{"id":"b2356dae-5119-4d5b-96cf-c857b27a69b8","arxiv_id":"2504.15426","paper_version":1,"verdict":"REJECT","confidence":"LOW","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":4,"one_line_summary":"Helicon modes in multi-Weyl semimetals keep the linear-plus-quadratic wavevector dispersion of single Weyl semimetals, with the frequency scale set by charge-dependent plasma frequencies.","lead":"This paper derives helicon modes, low-frequency electromagnetic waves in a magnetic field, for multi-Weyl semimetals with topological charge 2 and 3. It claims the dispersion shape is the same as in single Weyl semimetals but with charge-dependent renormalization.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Cyclotron-frequency ordering promised in the conclusion is contradicted by the paper's own Eqs. (35)-(37) and the listed leading values; this makes the central distinguishing claim unsupported.","rationale":"The reader's verdict REJECT is justified, but the single most load-bearing failure is not the epsilon_F^5 scaling of Eq. (44) in isolation; it is the internal contradiction in the cyclotron-frequency ordering, which is the paper's advertised way of distinguishing mWSMs. Eq. (44) is a corroborating symptom that the J-dependent algebra is unreliable: the J=1 case should reduce to the known single-Weyl Drude weight, and it does not. The proposed check would settle the ordering question directly by integrating Eq. (48) and locating the resonance. Because the manuscript gives no analytic transverse conductivity and the figures lack fitting functions or error analysis, the central claim cannot be accepted as it stands. The verdict does not change because the reader already recommended REJECT; the concern here is more central than the one named in the reader's weakest_assumption, hence partial agreement.","tokens_in":7323,"tokens_out":10650,"duration_ms":97726,"concrete_test":"Recompute the leading-B cyclotron resonance from the pole of sigma_xy(omega) by numerical quadrature of Eq. (48) for J=1,2,3 at the Fig. 2 parameters (v_F=0.005, mu=0.4, alpha2=3.9e-5, alpha3=2.298e-6, B=3), and compare the ordering with Eqs. (35)-(37). If the extracted ordering matches the equations, increasing with J, then the conclusion stating the opposite must be revised; if it matches the conclusion, Eqs. (35)-(37) or their numerical evaluation are wrong. Either outcome settles whether the paper's central differentiator is supported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The abstract and conclusion make the ordering of the cyclotron frequency the distinguishing observable: lowest in the triple-WSM, highest in the single-WSM. But Eqs. (35)-(37), with the numerical values quoted after Eq. (37), give omega0_c1 = 5.68e-5, omega0_c2 = 7.09e-5 sin(phi), and omega0_c3 = 3.50e-4 sin(phi)^(4/3), which increase with J for generic phi, while the text says the frequencies decrease and the conclusion restates the decrease. Since omega_cJ is used in Eqs. (54)-(56) to define the plasma frequencies and to distinguish the modes, this contradiction removes the main quantitative support for the paper's differentiator. The transverse conductivities from which the helicon dispersions are extracted are left as unevaluated integrals, Eqs. (47)-(48), plus numerical plots, so the claimed linear/quadratic dispersions in Fig. 4 cannot be checked analytically from the manuscript. A separate internal-consistency symptom is that the J=1 zero-field limit of Eq. (44) is proportional to epsilon_F^3/(v_F omega), whereas the standard Boltzmann result for an isotropic Weyl node is proportional to epsilon_F^2/(v_F omega); even if the ordering typo were fixed, this suggests the conductivity algebra is not reliable.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript extends the semiclassical Boltzmann calculation of helicons in Weyl semimetals to multi-Weyl semimetals with topological charge J=2 and J=3. It derives longitudinal and transverse conductivities, defines charge-dependent cyclotron and plasma frequencies, and claims that helicon modes preserve the linear and quadratic dispersion of single-Weyl helicons while being renormalized by J-dependent plasma frequencies. It further argues that the cyclotron frequency is lowest in a triple-Weyl semimetal and highest in a single-Weyl semimetal, and that the axion term lifts the degeneracy of the gapped collective modes at k=0.","tokens_in":7519,"tokens_out":7150,"duration_ms":61681,"significance":"If the results were correct, the paper would offer a potentially testable distinction among single, double, and triple Weyl semimetals through helicon spectroscopy, and it would be a natural extension of the earlier single-Weyl calculation by Pellegrino, Katsnelson, and Polini. The semiclassical Boltzmann framework with Berry curvature and orbital magnetic moment is standard, and the calculation is direct rather than a fit to data, which is a strength. However, the manuscript as written contains internal contradictions and an incorrect reduction to the known J=1 limit, so the significance of the claimed results cannot be assessed until these issues are resolved.","major_comments":[{"comment":"The cyclotron frequency is introduced in Eq. (34) as ω_cJ = eBk_⊥/(Dk_⊥), where the k_⊥ factors cancel and no J-dependence survives, so this definition cannot generate the J-dependent expressions in Eqs. (35)-(37). More importantly, the ordering claim is contradicted by the paper's own numbers: with the quoted values, ω0_c1 = 5.68×10^-5, ω0_c2 = 7.09×10^-5 sinφ, and ω0_c3 = 3.50×10^-4 sin^(4/3)φ, which increase with J for generic φ, whereas the text and the Conclusion state that the frequency is lowest in the triple-WSM and highest in the single-WSM. Since this ordering is the paper's principal distinguishing observable, the central claim is unsupported as written.","section":"II, Eqs. (33)-(37) and text after Eq. (37)"},{"comment":"At B=0, Eq. (44) reduces to σ1_zz(ω) = i e^2 ε_F^5/(6π^2 v_F ω). For the same model (one isotropic Weyl node, zero temperature, no vertex corrections), the standard Boltzmann result is σ1_zz(ω) = i e^2 ε_F^2/(6π^2 v_F ω). The ε_F^5 scaling is not a harmless normalization issue; it indicates that the phase-space or velocity algebra entering Eqs. (44)-(46) is not reliable. Because the plasma frequencies and helicon dispersions are built on these conductivities, the J=2 and J=3 results inherit this problem.","section":"II, Eq. (44)"},{"comment":"The transverse conductivities that determine the helicon dispersion are left as unevaluated integrals, and no closed-form low-frequency or weak-field reduction is shown. The claim that the linear and quadratic powers of k remain intact is therefore not demonstrated analytically; Fig. 4 alone, with no specification of how Eqs. (47)-(48) were evaluated, is insufficient to support the central result. The manuscript should provide either the explicit ω(k) relation or a precise description of the numerical evaluation.","section":"II, Eqs. (47)-(48), (50) and Fig. 4"},{"comment":"Eq. (54) defines the J=1 plasma frequency as ω^2_p,1 = 4 e^2 ω_c1^2/(3πℏv_F), but ω_c1 from Eq. (35) vanishes at B=0, whereas ω_p,J is used as a zero-field collective-mode frequency in Eqs. (51)-(53). This makes ω_p,1 B-dependent and zero in the very limit in which the gapped modes are defined, so the definition is internally inconsistent unless a different ω_c1 is intended.","section":"II, Eq. (54)"}],"minor_comments":[{"comment":"The manuscript contains numerous typos and grammar errors, including 'This modes', 'three dimensional', 'frequeny', 'topolgoical', 'anistropic', and the truncated phrase 'orWe have cal...' in the Conclusion; these should be corrected.","section":"Throughout"},{"comment":"The parameters b and b0 are introduced in the axion term but are not clearly related to the node separation or to the prefactors in Eqs. (9) and (49)-(50); please define all quantities and reconcile the α/π and αc/(2π^2) prefactors.","section":"II, Eqs. (3)-(9) and (49)-(50)"},{"comment":"The figure captions do not specify units for B, α_2, α_3, μ, or the plotted conductivities; statements such as 'B = 3' are ambiguous and should be made dimensionally explicit.","section":"Figs. 1-4"},{"comment":"Reference [21] is an arXiv preprint from 2017; if a published version exists, it should be cited instead.","section":"References"},{"comment":"The text says the authors 'extend our corresponding study' to multi-Weyl semimetals, but the earlier study is not identified; please cite the relevant previous work.","section":"Introduction"}],"recommendation":"reject","confidential_remarks":"The central claim is internally contradicted by the paper's own equations, and the J=1 reduction fails in a known limit. Even a major revision would require a complete re-derivation of the conductivity and cyclotron frequency, so I recommend rejection rather than revision, although the underlying question may be worth revisiting in a corrected manuscript."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper extends Pellegrino et al.'s helicon calculation to multi-Weyl semimetals with topological charge J=2 and J=3. That's genuinely new: the J=2,3 longitudinal conductivities and the charge-dependent plasma frequencies in Eqs. (54)-(56) aren't in the cited literature, and the Boltzmann machinery is applied in a straightforward way. The qualitative point—that the helicon keeps its k-linear and k^2 structure with renormalized coefficients—is plausible from symmetry alone, and the derivation is a direct computation rather than a fit to data, so circularity is not the issue.\n\nThe problem is that the paper's central differentiating claim is contradicted by its own equations. The abstract and conclusion tout the cyclotron frequency ordering as the observable that distinguishes single from multi-Weyl nodes, claiming it is lowest in triple-WSM and highest in single-WSM. But Eqs. (35)-(37), with the numerical values given just after, yield omega_c1 = 5.68e-5, omega_c2 = 7.09e-5 sin(phi), omega_c3 = 3.50e-4 sin(phi)^(4/3), which increase with J for generic phi. This is not a typo in one line; the ordering is what the paper sells. The stress-test also caught a second red flag: Eq. (44) for the J=1 zero-field longitudinal conductivity scales as epsilon_F^5, whereas the standard Boltzmann result for a single Weyl node scales as epsilon_F^2. If the J=1 reduction is wrong, the J=2,3 expressions built on the same algebra are suspect too.\n\nThere are also smaller issues throughout: Eq. (34) defines omega_cJ in a way that cancels J-dependence before the expanded forms appear; the conclusion has a visibly broken sentence; and the transverse conductivities are left as unevaluated integrals plus numerical plots, so the claimed linear/quadratic dispersions in Fig. 4 cannot be checked analytically.\n\nProportionately: the framework is sound and the extension is a legitimate exercise, but the manuscript in its current state cannot support its own headline result. I would not reject the idea; I would ask for a corrected version with the cyclotron ordering fixed and the J=1 reduction verified. That is referee work, not a desk reject.","headline":"A plausible extension of helicon physics to multi-Weyl semimetals is undermined by the paper's own equations contradicting its central cyclotron-frequency ordering claim.","tokens_in":8144,"tokens_out":2335,"would_cite":false,"duration_ms":19773,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper shows that helicon waves in double and triple Weyl semimetals keep the same linear and quadratic dispersion as in single Weyl semimetals, with frequencies set by a charge-dependent plasma frequency.","keywords":["helicons","multi-Weyl semimetal","topological charge","cyclotron frequency","plasma frequency","semiclassical Boltzmann transport","orbital magnetic moment"],"falsifier":"Evaluate Eq. (44) at zero magnetic field and compare with the accepted single-Weyl longitudinal conductivity: the paper's expression scales as $ε_F^{5}$ while the standard result scales as $ε_F^{2}$, so checking this reduction directly would settle the reliability of the derived multi-Weyl helicon dispersion.","tokens_in":7022,"feed_emoji":"🌀","tokens_out":11531,"duration_ms":84434,"temperature":0.7,"pith_summary":"This paper asks whether helicon waves—low-frequency circularly polarized electromagnetic modes that propagate through a conductor in a magnetic field—still exist in multi-Weyl semimetals, materials whose band touchings carry topological charge J larger than 1. Using a semiclassical Boltzmann approach with Berry curvature and orbital magnetic moment, the authors find that double (J=2) and triple (J=3) Weyl semimetals host helicons with the same linear and quadratic wavevector dispersion as in the single Weyl case, but renormalized by a charge-dependent plasma frequency. They also derive the cyclotron frequency to second order in the magnetic field and find it decreases with topological charge, being lowest in the triple Weyl semimetal and highest in the single Weyl semimetal. If correct, these results give a practical way to distinguish multi-Weyl semimetals through their helicon spectra.","feed_headline":"Helicons in double, triple Weyl semimetals follow single-Weyl law","feed_subtitle":"Cyclotron frequency shrinks with topological charge, a fingerprint for double and triple Weyl materials.","key_machinery":"The load-bearing object is the low-energy Hamiltonian H(k)=d_s(k)·σ with d_s(k)=(α_J k_⊥^J cos(Jφ), α_J k_⊥^J sin(Jφ), s v_F k_z), which describes a Weyl node of topological charge J (J=1,2,3) with anisotropic dispersion k_⊥^{2J} + $k_z^{2}$. The argument runs through the semiclassical Boltzmann equation in the presence of a magnetic field, using the Berry curvature and orbital magnetic moment of the multi-Weyl node (Eqs. (18)–(19)), related by the identity m_{k,s}=-e ε_k Ω_k^s. The distribution function is expanded to linear order in the electric field, yielding longitudinal conductivities analytically and transverse conductivities numerically; these feed the dielectric tensor modified by the axion term θE·B, whose pole structure gives the plasma frequencies ω_p,J and the helicon dispersion relation. The key identity linking all three cases is that the wavevector dependence of the helicon dispersion is unchanged by the topological charge, only the overall frequency scale set by ω_p,J changes.","core_discovery":"The paper's central claim is that the helicon modes of gapless multi-Weyl semimetals with topological charge J=2 and J=3 retain the same qualitative wavevector dependence as in an isotropic single Weyl semimetal (J=1): the dispersion stays linear and quadratic in the wavevector at low and intermediate k, with coefficients set by the charge-dependent plasma frequency ω_p,J rather than the single-Weyl plasma frequency. The cyclotron frequency ω_cJ, computed to quadratic order in the magnetic field, differs across J, dropping as the topological charge grows. The axion term in the electromagnetic response, which arises from the separation of Weyl nodes, lifts the degeneracy of the three gapped collective modes at zero wavevector, so the modes become distinguishable through ω_p,J. The whole analysis is performed within a semiclassical Boltzmann framework that includes Berry curvature and orbital magnetic moment, with the transverse conductivities evaluated numerically.","pith_inferences":["Because the whole chain depends on the J=1 zero-field conductivity reduction, a quick numerical check of that reduction against the known single-Weyl Drude weight would validate or invalidate the multi-Weyl predictions before any experimental effort.","The same semiclassical machinery could be applied to tilted or strained multi-Weyl semimetals, where strain-induced pseudofields might produce J-dependent pseudohelicon modes.","The predicted ordering of cyclotron frequencies suggests that helicon spectroscopy could serve as a bulk probe of topological charge, complementing surface-sensitive Fermi-arc measurements.","Measured plasma frequencies ω_p,J would give a direct estimate of the anisotropic velocity parameters α_J and v_F for each node, since ω_p,J depends on them."],"forward_implications":["Helicon dispersion in double and triple Weyl semimetals preserves the single-Weyl form ω ∝ k^2 at low wavevector and ω ∝ k at higher wavevector, with the topological charge entering only through the plasma frequency scale.","The cyclotron frequency is highest for single Weyl and lowest for triple Weyl semimetals, giving a bulk transport signature that distinguishes the three materials.","The axion term lifts the degeneracy of the three gapped collective modes at zero wavevector, so the plasma frequencies ω_p,J label each multi-Weyl node.","The numerically computed transverse conductivities predict specific magnetic-field-dependent features in the optical and Hall response of multi-Weyl semimetals."],"supporting_citations":[{"why":"Supplies the single-Weyl semimetal helicon dispersion and the axion-modified wave equation that this paper extends to multi-Weyl systems.","marker":"[11]"},{"why":"Gives the Berry curvature and orbital magnetic moment expressions for multi-Weyl nodes used in the Boltzmann derivation.","marker":"[25]"},{"why":"Provides the kinetic-theory approach and the multi-Weyl model Hamiltonian that the calculation adopts.","marker":"[24]"},{"why":"Establishes the semiclassical wave-packet equations with orbital magnetic moment on which the transport theory is built.","marker":"[12]"},{"why":"Contributes the coordinate transformation and magnetoconductivity framework used to obtain the analytical longitudinal conductivities.","marker":"[26]"}],"fun_headline_variants":["Multi-Weyl helicons mimic single Weyl dispersion, shrink frequency","Topological charge tunes helicon frequency in multi-Weyl semimetals","Double, triple Weyl helicons follow single-Weyl law","Helicon frequency shrinks as Weyl charge grows"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The derivation assumes that the zero-field longitudinal conductivity for topological charge J=1, given in Eq. (44), reduces correctly to the known single-Weyl result; if that reduction is wrong, the J=2 and J=3 conductivities and the helicon dispersions built on them would be unreliable.","fun_headline_variants_meta":{"raw":{"variants":["Multi-Weyl helicons mimic single Weyl dispersion, shrink frequency","Topological charge tunes helicon frequency in multi-Weyl semimetals","Double, triple Weyl helicons follow single-Weyl law","Helicon frequency shrinks as Weyl charge grows"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001034,"raw_usage":{"total_tokens":4292,"prompt_tokens":823,"completion_tokens":3469,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":439,"completion_tokens_details":{"reasoning_tokens":3394}},"tokens_in":439,"tokens_out":3469,"duration_ms":26084,"temperature":1.0,"reasoning_tokens":3394,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T11:26:59.352261+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Evaluate Eq. (44) at zero magnetic field and compare with the accepted single-Weyl longitudinal conductivity: the paper's expression scales as $ε_F^{5}$ while the standard result scales as $ε_F^{2}$, so checking this reduction directly would settle the reliability of the derived multi-Weyl helicon dispersion.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the single-Weyl semimetal helicon dispersion and the axion-modified wave equation that this paper extends to multi-Weyl systems."},{"cited_title":"Nandy, C","cited_arxiv_id":null,"evidence_quote":"Gives the Berry curvature and orbital magnetic moment expressions for multi-Weyl nodes used in the Boltzmann derivation."},{"cited_title":"Dantas, F","cited_arxiv_id":null,"evidence_quote":"Provides the kinetic-theory approach and the multi-Weyl model Hamiltonian that the calculation adopts."},{"cited_title":"Sundaram and Q","cited_arxiv_id":null,"evidence_quote":"Establishes the semiclassical wave-packet equations with orbital magnetic moment on which the transport theory is built."},{"cited_title":"Medel, R","cited_arxiv_id":null,"evidence_quote":"Contributes the coordinate transformation and magnetoconductivity framework used to obtain the analytical longitudinal conductivities."}],"review_version":1}