors to provide the SM and to add a film-specific Hall angle measurement or a clear estimate. The typo in the definition of ΔV_i must also be fixed. These are fixable within the scope of a revision, so I do not recommend rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe paper reports the first experiment I know of showing a nonreciprocal transverse (Hall) voltage in the vortex-flow regime of a centrosymmetric 2D superconductor when the in-plane field is parallel to the current. That is a genuinely new result, and the symmetry checks look careful: rotating H by 180 degrees flips the transverse signal as expected, the angular scans match the expected sin/cos forms, and the authors make a decent argument against a vortex Nernst artifact by comparing the longitudinal-to-transverse ratio with the sample aspect ratio.\n\nThe weak spot is the proposed mechanism, which is explicitly tentative. The model requires a sizable vortex Hall angle in the 23-nm film to convert asymmetric (anti)vortex motion into a transverse voltage. The paper leans on the ~0.5 Hall angle reported for FeSe single crystals, but never measures the flux-flow Hall angle in this film. In a dirty thin film with different top/bottom interfaces, that angle could be much smaller or even change sign, and the entire magnitude of the predicted signal hinges on it. The model calculation itself is in the Supplemental Material, which is not available on arXiv, so the referee cannot check the derivation of the ratio prediction (3 vs measured 2-4) or the cancellation-breaking terms. That is a practical problem for evaluation, not a fatal one: the data stand, and the mechanism is offered as an attribution, not a proof.\n\nMinor issues: no error bars on ΔR values, and the Methods text defines ΔV_i with a plus sign where I think they mean the antisymmetrized difference; that needs cleaning up.\n\nThe citation to Hoshino's earlier theory is fine—this is exactly the prediction they say they are testing. Self-citation is not a problem here.\n\nNet: the experimental observation is likely real and interesting, but the theoretical interpretation is under-supported at present. I would send it to a serious referee, with the explicit request to examine the SM and to ask the authors for a direct measurement or at least a bound on the flux-flow Hall angle in the film. The paper will be a solid addition once that gap is addressed.","headline":"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.","tokens_in":10160,"tokens_out":3522,"would_cite":true,"duration_ms":39536,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["74.25.F-","74.25.Wx"],"model":"deepseek-v4-flash","headline":"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.","keywords":["nonreciprocal transport","nonlinear Hall effect","vortex ratchet","vortex-antivortex pairs","FeSe thin film","two-dimensional superconductor","vortex Hall effect","centrosymmetric superconductor"],"falsifier":"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.","tokens_in":9321,"feed_emoji":"🌀","tokens_out":9257,"duration_ms":105125,"temperature":0.7,"pith_summary":"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.","feed_headline":"Thermal vortex pairs give FeSe a sideways nonlinear voltage","feed_subtitle":"First nonreciprocal Hall signal under a current-parallel field in a centrosymmetric 2D superconductor.","key_machinery":"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","core_discovery":"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","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Theory of nonreciprocal charge transport in two-dimensional noncentrosymmetric superconductors; supplies the (anti)vortex contribution and the Ginzburg-Landau plus Rashba model used for the calculation.","marker":"[25]"},{"why":"Trigonal-superconductor vortex ratchet study whose force-velocity relation is mirrored by the model calculation presented here.","marker":"[27]"},{"why":"Earlier theoretical prediction of a nonreciprocal transverse signal in two-dimensional centrosymmetric superconductors under an in-plane field, which this experiment claims to demonstrate.","marker":"[28]"},{"why":"Demonstration that asymmetric surface barriers can rectify vortex motion, used to argue that interface symmetry breaking drives the effect.","marker":"[29]"},{"why":"Growth of FeSe thin films by pulsed laser deposition; source of the measured samples.","marker":"[30]"},{"why":"Critical-field anisotropy in thin-flake FeSe supporting the two-dimensional character invoked for thermally excited (anti)vortices.","marker":"[41]"},{"why":"Excess-conductivity and Berezinskii-Kosterlitz-Thouless transition analysis in FeSe thin films, supporting the two-dimensional vortex-antivortex physics.","marker":"[43]"},{"why":"Reports a large vortex Hall angle in FeSe single crystals, the premise for asymmetric (anti)vortex motion in the proposed mechanism.","marker":"[45]"}],"fun_headline_variants":["Vortex pairs produce transverse nonlinear voltage in FeSe","Sideways nonlinear effect from vortex-antivortex pairs","2D superconductor shows nonreciprocal Hall from thermal vortices","Thermal vortex pairs break mirror symmetry for a planar Hall signal","FeSe's vortex motion yields a nonlinear planar Hall effect"],"cache_read_input_tokens":2688,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Vortex pairs produce transverse nonlinear voltage in FeSe","Sideways nonlinear effect from vortex-antivortex pairs","2D superconductor shows nonreciprocal Hall from thermal vortices","Thermal vortex pairs break mirror symmetry for a planar Hall signal","FeSe's vortex motion yields a nonlinear planar Hall effect"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000693,"raw_usage":{"total_tokens":2924,"prompt_tokens":644,"completion_tokens":2280,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":388,"completion_tokens_details":{"reasoning_tokens":2211}},"tokens_in":388,"tokens_out":2280,"duration_ms":17867,"temperature":1.0,"reasoning_tokens":2211,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-04T23:49:22.307951+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Hoshino, R","cited_arxiv_id":null,"evidence_quote":"Theory of nonreciprocal charge transport in two-dimensional noncentrosymmetric superconductors; supplies the (anti)vortex contribution and the Ginzburg-Landau plus Rashba model used for the calculation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Trigonal-superconductor vortex ratchet study whose force-velocity relation is mirrored by the model calculation presented here."},{"cited_title":"Daido and Y","cited_arxiv_id":null,"evidence_quote":"Earlier theoretical prediction of a nonreciprocal transverse signal in two-dimensional centrosymmetric superconductors under an in-plane field, which this experiment claims to demonstrate."},{"cited_title":"Lustikova, Y","cited_arxiv_id":null,"evidence_quote":"Demonstration that asymmetric surface barriers can rectify vortex motion, used to argue that interface symmetry breaking drives the effect."},{"cited_title":"Nabeshima, M","cited_arxiv_id":null,"evidence_quote":"Growth of FeSe thin films by pulsed laser deposition; source of the measured samples."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Critical-field anisotropy in thin-flake FeSe supporting the two-dimensional character invoked for thermally excited (anti)vortices."},{"cited_title":"Schneider, A","cited_arxiv_id":null,"evidence_quote":"Excess-conductivity and Berezinskii-Kosterlitz-Thouless transition analysis in FeSe thin films, supporting the two-dimensional vortex-antivortex physics."},{"cited_title":"Ogawa, F","cited_arxiv_id":null,"evidence_quote":"Reports a large vortex Hall angle in FeSe single crystals, the premise for asymmetric (anti)vortex motion in the proposed mechanism."}],"review_version":1}