{"id":"580b2b59-45ea-4a3a-815d-cbca0153995e","arxiv_id":"2607.24671","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"In TRS-broken 3D Weyl semimetals, third-order skew scattering dominates extrinsic orbital Hall conductivity, scales linearly with disorder strength, and can exceed the intrinsic response.","lead":"Disorder-driven skew scattering, not band geometry, can dominate the orbital Hall effect in magnetic Weyl semimetals under an AC field. The result suggests orbitronic signals can be tuned by impurity strength and node separation rather than only by topology.","discovery_kind":"extension","skeptic_critique":{"model":"moonshotai/kimi-k3","headline":"The claimed linear-in-U skew-scattering dominance (and U-independence of the Born-level terms) silently assumes the dirty regime ℏ/τ ≫ ℏω; at the headline ℏω = 20 meV this requires τ ≪ 33 fs, a condition never stated or checked.","rationale":"Read in good faith: the paper is a competent, standard quantum-kinetic calculation, and the physics (third-order skew dominating in a TRS-broken Weyl system) is plausible and consistent with the cited Culcer-group machinery. The reader flagged the disorder model and Born truncation as the weak point — I agree that region of the argument is where the risk lives, but the reader's formulation is about realism of white-noise disorder, whereas the sharpest load-bearing issue is internal: the claimed U-scalings, which are the paper's headline signatures (linear-in-U, 10⁵ suppression of Born-level channels, disorder-tunability), follow analytically only in the ωτ ≪ 1 regime, and the paper never demonstrates that its own headline parameter point sits there. This is checkable with the paper's own equations and parameters, needs no new physics, and directly qualifies how the abstract's claims should be read. I considered two alternatives and ranked them lower: (a) the unstated third cumulant — real, but implicit-and-standard for fixed-sign delta impurities, so likely present in the authors' intent; (b) higher-Born/vertex corrections — generic to all such kinetic treatments. Neither is as concrete or as decisive as the ωτ regime assumption. On the verdict: the reader's CONDITIONAL is correct and my concern does not overturn it — it sharpens the operative condition from \"realistic disorder may differ\" to \"the stated scalings are dirty-limit results whose regime must be verified at the quoted parameters.\" Hence UNCHANGED, with the concrete test defining the condition the community should demand before ACCEPT. Confidence in the critique is moderate-high on the algebra (the denominators are printed in the paper), lower on whether the authors' numerics already implicitly live in ωτ ≪ 1 — which the proposed test settles.","tokens_in":17523,"tokens_out":8214,"duration_ms":316800,"concrete_test":"Within the paper's own framework: (i) numerically evaluate 1/τ from Eq. (9) at the headline parameters and report ωτ; (ii) recompute σ_ext_yx(U) from Eqs. (12)–(14) retaining the full complex denominators (ω + i/τ) and (1/τ + iω) — no τ-approximation — sweeping U so that ωτ crosses 1, and extract the local scaling exponent d ln σ/d ln U and the ratio σ_BBA/σ_BA. If the exponent stays ≈ 1 and the ratio ≈ 10⁵ across the sweep, the concern fails; if the exponent drifts toward 3–5 for ωτ ≳ 1, the linear-U claim and hierarchy must be re-stated as dirty-regime results. Also state ⟨UUU⟩_c explicitly.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's scaling narrative is analytic, not just numerical, and it rests on one unexamined step. The Boltzmann solution is f_mm_E = eE(t)∂_q f0 /(ω + i/τ) (text after Eq. 8). The claim that \"τ ∝ U⁻² ... these two will cancel\" for the side jump (Eq. 8) and first-Born skew (Eq. 10), and that Re f_sk_1E ∝ U³·τ ∝ U for the beyond-Born term (Eqs. 13–14), holds only if |ω + i/τ| ≈ 1/τ, i.e., ωτ ≪ 1. In the opposite (arguably natural AC) limit ωτ ≫ 1: Re[1/(1/τ + iω)] ≈ (1/τ)/ω² ∝ U², so the diagonal skew term f_sk,mm_1E scales as U⁵, not U; f_sj ∝ U² rather than U-independent; and the σ_BBA/σ_BA ~ 10⁵ hierarchy becomes a different (U³-growing rather than U-growing) function. Nothing in the paper evaluates 1/τ from its own Eq. (9) at the headline point (U = 50 meV·Å³, ε_f = 10 meV, b = 0.04 Å⁻¹); n_i is not even specified, so ωτ cannot be reconstructed by the reader. With ℏω = 20 meV, ωτ ≪ 1 demands τ ≪ 33 fs — very dirty for the candidate materials cited (Co₃Sn₂S₂, Mn₃Sn) — while the Born-series truncation itself wants U small. The claimed scaling window (Born truncation valid AND ωτ ≪ 1) may be narrow or empty. Secondary caveat: J1 ≠ 0 requires a nonzero third cumulant ⟨UUU⟩_c ∝ n_i U0³; only the second correlator is written, so this is implicit (standard for fixed-sign delta impurities, zero for Gaussian or sign-symmetric disorder).","agreement_with_reader":"partial"},"referee_report":{"model":"moonshotai/kimi-k3","summary":"The manuscript computes the disorder-induced (extrinsic) orbital Hall conductivity of a three-dimensional time-reversal-symmetry-broken two-node Weyl semimetal under an AC electric field, using the quantum Liouville/kinetic-equation formalism. Within the first Born approximation the authors identify a disorder-independent side-jump contribution (Eq. (8)) and a disorder-independent diagonal skew contribution (Eq. (10)); going to third order in the impurity potential (collision integral J1, Eqs. (11)–(12)) they obtain a skew-scattering correction (Eqs. (13)–(14)) whose real part is argued to scale linearly with the disorder strength U because the explicit U³ is reduced by one power of the transport time τ ∝ U⁻². Numerically, they report that this beyond-Born skew term dominates: σ_BBA ≈ 10⁵ σ_BA, the total extrinsic conductivity reaches ~1 (e/2π) at ε_f = 10 meV, b = 0.04 Å⁻¹, ℏω = 20 meV, U = 50 meV·Å³ — about 10× the intrinsic value quoted from Ref. [63] — and exhibits a plateau for |ε_f| < ℏω/2, suppression with increasing node separation, and enhancement with drive energy. Experimental detection via MOKE and optical conductivity in Co₃Sn₂S₂ and Mn₃Sn is proposed.","tokens_in":18914,"tokens_out":2351,"duration_ms":163860,"significance":"If the central claims hold, this is the first systematic treatment of extrinsic (side-jump and skew-scattering) orbital Hall response in a three-dimensional time-reversal-broken Weyl semimetal, extending recent 2D results (e.g., Ref. [26]) to a realistic 3D platform. The derivation follows a recognized quantum-kinetic path and does not fit to data; it yields concrete, falsifiable predictions — a linear-in-U scaling of σ_yx, a plateau pinned to the interband threshold ℏω = 2|ε_f|, suppression with node separation b, and chirality independence — that are directly testable by doping-dependent and terahertz/optical measurements in materials such as Co₃Sn₂S₂. The identification of the beyond-first-Born channel as the potentially dominant extrinsic mechanism in 3D is a genuine conceptual contribution to orbitronics. These strengths are real, but the magnitude claims (10⁵ hierarchy, 10× intrinsic) currently rest on an unstated regime assumption and unspecified numerical parameters, which tempers the significance as presented.","major_comments":[{"comment":"The central scaling claims — U-independence of the side-jump (text after Eq. (8)) and first-Born skew (Eq. (10)) terms, and the linear-in-U scaling of the beyond-Born skew term (Eqs. (13)–(14)) — all rest on the cancellation of the explicit U² in the collision integrals against τ ∝ U⁻² entering through f_mm_E = eE(t)∂_q f_0/(ω + i/τ). This cancellation requires |ω + i/τ| ≈ 1/τ, i.e. the dirty regime ωτ ≪ 1. The manuscript never states this assumption. In the opposite (and for AC optics arguably natural) regime ωτ ≫ 1, Re[1/(1/τ+iω)] ∝ τ⁻¹ω⁻² ∝ U², so f_sk,1E scales as U⁵ rather than U, the side-jump becomes U²-dependent rather than U-independent, and the claimed hierarchy σ_BBA/σ_BA ∼ 10⁵ becomes a different function of U. At the headline drive ℏω = 20 meV, ωτ ≪ 1 demands τ ≪ 33 fs, which is very dirty for the proposed candidate materials Co₃Sn₂S₂ and Mn₃Sn (§IV). Meanwhile the Born-seri","section":"§II, Eqs. (8)–(14)"},{"comment":"The entire dominant contribution, J1 (Eqs. (11)–(12)), is proportional to the third disorder cumulant ⟨UUU⟩_c. Yet §II specifies only the second correlator ⟨U(r)U(r')⟩ = n_iU₀²δ(r−r'). For dilute point impurities the third cumulant is n_iU₀³ and the skew term is nonzero — this is standard — but for Gaussian or sign-symmetric disorder it vanishes identically, in which case the paper's dominant channel does not exist. The assumed impurity statistics (fixed-sign delta scatterers, third cumulant n_iU₀³) must be stated explicitly where the disorder model is introduced, since the paper's central result depends on it.","section":"§II disorder model / §II.A, Eqs. (11)–(12)"},{"comment":"The numerical results cannot be reproduced or independently checked as presented. The impurity density n_i (equivalently the combination n_iU₀²) is never given a value, so τ from Eq. (9) and the absolute magnitude of σ_ext_yx in Fig. 2 cannot be reconstructed. The Fermi velocity v_f entering the Hamiltonian (19) and the regulator η are also unspecified. Since the headline quantitative claims (σ_ext ≈ 10 σ_int; σ_BBA ≈ 10⁵ σ_BA) are numerical, the full parameter set used in Figs. 2 and 3 — n_i, v_f, η, momentum cutoffs, and the resulting τ — must be tabulated. Ideally the authors would also show σ_yx vs. ωτ to demonstrate which regime the plotted points occupy.","section":"§III, Fig. 2; Appendix B, Fig. 3"},{"comment":"The claim σ_BBA_yx ≈ 10⁵ σ_BA_yx (§III, Appendix B) is load-bearing for the abstract's assertion of skew-scattering dominance, yet it is presented purely as a numerical observation with no analytic estimate of its origin (e.g., which momentum/energy denominators or matrix-element structures suppress the Born-level terms). Five orders of magnitude is an extreme hierarchy; the authors should provide at least a parametric argument for its size, and state over what range of U, b, and ℏω it holds. As written, a reader cannot tell whether 10⁵ is generic or an artifact of the chosen parameter point.","section":"§III and Appendix B, Fig. 3"}],"minor_comments":[{"comment":"Internal tension in the disorder-scaling language: the Introduction describes the skew contribution as having 'disorder dependence of the U³', while §II.A and Fig. 2(a) emphasize that the conductivity is linear in U (the U³ of J1 being reduced by τ ∝ U⁻²). The abstract similarly says the 'third power of disorder potential' dominates. Please harmonize: the microscopic collision integral is O(U³), the observable conductivity is claimed linear in U.","section":"Abstract / §I / §II.A"},{"comment":"Eq. (10) uses the denominator (1/τ + iω) for the diagonal skew correction while Eq. (8) uses the band-energy denominator (i/ℏ)(ε_m−ε_p) − iω without a scattering rate; the rationale for including τ in one and not the other (and for its absence from the intrinsic term, Eq. (7)) should be stated in one sentence.","section":"§II, Eqs. (7), (8), (10)"},{"comment":"Eq. (9): for short-range delta impurities the scattering is s-wave/isotropic, so the (1−cosΔϕ) transport-weighting factor is redundant (transport and single-particle times coincide). Worth a clarifying remark, especially since τ's U-scaling is central to the argument.","section":"§II, Eq. (9)"},{"comment":"Several typographical/rendering issues: 'EXPERIMENT AL RELEV ANCE' and 'SUMMAR Y' section headings; 'cooresponding' (§III); 'theU³' (§I); 'Universit` a' in affiliation 2; garbled axis labels in Figs. 2 and 3 as rendered. Please proofread.","section":"Throughout"},{"comment":"Ref. [75] is an arXiv preprint cited for Co₃Sn₂S₂/Mn₃Sn as magnetic Weyl semimetals; a published reference (e.g., the original experimental identification papers for these compounds) would be more appropriate for this load-bearing materials claim.","section":"§IV, Ref. [75]"},{"comment":"The statement that the extrinsic response 'remains finite' in the Dirac limit b → 0 'irrespective of ... time reversal symmetry' (§III) is interesting and potentially surprising, since skew scattering usually requires broken symmetries or non-Gaussian disorder statistics; one sentence explaining what keeps it finite at b = 0 would strengthen the discussion.","section":"§III, discussion of Fig. 2(b)"}],"recommendation":"major_revision","confidential_remarks":"The intrinsic reference point (σ_int from Ref. [63]) is the authors' own prior work, which is natural here but means the extrinsic/intrinsic comparison inherits whatever approximations that calculation made. The manuscript fits the journal's scope on extrinsic orbital transport. My main hesitation in recommending against outright acceptance is not the formalism — which follows a well-trodden kinetic path — but that the headline quantitative claims (linear-U scaling, 10⁵ hierarchy, 10× intrinsic) are numerics-only statements whose validity regime (ωτ ≪ 1, nonzero third disorder cumulant, specified n_i and v_f) is never demonstrated. These are fixable within the manuscript's scope, hence major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"The one thing worth knowing: they push quantum kinetics through side-jump and first- plus third-order skew for AC orbital Hall conductivity in a TRS-broken 3D Weyl model, and claim beyond-Born skew (∝ U³ in the collision integral, linear in U after τ cancellation) swamps side-jump and first-Born channels by ~10⁵ and can sit ~10× above the intrinsic piece at weak U, small b, and ℏω ~ 20 meV.\n\nWhat is actually new is the 3D Weyl + AC setting for the extrinsic channels. Side-jump/skew OHE already exists in 2D Dirac/TMD work (Liu–Culcer and related), and the intrinsic AC Weyl piece is in their own prior paper. The machinery is standard Culcer-style kinetics. They do the bookkeeping carefully: diagonal/off-diagonal J in the appendices, clear separation of f_int, f_sj, f_sk, f_sk1, and explicit j_y operators for the two-band model. Parameter maps vs U, b, ℏω, T are readable, and they name Co₃Sn₂S₂ / Mn₃Sn as candidates. That is useful for people already in orbitronics transport theory.\n\nThe soft spot that matters is the scaling narrative. After Eq. (8) they write f_mm_E ∝ 1/(ω + i/τ) and cancel τ ∝ U⁻² so side-jump and first-Born skew are U-independent while Re f_sk1 ∝ U. That cancellation is the dirty-limit statement ωτ ≪ 1. At their headline ℏω = 20 meV that means τ ≪ 33 fs. They never evaluate 1/τ from their own Eq. (9); n_i is free, so a reader cannot reconstruct ωτ. In the clean AC limit the powers change (skew1 no longer linear in U, side-jump no longer U-independent, hierarchy not a fixed 10⁵). The window where Born truncation is safe and ωτ ≪ 1 may be narrow for the materials they cite. Secondary and smaller: J₁ needs a nonzero third cumulant; only the second correlator is written (fine for fixed-sign deltas, zero for Gaussian disorder). Magnitude ratios are single-point numerics against their in-house intrinsic baseline, not a sweep.\n\nNone of that makes the algebra incoherent. It is a specialized theory note for people who already trust white-noise Born kinetics. I would send it to referees; they should force an explicit ωτ check (or a clean-limit rewrite) and a clearer statement of the disorder ensemble. I would not put it in next week’s reading group unless someone is actively doing extrinsic OHE, and I would only cite it if I needed the 3D Weyl extrinsic formulas myself.","headline":"Solid kinetic calculation of extrinsic AC orbital Hall in 3D Weyl, but the headline U-linear skew dominance quietly needs the dirty limit ωτ ≪ 1, which is never checked.","tokens_in":18565,"tokens_out":700,"would_cite":false,"duration_ms":21111,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"In time-reversal-broken 3D Weyl semimetals, third-order skew scattering dominates extrinsic orbital Hall conductivity and can exceed the intrinsic response.","keywords":["orbital Hall effect","skew scattering","side jump","Weyl semimetals","quantum kinetic theory","disorder","orbitronics","time-reversal symmetry breaking"],"falsifier":"In a magnetic Weyl candidate (for example Co3Sn2S2 or Mn3Sn), measure the orbital Hall response while systematically changing impurity concentration at fixed band structure: the extrinsic signal should rise linearly with disorder strength and show a conductivity plateau for |ε_f| < ℏω/2, unlike a disorder-independent intrinsic or side-jump background.","tokens_in":18214,"feed_emoji":"⚛️","tokens_out":944,"duration_ms":21245,"temperature":0.7,"pith_summary":"This paper asks how impurities reshape the orbital Hall effect in three-dimensional Weyl semimetals that break time-reversal symmetry. Using a quantum kinetic treatment of an oscillating electric field, it separates side-jump and skew-scattering channels and shows that the leading extrinsic orbital Hall conductivity comes from skew scattering built from the third power of the disorder potential. That channel scales linearly with disorder strength, overwhelms side-jump and first-Born skew terms by many orders of magnitude, and can reach roughly ten times the intrinsic orbital Hall conductivity for weak disorder, small Weyl-node separation, and applied energies of tens of meV. The response can be tuned by disorder strength, drive frequency, Fermi energy, and node separation, and it remains finite even as the nodes merge toward a Dirac limit. The authors argue this gives a practical route to engineer orbital currents for orbitronics in magnetic Weyl materials.","feed_headline":"Skew scattering rules orbital Hall response in Weyl metals","feed_subtitle":"Third-order disorder terms dominate, scale with impurity strength, and can beat the intrinsic signal","key_machinery":"The quantum kinetic (Liouville) equation for the disorder-averaged density matrix, with collision integrals carried through third order in the impurity potential; the third-order skew corrections f_sk_1E to the density matrix then enter the orbital Hall current via the operator (1/2){L_z, v_y}.","core_discovery":"Under an oscillating electric field in a time-reversal-symmetry-broken three-dimensional Weyl semimetal, the extrinsic orbital Hall conductivity is dominated by skew scattering beyond the first Born approximation—specifically the third-order disorder contribution—which scales linearly with disorder potential U, suppresses side-jump and first-Born channels (σ_BBA ≈ 10^5 σ_BA), and can be about ten times larger than the intrinsic orbital Hall conductivity for weak U, small node separation, and ℏω around 20 meV.","pith_inferences":["If long-range or resonant impurities reorganize the Born series, the claimed U-linear hierarchy may invert, so comparing short-range dopants with Coulomb scatterers is a natural next experiment.","The survival of a finite extrinsic orbital Hall signal at vanishing node separation suggests disorder-driven orbitronics could remain useful in Dirac and near-Dirac 3D materials where intrinsic OHE is symmetry-forbidden.","AC-drive plateaus tied to interband thresholds offer a spectroscopic fingerprint that could map orbital Hall response without needing spin-orbit-strong hosts."],"forward_implications":["Extrinsic orbital Hall conductivity in TRS-broken Weyl semimetals is primarily a skew-scattering effect linear in U, not a side-jump effect.","Smaller Weyl-node separation and higher drive frequency strengthen the extrinsic orbital Hall signal, while larger separation and higher temperature suppress it.","Disorder engineering and controlled doping become direct knobs for orbital-current magnitude in orbitronic devices.","Magneto-optical Kerr and THz/infrared conductivity measurements under gating can separate the extrinsic plateau and U-linear scaling from intrinsic band-geometry contributions."],"fun_headline_variants":["Third-order skew scattering dominates orbital Hall in Weyl metals","Skew disorder terms beat side-jump in orbital Hall response","Higher-order skew scattering drives extrinsic orbital Hall signal","Third-power disorder rules orbital Hall under oscillating fields","Skew scattering beyond Born approx leads orbital Hall conductivity"],"cache_read_input_tokens":128,"weakest_assumption_plain":"The impurities are treated as uncorrelated short-range delta scatterers whose effects are captured by a Born series stopped at third order, so that the transport time cancels to leave a response linear in disorder strength.","fun_headline_variants_meta":{"raw":{"variants":["Third-order skew scattering dominates orbital Hall in Weyl metals","Skew disorder terms beat side-jump in orbital Hall response","Higher-order skew scattering drives extrinsic orbital Hall signal","Third-power disorder rules orbital Hall under oscillating fields","Skew scattering beyond Born approx leads orbital Hall conductivity"]},"model":"grok-4.5","effort":"low","cost_usd":0.00427,"raw_usage":{"total_tokens":1230,"prompt_tokens":723,"num_sources_used":0,"completion_tokens":60,"cost_in_usd_ticks":42704000,"prompt_tokens_details":{"text_tokens":723,"audio_tokens":0,"image_tokens":0,"cached_tokens":128},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":447,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":723,"tokens_out":60,"duration_ms":8358,"temperature":1.0,"reasoning_tokens":447,"cache_read_input_tokens":128,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-31T08:14:51.952816+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"In a magnetic Weyl candidate (for example Co3Sn2S2 or Mn3Sn), measure the orbital Hall response while systematically changing impurity concentration at fixed band structure: the extrinsic signal should rise linearly with disorder strength and show a conductivity plateau for |ε_f| < ℏω/2, unlike a disorder-independent intrinsic or side-jump background.","supporting_citations":[],"review_version":1}