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REVIEW 3 major objections 5 minor 67 references

Localized surface plasmons in a Weyl semimetal nanosphere

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Pith's one-line read This paper claims that in a sub-wavelength Weyl semimetal nanosphere the axion term turns the single dipole localized-surface-plasmon resonance into three non-degenerate, polarization-dependent resonances and the single quadrupole…

desk verdict Clean quasistatic derivation of modified Fröhlich conditions for a WSM nanosphere; quadrupole and TE-excitation results are new, the dipole condition is already in the heat-transfer literature, and the local-model caveats are real but not fatal. read the letter →

arxiv 2505.23626 v3 pith:BUZ3VXIZ submitted 2025-05-29 cond-mat.mes-hall physics.app-phphysics.optics

Francesco M. D. Pellegrino , Francesco Buccheri , G. G. N. Angilella This is my paper · ORCID
classification cond-mat.mes-hallphysics.app-phphysics.optics
keywords WeylsemimetallocalizedsurfaceplasmonsaxionelectrodynamicsgyrotropicpermittivityFröhlichconditionquasistaticapproximationnanospheremagnetoelectricexcitation
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 argues that the axion term in Weyl semimetal electrodynamics restructures the localized surface plasmon (LSP) spectrum of a sub-wavelength nanosphere, replacing the single-mode response of an isotropic metal with a multiplet. Solving the quasistatic boundary-value problem with the WSM's skew-symmetric permittivity tensor, the authors derive modified Fröhlich conditions: three non-degenerate dipole resonances at $\operatorname{Re}(\varepsilon_\parallel)+m\varepsilon_\perp+2\varepsilon_M=0$ for $m=0,\pm1$, and five quadrupole resonances at $2\operatorname{Re}(\varepsilon_\parallel)+m\varepsilon_\perp+3\varepsilon_M=0$ for $m=0,\pm1,\pm2$, where $\varepsilon_\perp=2\alpha c b/(\pi\omega)$ is the axion-induced off-diagonal permittivity component. Because each resonance belongs to an eigenvector of the permittivity tensor, the absorption cross section becomes polarization-dependent in a way that is absent in conventional metallic nanoparticles. The paper further claims that the axion magnetoelectric effect allows a purely transverse electric field to excite quadrupole LSPs with $m=0,\pm1$, a channel that an isotropic metallic sphere does not possess. If these results hold, a single WSM nanosphere is a tunable platform in which a topological bulk response shows up directly as a measurable restructuring of the plasmonic spectrum.

What carries the argument

The load-bearing object is the local, homogeneous permittivity tensor $\epsilon=\epsilon_\parallel e_z\otimes e_z+(\epsilon_\parallel+\epsilon_\perp)e_+\otimes e_+^\star+(\epsilon_\parallel-\epsilon_\perp)e_-\otimes e_-^\star$, whose off-diagonal component $\varepsilon_\perp=2\alpha c b/(\pi\omega)$ encodes the axion/anomalous-Hall response and scales as $1/\omega$ rather than the $1/\omega^3$ of a magnetic-field-induced gyrotropy. The calculation expands the scalar potential in vector spherical harmonics, imposes continuity of tangential $\mathbf{E}$ and normal $\mathbf{D}$ at the sphere surface, and reads resonances off the denominators of the induced multipole coefficients. The axion term couples multipole channels that are independent in an isotropic sphere, producing the modified Fröhlich conditions and the polarization-dependent absorption; the same term, through the axion contribution to the polarization $\mathbf{P}_{\rm ax}=-\alpha b\cdot\mathbf{r}\mathbf{B}/(2\pi^2)$, is what lets a TE field drive quadrupole modes.

What would settle it

Measure the extinction spectrum of monodisperse, sub-wavelength Weyl semimetal nanospheres (for example Co3Sn2S2) at frequencies below the interband threshold $2\varepsilon_F$. The central claim requires three separate dipole absorption peaks obeying Eq. (46) with energies split linearly in $b$, different absorbance for left- and right-circular polarization, and a quadrupole response when the incident field is transverse-electric with no radial electric-field component. A single polarization-independent dipole peak, or zero quadrupole absorption under TE illumination, would falsify the predicted axion restructuring.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is that the axion term converts the single Fröhlich resonance of an isotropic metal sphere into a polarization-resolved multiplet for each multipole order. For a WSM sphere described by the local permittivity tensor $\epsilon=\epsilon_\parallel e_z\otimes e_z+(\epsilon_\parallel+\epsilon_\perp)e_+\otimes e_+^\star+(\epsilon_\parallel-\epsilon_\perp)e_-\otimes e_-^\star$, the induced dipole and quadrupole coefficients have denominators $\epsilon_\parallel+m\epsilon_\perp+2\epsilon_M$ and $2\epsilon_\parallel+m\epsilon_\perp+3\epsilon_M$, respectively. When the real part of one of these denominators vanishes and the imaginary part is small, one obtains Eqs. (46) and (70) of the paper, giving three and five non-degenerate LSP frequencies whose splitting grows with the Weyl-node separation $b$. Distinct from a merely anisotropic dielectric, the dipole modes with $m=\pm1$ carry opposite circular polarizations, and the axion term makes a TE-polarized incident field able to excite quadrupole modes with $m=0,\pm1$ through the magnetoelectric coupling that enters Gauss's law as an effective charge density $\alpha b\cdot\mathbf{B}/(2\pi^2)$.

Load-bearing premise

Everything rests on treating the nanosphere as a homogeneous piece of bulk Weyl semimetal described by the local permittivity tensor of Eqs. (8)–(10) with ordinary boundary conditions, so that Fermi-arc surface states, nonlocal optical response, and near-surface spatial variation of the axion angle are all neglected.

Editorial extensions

If this is right

  • Three dipole and five quadrupole LSP resonances replace the single dipole and single quadrupole Fröhlich resonances of an isotropic metal sphere; their energies are given explicitly by the analytical formulas in Eqs. (48) and (71), with splittings that grow linearly with the Weyl-node separation $b$ for small $b$.
  • Because each mode is tied to an eigenvector of the permittivity tensor, the extinction spectrum depends on the polarization angle $\beta$ and distinguishes left- and right-circular polarization via the $m=\pm1$ dipole modes.
  • A transverse electric field with no radial electric-field component can excite quadrupole LSPs with $m=0,\pm1$ through the axion magnetoelectric effect, while the homogeneous TE field cannot excite the $m=\pm2$ quadrupole channel.
  • Interference between an incident TE field and the TM-scattered field produces an absorption mixing term proportional to $\epsilon_\perp$, an additional heating pathway that has no counterpart in an isotropic metallic nanosphere.
  • In the ultraclean limit, resonances below the interband threshold $2\varepsilon_F$ have vanishing imaginary part of $\epsilon_\parallel$, so within the model the predicted LSPs are infinitely long-lived.

Reading between the lines

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

  • If Fermi-arc surface states and nonlocal corrections do not destroy the bulk axion picture, single-nanoparticle extinction spectroscopy in the relevant THz-to-far-IR range should reveal the $b$-linear splitting of the dipole peaks, a signature that cleanly separates the axion response from a Drude gyrotropy induced by an external magnetic field.
  • The TE-field excitation mechanism suggests an unprobed design rule for WSM nanoantennas: quadrupole modes can be driven without any radial electric field component, which may be useful for polarization-selective or chiral sensing once the circularly split $m=\pm1$ modes are exploited.
  • Applying the same electrostatic machinery to dimers or arrays of WSM nanospheres, or to spheres with an anisotropic permittivity axis not aligned with the incoming field, could produce direction-dependent emission and nonreciprocal near-field heat transfer; the paper cites earlier work on heat-flux rectification between WSM nanoparticles but does not itself construct these geometries.
  • A direct quantitative test would be to measure the extinction of a dilute suspension of monodisperse WSM nanospheres for left- and right-circular polarization and check that the three dipole peaks shift and change weight according to Eq. (45).
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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 / 5 minor

Summary. The paper studies localized surface plasmons (LSPs) of a sub-wavelength Weyl semimetal (WSM) nanosphere, using axion-modified Maxwell equations and a local, homogeneous, gyrotropic permittivity tensor. The authors derive, in the quasistatic approximation, modified dipole Fröhlich conditions Re(ε∥)+mε⊥+2εM=0 for m=0,±1 (Eq. 46) and quadrupole conditions 2Re(ε∥)+mε⊥+3εM=0 for m=0,±1,±2 (Eq. 70), predicting three and five non-degenerate polarization-dependent LSP resonances, respectively. They also propose that a transverse electric (TE) field can excite LSPs through the axion magnetoelectric effect (Section VII), including a mixing term in the absorption rate. The analytical resonance formulas (Eqs. 48 and 71) are checked against numerical solutions of the resonance conditions for a range of the axion parameter b.

Significance. If the local bulk axion response is a valid description for a finite WSM sphere, the paper gives a clean analytical demonstration that the axion term qualitatively enriches the LSP spectrum relative to an isotropic metal sphere, producing multiple non-degenerate resonances and a polarization-dependent absorption cross section. The derivation is coherent within the stated local model, and the agreement between the numerical solutions of Eqs. (46)/(70) and the analytical approximations (48)/(71) is a useful internal consistency check. The TE-excitation mechanism is conceptually interesting and could be of practical relevance for nanophotonics or thermoplasmonics. However, the paper's central predictions depend on model assumptions—bulk local response and standard boundary conditions at a sharp WSM-vacuum interface—that are not fully justified for the nanosphere geometry, and at least one algebraic step in Section VII needs re-examination.

major comments (3)
  1. [Sections II–III and Eqs. (18)–(19)] The paper treats the WSM nanosphere as a homogeneous bulk medium with the local permittivity tensor of Eq. (8) and applies the standard boundary conditions of tangential E and normal D continuity. In a finite WSM sphere, the axion angle θ(r)=2b·r inside must match to θ=0 outside, which gives an abrupt change in the axion field at r=R and is associated with Fermi-arc surface states that the paper itself cites as important for extended WSM samples (Refs. [28,29]). Such surface contributions are not included in the boundary conditions, and the manuscript does not justify neglecting them for radii R≲10 nm. Since the resonance poles in Eqs. (46) and (70) and the TE-excitation mechanism in Section VII are derived from this boundary-value problem, this is a load-bearing model-validity assumption. The authors should state the range of R for which the bulk local response dominates, estimate surface/nonlocal corrections, or explicitly frame the results as valid only in the strict local bulk limit.
  2. [Section II, Eq. (6), and Section V] The optical conductivity in Eq. (6) is the long-wavelength (q=0) limit, but the quadrupole modes considered in Sections V–VI have internal fields that vary on a length scale set by R (e.g., Eq. (51b)). For the parameters quoted in the captions (εF=40 meV, vD=c/1000), kF=εF/(ℏvD)≈0.2 nm⁻¹, so for R≲10 nm the relevant internal wavevector q~1/R is comparable to kF and nonlocal corrections to the permittivity are not obviously negligible. The paper does not discuss this regime or provide an estimate of how nonlocal effects would shift the Fröhlich conditions. Given that the central quantitative predictions are the resonance frequencies (48) and (71), the authors should either restrict their claims to radii for which the local approximation is controlled or estimate the magnitude of nonlocal corrections.
  3. [Section V, Eq. (54a), and Section VII, Eqs. (79d)–(79e)] The coupling coefficients between the ℓ=1 and ℓ=2 vector spherical harmonics in Eq. (54a) appear to be incorrect. Direct evaluation in Cartesian coordinates for the m=0 component gives ε·(rΦ_10) = ε∥(rΦ_10) − i(√3/(4√5)) ε⊥ r[2Y20+Ψ20] + ..., rather than the coefficient −i√3 ε⊥ quoted in Eq. (54a). Similar normalization issues may affect Eq. (54b). This propagates to the TE-induced amplitudes in Eqs. (79d) and (79e) and hence to the mixing term in Eq. (80). The authors should re-derive the matrix elements in Eq. (54) from the definitions of the vector spherical harmonics and update the downstream formulas accordingly.
minor comments (5)
  1. [Section IV, Eq. (45)] In Eq. (45), the denominator of the m=0 term is written as 2ε∥+εM, but from Eq. (28) the correct denominator is ε∥+2εM. This appears to be a typographical error.
  2. [Section III] The statement that one can write D=−∇F and solve the Laplace equation for F is not generally valid in a gyrotropic medium. For the dipole (ℓ=1) problem it can be justified because D inside the sphere is uniform, but the text should say so explicitly rather than presenting the ansatz as general.
  3. [Sections IV and VI] The assertion that the magnetic field is continuous across the sphere surface is stated without proof. The authors should either derive it from the axion-modified boundary conditions or clarify which boundary condition is being used.
  4. [Section VIII] In the concluding section, the word 'quadruple' should be 'quadrupole.'
  5. [Section VIII] The statement that the LSP splitting shares the robustness of the bulk WSM phase against disorder is an unsupported extrapolation; disorder could affect surface states and nonlocal corrections in ways that are not analyzed here. This should be softened or removed.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the modified Fröhlich conditions and the TE-excitation mechanism follow algebraically from a standard axion-Maxwell permittivity model, with no fitted parameter renamed as a prediction.

full rationale

The derivation is self-contained. The WSM permittivity tensor (Eqs. 8-10) is taken from standard axion electrodynamics and published optical-conductivity results, not fitted to the LSP spectra. The dipole pole condition Re(ε∥) + m ε⊥ + 2εM = 0 (Eq. 46) follows directly from the boundary-condition denominator in Eq. (25a), and the quadrupole condition 2Re(ε∥) + m ε⊥ + 3εM = 0 (Eq. 70) follows from Eq. (59a); neither condition is inserted by hand. The analytical energies Ω_m (Eqs. 48 and 71) use the interband renormalization ε*_b evaluated at the axion-free Fröhlich frequency w0 or wQ; this is an explicitly stated approximation for the frequency-dependent interband term, not a fit of the predicted resonance positions, and it is checked against the numerical solution of Eqs. (46) and (70). Section VII's TE excitation of quadrupole modes follows from the same boundary conditions (Eqs. 79d-79e) and the axion magnetoelectric coupling; the contrast with isotropic metals is a comparison, not a renaming. The self-citations (e.g., Refs. [26,28]) appear as background or analogy and are not load-bearing for the central result: the Fröhlich conditions are derived from the model equations in the paper rather than imported from those citations. Model-validity caveats about Fermi arcs, nonlocality, and surface states are physical-risk concerns, not circularity.

Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

The free parameters are illustrative input values, not fitted to any experimental data; they set the scale of the predicted resonance frequencies but not the structure of the Fröhlich conditions. The axioms capture the main model choices: the minimal WSM description, local response, quasistatic limit, and the interband renormalization approximation. No new entities are introduced; the axion term is an established electromagnetic response of WSMs.

free parameters (6)
  • b (Weyl node separation wavevector) = 0.02π/a to 0.16π/a in plots
    Controls the axion off-diagonal permittivity ε⊥ = 2αcb/(πω); the paper scans it to show the splitting of the LSP resonances. Not fitted to data.
  • εF (Fermi energy) = 40 meV
    Sets the intraband Drude weight and the interband threshold 2εF; chosen as a representative value.
  • vD (Dirac-Weyl velocity) = c/1000
    Sets the cyclotron mass m_c = εF/vD² and the plasma frequency; representative value.
  • εb (bound dielectric constant) = 5
    Background dielectric constant of the lattice; representative value.
  • Λ (ultraviolet cutoff) = ℏvDπ/a with a=3.5 Å
    Appears in the interband optical conductivity logarithm; chosen according to the lattice model.
  • γ (damping rate) = 0 (ultraclean limit)
    Set to 0+ in the resonance formulas; finite values would broaden the modes.
assumptions (6)
  • domain assumption The minimal two-node model of a WSM, with Hamiltonian H = ℏvD τ^z σ·(-i∇ + τ^z b), is adequate, and the chiral anomaly induces the axion term Lθ = -(α/4π²) θ E·B with θ = 2b·r.
    Invoked in Section II, Eqs. (1)-(3). Real WSMs may have multiple node pairs; the minimal model is a simplification.
  • domain assumption The electromagnetic response is local and homogeneous, described by the permittivity tensor (8)-(10) with the optical conductivity of Eqs. (6); Fermi arc surface states and nonlocal corrections are neglected.
    Adopted in Section II and applied to the nanosphere in Section III; this is the main unverified assumption for finite systems.
  • domain assumption The quasistatic approximation applies: R << c/(√εM ω), so retardation is negligible and the potential obeys Laplace-type equations.
    Stated in Sections IV and VI; valid for sub-wavelength particles but not for larger spheres.
  • ad hoc to paper The interband contribution to the permittivity can be approximated by a frequency-independent renormalization εb → εb*(w0), Eq. (47), when deriving the analytical resonance formulas (48) and (71).
    Used in Sections IV and VI; the approximation fails near 2εF, a discrepancy the authors acknowledge in the figures.
  • standard math Standard vector spherical harmonic expansion and boundary conditions (continuity of tangential E and normal D) apply.
    Used throughout Sections III-VII.
  • domain assumption The magnetic field boundary condition (continuity of tangential B) is preserved in the quasistatic approximation; asserted without proof.
    Mentioned in Section IV after Eq. (33); not demonstrated in the text.

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Cite this review

Pith. "Pith review of Localized surface plasmons in a Weyl semimetal nanosphere." pith.science (2026). https://pith.science/paper/BUZ3VXIZ

@misc{pith2026250523626,
  author       = {Pith},
  title        = {Pith review of: Localized surface plasmons in a Weyl semimetal nanosphere},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BUZ3VXIZ}},
  note         = {Machine review of arXiv:2505.23626}
}
read the original abstract

In this study, we investigate the localized surface plasmon modes of a sub-wavelength spherical nanoparticle composed of a Weyl semimetal, taking into account the axion modification of electrodynamics. We derive analytical solutions for dipole and quadrupole normal modes by employing the quasistatic approximation. The axion term leads to modified Fr\"ohlich conditions, resulting in multiple non-degenerate plasmonic resonances with distinct polarization dependencies. In contrast to isotropic conventional metals, the magnetoelectric properties of Weyl semimetals enable an incident electromagnetic field, with the electric field transverse to the surface of the sphere, to excite a localized surface plasmon.

Figures

Figures reproduced from arXiv: 2505.23626 by the authors.

Figure 1
Figure 1. FIG. 1. Dipole surface plasmonic resonance conditions. a) Re( [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Quadrupole surface plasmonic resonance conditions. a) 2 Re( [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗

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Reference graph

Works this paper leans on

67 extracted references · 62 canonical work pages

  1. [1]

    Maier, Plasmonics: Fundamentals and Applications (Springer, New York, 2007)

    H. Maier, Plasmonics: Fundamentals and Applications (Springer, New York, 2007)

    work page 2007

  2. [2]

    S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, Channel plasmon subwave- length waveguide components including interferometers and ring resonators, Nature 440, 508 (2006)

    work page 2006

  3. [3]

    Z. Li, S. Butun, and K. Aydin, Ultranarrow Band Ab- sorbers Based on Surface Lattice Resonances in Nanos- tructured Metal Surfaces, ACS Nano 8, 8990 (2014)

    work page 2014

  4. [4]

    J. S. Fakonas, H. Lee, Y. A. Kelaita, and H. A. Atwater, Two-plasmon quantum interference, Nature Photonics 8, 317 (2014). 12

    work page 2014

  5. [5]

    D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, Quantum Optics with Surface Plasmons, Phys. Rev. Lett. 97, 053002 (2006)

    work page 2006

  6. [6]

    Ridolfo, O

    A. Ridolfo, O. Di Stefano, N. Fina, R. Saija, and S. Savasta, Quantum Plasmonics with Quantum Dot- Metal Nanoparticle Molecules: Influence of the Fano Ef- fect on Photon Statistics, Phys. Rev. Lett. 105, 263601 (2010)

    work page 2010

  7. [7]

    Baffou, F

    G. Baffou, F. Cichos, and R. Quidant, Applications and challenges of thermoplasmonics, Nature Materials 19, 744 (2020)

    work page 2020

  8. [8]

    M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, Nanostructured plasmonic sensors, Chemical reviews 108, 494–521 (2008)

    work page 2008

Show all 67 references
  1. [9]

    B. P. Nanda, P. Rani, P. Paul, Aman, S. S. Ganti, and R. Bhatia, Recent trends and impact of localized sur- face plasmon resonance (LSPR) and surface-enhanced Raman spectroscopy (SERS) in modern analysis, Journal of Pharmaceutical Analysis 14, 100959 (2024)

    2024

  2. [10]

    Abramovich, D

    S. Abramovich, D. Dutta, C. Rizza, S. Santoro, M. Aquino, A. Cupolillo, J. Occhiuzzi, M. F. L. Russa, B. Ghosh, D. Farias, A. Locatelli, D. W. Boukhvalov, A. Agarwal, E. Curcio, M. Bar Sadan, and A. Poli- tano, NiSe and CoSe Topological Nodal-Line Semimetals: A Sustainable Pla...

    2022

  3. [11]

    Santoro, A

    S. Santoro, A. H. Avci, A. Politano, and E. Curcio, The advent of thermoplasmonic membrane distillation, Chemical Society Reviews 51, 6087 (2022)

    2022

  4. [12]

    Politano, G

    A. Politano, G. D. Profio, E. Fontananova, V. Sanna, A. Cupolillo, and E. Curcio, Photothermal Membrane Distillation for Seawater Desalination, Advanced Mate- rials 29, 1603504 (2017)

    2017

  5. [13]

    Santoro, A

    S. Santoro, A. Politano, and E. Curcio, Photothermal- enhanced membrane distillation by plasmonic heating of silver nanoparticles, Journal of Membrane Science 658, 120761 (2022)

    2022

  6. [14]

    Santoro, A

    S. Santoro, A. Politano, and E. Curcio, Photothermal- enhanced membrane distillation by plasmonic heating of silver nanoparticles, Journal of Membrane Science 682, 121837 (2023)

    2023

  7. [15]

    Lupi and A

    S. Lupi and A. Molle, Emerging Dirac materials for THz plasmonics, Applied Materials Today 20, 100732 (2020)

    2020

  8. [16]

    Huang, L

    X. Huang, L. Zhao, Y. Long, P. Wang, D. Chen, Z. Yang, H. Liang, M. Xue, H. Weng, Z. Fang, X. Dai, and G. Chen, Observation of the Chiral-Anomaly-Induced Negative Magnetoresistance in 3D Weyl Semimetal TaAs, Phys. Rev. X 5, 031023 (2015)

    2015

  9. [17]

    B. Q. Lv, Xu, N., H. M. Weng, J. Z. Ma, P. Richard, X. C. Huang, L. X. Zhao, G. F. Chen, C. E. Matt, F. Bisti, V. N. Strocov, J. Mesot, Z. Fang, X. Dai, T. Qian, M. Shi, and H. Ding, Experiments show that TaAs is a three- dimensional topological Weyl semimetal, Nature Physics ...

    2015

  10. [18]

    S.-Y. Xu, C. Liu, S. K. Kushwaha, R. Sankar, J. W. Krizan, I. Belopolski, M. Neupane, G. Bian, N. Ali- doust, T.-R. Chang, H.-T. Jeng, C.-Y. Huang, W.-F. Tsai, H. Lin, P. P. Shibayev, F.-C. Chou, R. J. Cava, and M. Z. Hasan, Observation of Fermi arc surface states in a topolog...

    2015

  11. [19]

    N. P. Armitage, E. J. Mele, and A. Vishwanath, Weyl and Dirac semimetals in three-dimensional solids, Rev. Mod. Phys. 90, 015001 (2018)

    2018

  12. [20]

    Ma, S.-Y

    Q. Ma, S.-Y. Xu, C. Zhang, G. Belvin, N. L. Wang, B. S. Deger, T. Morimoto, H. W. S. Lee, S. K. Kushwaha, N. Gedik, Z. Hasan, L. Fu, and P. Jarillo-Herrero, Topo- logical Axion States in Magnetic Insulators, Nature 575, 315 (2019)

    2019

  13. [21]

    Bonasera, S.-B

    F. Bonasera, S.-B. Zhang, L. Privitera, and F. M. D. Pel- legrino, Tunable interface states between Floquet-Weyl semimetals, Phys. Rev. B 106, 195115 (2022)

    2022

  14. [22]

    Wilczek, Two applications of axion electrodynamics, Phys

    F. Wilczek, Two applications of axion electrodynamics, Phys. Rev. Lett. 58, 1799 (1987)

    1987

  15. [23]

    Y. Chen, S. Wu, and A. A. Burkov, Axion response in Weyl semimetals, Phys. Rev. B 88, 125105 (2013)

    2013

  16. [24]

    A. A. Zyuzin and V. A. Zyuzin, Chiral electromagnetic waves in Weyl semimetals, Phys. Rev. B 92, 115310 (2015)

    2015

  17. [25]

    O. V. Kotov and Y. E. Lozovik, Giant tunable nonre- ciprocity of light in Weyl semimetals, Phys. Rev. B 98, 195446 (2018)

    2018

  18. [26]

    F. M. D. Pellegrino, M. I. Katsnelson, and M. Polini, Helicons in Weyl semimetals, Phys. Rev. B 92, 201407 (2015)

    2015

  19. [27]

    Zhou, H.-R

    J. Zhou, H.-R. Chang, and D. Xiao, Plasmon mode as a detection of the chiral anomaly in Weyl semimetals, Phys. Rev. B 91, 035114 (2015)

    2015

  20. [28]

    G. M. Andolina, F. M. D. Pellegrino, F. H. L. Koppens, and M. Polini, Quantum nonlocal theory of topological Fermi arc plasmons in Weyl semimetals, Phys. Rev. B 97, 125431 (2018)

    2018

  21. [29]

    J. C. W. Song and M. S. Rudner, Fermi arc plasmons in Weyl semimetals, Phys. Rev. B 96, 205443 (2017)

    2017

  22. [30]

    Heidari, D

    S. Heidari, D. Culcer, and R. Asgari, Anomalous plasmon mode in strained Weyl semimetals, Phys. Rev. B 103, 035306 (2021)

    2021

  23. [31]

    Tsuchikawa, S

    K. Tsuchikawa, S. Konabe, T. Yamamoto, and S. Kawa- bata, Characterization of a Weyl semimetal using a unique feature of surface plasmon polaritons, Phys. Rev. B 102, 035443 (2020)

    2020

  24. [32]

    Tamaya, T

    T. Tamaya, T. Kato, K. Tsuchikawa, S. Konabe, and S. Kawabata, Surface plasmon polaritons in thin-film Weyl semimetals, Journal of Physics: Condensed Mat- ter 31, 305001 (2019)

    2019

  25. [33]

    O. V. Bugaiko, E. V. Gorbar, and P. O. Sukhachov, Surface plasmon polaritons in strained Weyl semimetals, Phys. Rev. B 102, 085426 (2020)

    2020

  26. [34]

    Peluso, A

    M. Peluso, A. De Martino, R. Egger, and F. Buccheri, Nonreciprocal Weyl semimetal waveguide, Phys. Rev. Res. 7, 023195 (2025)

    2025

  27. [35]

    C. Guo, V. S. Asadchy, B. Zhao, Q. Jiang, R. Liu, Y. Jin, F. Liu, Y. D. Chong, and P. Genevet, Light control with Weyl semimetals, eLight 3, 2 (2023)

    2023

  28. [36]

    Fr¨ ohlich,Theory of dielectrics; dielectric constant and dielectric loss (Clarendon Press, Oxford, 1949)

    H. Fr¨ ohlich,Theory of dielectrics; dielectric constant and dielectric loss (Clarendon Press, Oxford, 1949)

    1949

  29. [37]

    Bohren and D

    C. Bohren and D. Huffman, Absorption and scattering of light by small particles (John Wiley and Sons, New York, 1983)

    1983

  30. [38]

    T. J. Davis and D. E. G´ omez, Colloquium: An algebraic model of localized surface plasmons and their interac- tions, Rev. Mod. Phys. 89, 011003 (2017)

    2017

  31. [39]

    A. A. Burkov and L. Balents, Weyl Semimetal in a Topo- logical Insulator Multilayer, Phys. Rev. Lett.107, 127205 (2011)

    2011

  32. [40]

    A. A. Burkov, M. D. Hook, and L. Balents, Topological nodal semimetals, Phys. Rev. B 84, 235126 (2011). 13

    2011

  33. [41]

    A. A. Zyuzin and A. A. Burkov, Topological response in Weyl semimetals and the chiral anomaly, Phys. Rev. B 86, 115133 (2012)

    2012

  34. [42]

    M. E. Peskin and D. V. Schroeder, An Introduction To Quantum Field Theory (Addison-Wesley, Cambridge, 1995)

    1995

  35. [43]

    G. Xu, H. Weng, Z. Wang, X. Dai, and Z. Fang, Chern semimetal and the quantized anomalous Hall effect in HgCr2Se4, Physical Review Letters 107, 186806 (2011)

    2011

  36. [44]

    J. Li, Y. Li, S. Du, Z. Wang, B.-L. Gu, S.-C. Zhang, K. He, W. Duan, and Y. Xu, Intrinsic magnetic topolog- ical insulators in van der Waals layered MnBi2Te4-family materials, Science Advances 5, eaaw5685 (2019)

    2019

  37. [45]

    Y. Gao, W. Wu, B.-C. Gong, H.-C. Yang, X.-F. Zhou, Y. Liu, S. A. Yang, K. Liu, and Z.-Y. Lu, Intrinsic ferro- magnetic axion states and single pair of Weyl fermions in the stable-state MnX2B2T6 family of materials, Physical Review B 107, 045136 (2023)

    2023

  38. [46]

    J. A. Boulton and K. W. Kim, Search for an an- tiferromagnetic Weyl semimetal in (MnTe) m(Sb2Te3)n and (MnTe)m(Bi2Te3)n superlattices, Journal of Physics: Condensed Matter 36, 405601 (2024)

    2024

  39. [47]

    H. Liu, J. Cao, Z. Zhang, J. Liang, L. Wang, and S. A. Yang, Ideal spin-polarized Weyl half-semimetal with a single pair of Weyl points in the half-Heusler compounds xCrTe (x = K, Rb), Physical Review B 109, 174426 (2024)

    2024

  40. [48]

    A. B. Sushkov, J. B. Hofmann, G. S. Jenkins, J. Ishikawa, S. Nakatsuji, S. Das Sarma, and H. D. Drew, Optical evi- dence for a Weyl semimetal state in pyrochlore Eu2Ir2O7, Physical Review B 92, 241108 (2015)

    2015

  41. [49]

    L. Y. Cao, Z. A. Xu, B. X. Gao, L. Wang, X. T. Zhang, X. Y. Zhang, Y. F. Guo, and R. Y. Chen, Optical study of the three-dimensional Weyl semimetal Mn 3Sn, Phys. Rev. B 108, 235109 (2023)

    2023

  42. [50]

    lohani, P

    H. lohani, P. Foulquier, P. Le F` evre, F. m. c. Bertran, D. Colson, A. Forget, and V. Brouet, Electronic struc- ture evolution of the magnetic Weyl semimetal Co 3Sn2 S2 with hole and electron doping, Phys. Rev. B 107, 245119 (2023)

    2023

  43. [51]

    Grosso and G

    G. Grosso and G. Pastori Parravicini, Solid State Physics (Elsevier Science, London, 2000)

    2000

  44. [52]

    Lv and S.-C

    M. Lv and S.-C. Zhang, Dielectric Function, Friedel os- cillation and plasmons in Weyl Semimetals, International Journal of Modern Physics B 27, 1350177 (2013)

    2013

  45. [53]

    Hofmann and S

    J. Hofmann and S. Das Sarma, Plasmon signature in Dirac-Weyl liquids, Phys. Rev. B 91, 241108 (2015)

    2015

  46. [54]

    O. V. Kotov and Y. E. Lozovik, Dielectric response and novel electromagnetic modes in three-dimensional Dirac semimetal films, Phys. Rev. B 93, 235417 (2016)

    2016

  47. [55]

    M. M. Vazifeh and M. Franz, Electromagnetic Response of Weyl Semimetals, Phys. Rev. Lett.111, 027201 (2013)

    2013

  48. [56]

    J. M. Ziman, Principles of the Theory of Solids , 2nd ed. (Cambridge University Press, 1972)

    1972

  49. [57]

    Chiriac` o and A

    G. Chiriac` o and A. J. Millis, Voltage-induced metal- insulator transition in a one-dimensional charge density wave, Phys. Rev. B 98, 205152 (2018)

    2018

  50. [58]

    Tarento, K.-H

    R.-J. Tarento, K.-H. Bennemann, P. Joyes, and J. Van de Walle, Mie scattering of magnetic spheres, Phys. Rev. E 69, 026606 (2004)

    2004

  51. [59]

    R. G. Barrera, G. A. Estevez, and J. Giraldo, Vector spherical harmonics and their application to magneto- statics, European Journal of Physics 6, 287 (1985)

    1985

  52. [60]

    J. D. Jackson, Classical electrodynamics; 2nd ed. (Wiley, New York, NY, 1975)

    1975

  53. [61]

    Li and H.-S

    E.-P. Li and H.-S. Chu, Plasmonic Nanoelectronics and Sensing (Cambridge University Press, Cambridge, 2014)

    2014

  54. [62]

    Hayashi and T

    S. Hayashi and T. Okamoto, Plasmonics: visit the past to know the future, J. Phys. D: Appl. Phys. 45, 433001 (2012)

    2012

  55. [63]

    Y. Hu, H. Liu, B. Yang, K. Shi, M. Antezza, X. Wu, and Y. Sun, High-rectification near-field radiative ther- mal diode using Weyl semimetals, Phys. Rev. Mater. 7, 035201 (2023)

    2023

  56. [64]

    Naeimi and S.-A

    A. Naeimi and S.-A. Biehs, Efficiency and mechanism of heat flux rectification with non-reciprocal surface waves in Weyl-Semi-Metals, Physical Review Materials 9, 045201 (2025)

    2025

  57. [65]

    Hofmann and S

    J. Hofmann and S. Das Sarma, Surface plasmon polari- tons in topological Weyl semimetals, Phys. Rev. B 93, 241402 (2016)

    2016

  58. [66]

    Sekine and K

    A. Sekine and K. Nomura, Axion electrodynamics in topological materials, Journal of Applied Physics 129, 141101 (2021)

    2021

  59. [67]

    Buchhold, S

    M. Buchhold, S. Diehl, and A. Altland, Nodal points of Weyl semimetals survive the presence of moderate disor- der, Phys. Rev. B 98, 205134 (2018)

    2018

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