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REVIEW 4 major objections 5 minor 28 references

Helicons in multi-Weyl semimetals

T0 review · 4 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read 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.

desk verdict 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. read the letter →

arxiv 2504.15426 v1 pith:HUSPD2Y6 submitted 2025-04-21 cond-mat.str-el cond-mat.other

Shiv Kumar Ram , Amit Gupta This is my paper · ORCID
classification cond-mat.str-elcond-mat.other
keywords heliconsmulti-WeylsemimetaltopologicalchargecyclotronfrequencyplasmasemiclassicalBoltzmanntransportorbitalmagneticmoment
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 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.

What carries the argument

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.

What would settle it

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.

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Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

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

  • 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.
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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

4 major / 5 minor

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.

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 (4)
  1. [II, Eqs. (33)-(37) and text after Eq. (37)] 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.
  2. [II, Eq. (44)] 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.
  3. [II, Eqs. (47)-(48), (50) and Fig. 4] 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.
  4. [II, Eq. (54)] 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.
minor comments (5)
  1. [Throughout] 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.
  2. [II, Eqs. (3)-(9) and (49)-(50)] 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.
  3. [Figs. 1-4] 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.
  4. [References] Reference [21] is an arXiv preprint from 2017; if a published version exists, it should be cited instead.
  5. [Introduction] 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.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the helicon analysis is a direct semiclassical computation from the multi-Weyl Hamiltonian and Maxwell equations, with no fitted parameters that are renamed as predictions.

full rationale

The paper's derivation chain is self-contained: it starts from the multi-Weyl Hamiltonian (Eq. 10), computes Berry curvature and orbital magnetic moment (Eqs. 18-19), solves the Boltzmann equation in a weak magnetic field, and obtains conductivities and collective-mode frequencies. There is no step in which an output quantity is defined in terms of the claimed result, and no parameter is fitted to data and then relabeled as a prediction. The self-citations (refs. 20-22) are used only as background references for multi-Weyl transport phenomena and are not load-bearing for the helicon calculation. The assertion that the transverse conductivities lead to the same linear and quadratic wavevector dependence as in single Weyl semimetals is presented as a numerical observation (Fig. 4) rather than as a derived equality, so it is a correctness or completeness concern, not a circularity. Similarly, the apparent inconsistency between the quoted cyclotron-frequency values (Eqs. 35-37 and the numbers after Eq. 37) and the conclusion's ordering claim is an internal consistency issue, not a circular reduction. Overall, the central results do not reduce by construction to the paper's inputs.

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

The central claim rests on standard multi-Weyl Hamiltonians, Berry curvature/OMM expressions, and axion electrodynamics from the cited literature; the paper introduces no new entities. The material parameters listed in the figure captions are chosen by hand for illustration, not fitted to data, but they set the numeric values quoted for the cyclotron frequencies.

free parameters (4)
  • Fermi velocity vF = 0.005
    Chosen in figure captions for all plots; sets the scale of the cyclotron and plasma frequencies.
  • Double-Weyl coupling alpha_2 = 3.9e-5
    Chosen in figure captions; appears in omega_c2 and omega_p2.
  • Triple-Weyl coupling alpha_3 = 2.298e-6
    Chosen in figure captions; appears in omega_c3 and omega_p3.
  • Fermi energy epsilon_F (mu) = 0.4
    Chosen in figure captions; sets the density of states and all energy scales.
assumptions (4)
  • domain assumption The multi-Weyl Hamiltonian H(k)=d_s(k) dot sigma with d_s=(alpha_J k_perp^J cos(J phi), alpha_J k_perp^J sin(J phi), s v_F k_z) describes the low-energy bands.
    Standard model for multi-Weyl semimetals cited from refs [24-26]; used for the Berry curvature and orbital moment in Eqs. (18)-(19).
  • domain assumption Semiclassical Boltzmann equation with Berry curvature and orbital magnetic moment, expanded to linear order in electric field and weak magnetic field, gives the conductivity.
    Inherited from Pellegrino et al. [11] and refs [12,27]; the paper does not re-derive this framework.
  • domain assumption Axion electrodynamics with theta(r,t)=2(b dot r - b0 t) modifies Maxwell's equations as in Eqs. (3)-(8).
    Standard topological response of Weyl semimetals, cited to refs [11,23]; used to obtain the helicon wave equation.
  • domain assumption The weak-field condition e|B dot Omega| << 1 justifies truncating the expansion to second order in B.
    Stated in Eq. (32); underpins the B^2 terms in the cyclotron frequency.

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Cite this review

Pith. "Pith review of Helicons in multi-Weyl semimetals." pith.science (2026). https://pith.science/paper/HUSPD2Y6

@misc{pith2026250415426,
  author       = {Pith},
  title        = {Pith review of: Helicons in multi-Weyl semimetals},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HUSPD2Y6}},
  note         = {Machine review of arXiv:2504.15426}
}
read the original abstract

Helicons are transverse electromagnetic modes in three dimension(3D) electron systems in the presence of a static magnetic field. This modes have been proposed in isotropic or single Weyl semimetals(sWSMs) (Francesco M.D. Pellegrino et al, Phys. Rev. B 92, 201407(R) (2015)). In this work, we extend our study to investigate helicons modes in gapless multi-Weyl semimetals(mWSMs) within semiclassical Boltzmann approach and discuss the differences that arise compared to single Weyl semimetals.

Figures

Figures reproduced from arXiv: 2504.15426 by the authors.

Figure 1
Figure 1. FIG. 1. The frequency dependence of the longitudal optical [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 3
Figure 3. FIG. 3. The frequency dependence of the transverse Hall [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. FIG. 4. The [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

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Reference graph

Works this paper leans on

28 extracted references · 20 canonical work pages

  1. [1]

    Kittel and P

    C. Kittel and P. McEuen, Introduction to solid state physics (John Wiley & Sons, 2018)

    2018

  2. [2]

    J. D. Jackson, Classical electrodynamics (John Wiley & Sons, 2021)

    2021

  3. [3]

    Konstantinov and V

    O. Konstantinov and V. Perel, Possible transmission of electromagnetic waves through a metal in a strong magnetic field, SOVIET PHYSICS JETP-USSR 11, 117 (1960)

    work page 1960

  4. [4]

    P. M. Platzman and P. A. Wolff, Waves and interac- tions in solid state plasmas , Vol. 13 (Academic Press New York, 1973)

    work page 1973

  5. [5]

    X. Wan, A. M. Turner, A. Vishwanath, and S. Y. Savrasov, Topological semimetal and fermi-arc surface states in the electronic structure of pyrochlore iridates, Physical Review B—Condensed Matter and Materials Physics 83, 205101 (2011)

    2011

  6. [6]

    Burkov and L

    A. Burkov and L. Balents, Weyl semimetal in a topo- logical insulator multilayer, Physical review letters 107, 127205 (2011)

    work page 2011

  7. [7]

    G. Xu, H. Weng, Z. Wang, X. Dai, and Z. Fang, Chern semimetal and the quantized anomalous hall effect in hgcr 2 se 4, Physical review letters 107, 186806 (2011)

    work page 2011

  8. [8]

    Huang, S.-Y

    S.-M. Huang, S.-Y. Xu, I. Belopolski, C.-C. Lee, G. Chang, B. Wang, N. Alidoust, G. Bian, M. Neupane, C. Zhang, et al. , A weyl fermion semimetal with sur- face fermi arcs in the transition metal monopnictide taas class, Nature communications 6, 7373 (2015)

    work page 2015

Show all 28 references
  1. [9]

    B. Lv, N. Xu, H. Weng, J. Ma, P. Richard, X. Huang, L. Zhao, G. Chen, C. Matt, F. Bisti, et al. , Observation of weyl nodes in taas, Nature Physics 11, 724 (2015)

    2015

  2. [10]

    S.-Y. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, G. Chang, Z. Yuan, C.-C. Lee, et al. , Discovery of a weyl fermion semimetal and topological fermi arcs, Science 349, 613 (2015)

    2015

  3. [11]

    F. M. Pellegrino, M. I. Katsnelson, and M. Polini, Heli- cons in weyl semimetals, Physical Review B 92, 201407 (2015)

    2015

  4. [12]

    Sundaram and Q

    G. Sundaram and Q. Niu, Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and 6 FIG. 2. The frequency dependence of the transverse optical conductivity at B = 3. The other parameters are taken as vF = 0.005, µ = 0.4, α2 = 3.9 × 10−5 and α3 = 2.298 × 10−6 ...

    1999

  5. [13]

    Gorbar, V

    E. Gorbar, V. Miransky, I. Shovkovy, and P. Sukhachov, Pseudomagnetic helicons, Physical Review B 95, 115422 (2017)

    2017

  6. [14]

    Huang, S.-Y

    S.-M. Huang, S.-Y. Xu, I. Belopolski, C.-C. Lee, G. Chang, T.-R. Chang, B. Wang, N. Alidoust, G. Bian, M. Neupane, et al. , New type of weyl semimetal with quadratic double weyl fermions, Proceedings of the Na- tional Academy of Sciences 113, 1180 (2016)

    2016

  7. [15]

    S. Ahn, E. Mele, and H. Min, Optical conductivity of multi-weyl semimetals, Physical Review B 95, 161112 (2017)

    2017

  8. [16]

    Mukherjee and J

    S. Mukherjee and J. Carbotte, Doping and tilting on op- tics in noncentrosymmetric multi-weyl semimetals, Phys- ical Review B 97, 045150 (2018)

    2018

  9. [17]

    T. Nag, A. Menon, and B. Basu, Thermoelectric trans- port properties of floquet multi-weyl semimetals, Physi- cal Review B 102, 014307 (2020). FIG. 3. The frequency dependence of the transverse Hall optical conductivity at B = 3. The other parameters are taken asvF = 0.005,µ =...

    2020

  10. [18]

    Nag and S

    T. Nag and S. Nandy, Magneto-transport phenomena of type-i multi-weyl semimetals in co-planar setups, Journal of Physics: Condensed Matter 33, 075504 (2020)

    2020

  11. [19]

    Menon and B

    A. Menon and B. Basu, Anomalous hall transport in tilted multi-weyl semimetals, Journal of Physics: Con- densed Matter 33, 045602 (2020)

    2020

  12. [20]

    Gupta, Novel electric field effects on landau levels in multi-weyl semimetals, Physics Letters A 383, 2339 (2019)

    A. Gupta, Novel electric field effects on landau levels in multi-weyl semimetals, Physics Letters A 383, 2339 (2019)

    2019

  13. [21]

    Gupta, Floquet dynamics in multi-weyl semimetals, arXiv preprint arXiv:1703.07271 (2017)

    A. Gupta, Floquet dynamics in multi-weyl semimetals, arXiv preprint arXiv:1703.07271 (2017)

    2017 arXiv

  14. [22]

    Gupta, Kerr effects in tilted multi-weyl semimetals, arXiv preprint arXiv:2209.07506 (2022)

    A. Gupta, Kerr effects in tilted multi-weyl semimetals, arXiv preprint arXiv:2209.07506 (2022)

    2022 arXiv

  15. [23]

    Zyuzin and A

    A. Zyuzin and A. Burkov, Topological response in weyl semimetals and the chiral anomaly, Physical Review B—Condensed Matter and Materials Physics 86, 115133 (2012)

    2012

  16. [24]

    Dantas, F

    R. Dantas, F. Pe˜ na-Benitez, B. Roy, and P. Sur´ owka, Magnetotransport in multi-weyl semimetals: A kinetic theory approach, Journal of High Energy Physics 2018, 1 (2018). 7 FIG. 4. The ω vs. k disersion for multi-WSMs at B = 3. The other parameters are taken as vF = 0.005, µ...

    2018

  17. [25]

    Nandy, C

    S. Nandy, C. Zeng, and S. Tewari, Chiral anomaly in- duced nonlinear hall effect in semimetals with multiple weyl points, Physical Review B 104, 205124 (2021)

    2021

  18. [26]

    Medel, R

    L. Medel, R. Ghosh, A. Mart´ ın-Ruiz, and I. Mandal, Electric, thermal, and thermoelectric magnetoconductiv- ity for weyl/multi-weyl semimetals in planar hall set-ups induced by the combined effects of topology and strain, Scientific Reports 14, 21390 (2024)

    2024

  19. [27]

    Xiao, M.-C

    D. Xiao, M.-C. Chang, and Q. Niu, Berry phase effects on electronic properties, Reviews of modern physics 82, 1959 (2010)

    2010

  20. [28]

    Gao, Z.-Q

    Y. Gao, Z.-Q. Zhang, H. Jiang, and K.-H. Ding, Suppres- sion of magneto-optical transport in tilted weyl semimet- als by orbital magnetic moment, Physical Review B 105, 165307 (2022)

    2022

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