Pith. sign in

REVIEW 5 major objections 4 minor 1 cited by

Cherenkov radiation in isotropic chiral matter: the space-frequency domain

T0 review · 5 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Cherenkov radiation survives below the usual velocity threshold in chiral matter, split into two independent polarization cones.

desk verdict Exact solution to a contested problem, with a clean two-cone prediction—but the threshold-free channel hinges on an energy-momentum tensor choice that the paper does not fully justify. read the letter →

arxiv 2507.06369 v1 pith:DKGAQMHX submitted 2025-07-08 hep-ph cond-mat.mes-hallhep-th

R. Martínez von Dossow , Eduardo Barredo-Alamilla , Maxim A. Gorlach , Luis F. Urrutia This is my paper
classification hep-phcond-mat.mes-hallhep-th
keywords CherenkovradiationisotropicchiralmatterCarroll-Field-Jackiwelectrodynamicsthreshold-freegaugeinvariancespace-frequencydomaincircularpolarizationmodesWeylsemimetals
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 tries to settle whether a uniformly moving charge in isotropic chiral matter radiates Cherenkov light, a question for which earlier calculations gave opposite answers. It solves Maxwell's equations with the extra magnetic-current term of Carroll-Field-Jackiw electrodynamics exactly in the space-frequency domain and derives a spectral energy distribution for each circular polarization. Each distribution is positive and gauge-invariant, and the two polarizations radiate independently at distinct angles. In the sector with $v

What carries the argument

The load-bearing machinery is a space-frequency-domain solution in cylindrical coordinates, using outgoing modified Bessel functions $K_0$ and $K_1$ as the radial basis. The normal modes are the two circular polarizations $\nu=\pm$, with squared transverse momenta set by a quartic dispersion relation whose causal branch is $Q_\nu=-i\sqrt{q_\nu}$, selecting only real frequencies and avoiding the imaginary-frequency runaway modes of plane-wave treatments. Gauge invariance of the radiated energy is restored by proving that the total time-integrated Poynting flux through a surface at infinity is invariant under $\delta A=\nabla\delta\Lambda$, despite the non-invariant local flux. Positivity is extracted by rewriting each $E_\nu$ in terms of the emission angle $\Theta_\nu$ and the positive quantity $F_\nu=\sqrt{1+\Sigma^2/4}-\nu\Sigma/2$.

What would settle it

Look for the predicted single cone from a sub-luminal electron beam in a Weyl semimetal with known $\sigma$ and $n$: for $n=3$, $\sigma=0.05$ eV, $\beta=0.1$, the paper predicts radiation only for $0<\omega<\sigma\beta/(1-n^2\beta^2)\approx5.5$ meV at angle $\cos\Theta_-=1/(n\beta F_-)$, with no such cone in standard Cherenkov theory; a null result at that angle and frequency would falsify the central claim.

Watch

Extended reading notes

Core claim

The central claim is that a charge moving at constant velocity through isotropic chiral matter radiates as an independent sum of two normal modes, $\nu=\pm$, with per-mode spectral energy $$E_\nu = \frac{$q^{2}$\omega}{$2c^{2}$}\left(1 - \frac{1}{$n^{2}$\$beta^{2}$} - \frac{\nu\$\sigma$}{\sqrt{\$sigma^{2}$+$4n^{2}$\$omega^{2}$}}\left(1+\frac{1}{$n^{2}$\$beta^{2}$}\right)\right),$$ which is positive because it can be written as $\frac{q^2\omega}{2c^2}\frac{F_\nu}{\sqrt{1+\Sigma^2/4}}\sin^2\Theta_\nu$. The interference term vanishes exactly, so the total spectrum is $E=E_+ + E_-$; when both channels are open this sum reduces to the standard Cherenkov spectrum and is independent of $\sigma$. Causality fixes each mode's dispersion by demanding outgoing waves at infinity, and the potential-dependent part of the Poynting flux is shown to be gauge invariant even though the local Poynting vector is not.

Load-bearing premise

The result depends on the paper's chosen conserved energy-momentum tensor, including the potential-dependent Poynting flux, as the physical measure of radiated energy; an equally justified alternative measure could change or erase the predicted radiation.

Editorial extensions

If this is right

  • When both polarization channels are open ($v>c/n$ and $\omega>\sigma\beta/(n^2\beta^2-1)$), the total spectral energy $E_+ + E_-$ equals the standard Cherenkov result and is independent of $\sigma$.
  • When $v<c/n$, the negative-polarization mode radiates in the window $0<\omega<\sigma\beta/(1-n^2\beta^2)$, so slowly moving charges emit Cherenkov light without reaching the standard threshold.
  • The two modes emit at distinct angles $\Theta_\nu$ given by $\cos\Theta_\nu=1/(n\beta F_\nu)$, so an angle-resolved detector can see one cone, two cones, or none as the frequency is swept.
  • For $n=1$ and $\sigma\neq0$, the same calculation predicts vacuum Cherenkov radiation in a finite low-frequency window, contrary to earlier no-radiation results.

Reading between the lines

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

  • Beyond the paper, the angular separation between the two cones could serve as a frequency-dependent probe of $\sigma$: because $\Theta_\nu$ depends on $\sigma$ at fixed $n$ and $\beta$, fitting the cone angles would measure the magnetoelectric parameter without requiring absolute intensity calibration.
  • Beyond the paper, the time-domain fate of the unstable runaway modes is not settled by the radiation-zone calculation, so transient energy flows at entry and exit remain untested.
  • Beyond the paper, because the total $E_+ + E_-$ is $\sigma$-independent while the individual cones are not, an experiment with poor angular resolution could miss the anomaly; resolving the two cones may be necessary to test the model.
  • Beyond the paper, the threshold-free channel's $1/(\gamma-1)$ enhancement suggests tabletop electron beams rather than accelerator beams could test the prediction.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 4 minor

Summary. The paper studies Cherenkov radiation from a charge moving at constant velocity in isotropic chiral matter described by Carroll-Field-Jackiw electrodynamics. Working in the space-frequency domain with cylindrical coordinates, the authors obtain closed-form expressions for the electromagnetic fields as superpositions of two circular polarization modes, determine the coefficients from boundary conditions, and compute the spectral energy distribution for each mode. Their central results are that the interference term between the two polarization modes vanishes exactly, that each mode has a positive, gauge-invariant spectral energy distribution (Eq. 18), and that the two modes radiate at distinct Cherenkov angles. For subluminal charges (v < c/n), the ν = − mode radiates in a finite frequency window, which the authors present as threshold-free Cherenkov radiation, including in the n = 1 'vacuum' case. The paper claims this resolves the controversy between Refs. [63,64] (no vacuum Cherenkov losses) and Refs. [67,70] (nonzero radiation).

Significance. If the results are correct, the paper provides an exact, parameter-free solution for a longstanding controversy in CFJ electrodynamics. The derivation is self-contained and the central formula (18) is closed-form; the positivity proof for each polarization and the distinct emission angles are experimentally falsifiable predictions. The paper also gives concrete estimates for the photon extraction efficiency in Weyl semimetals. The main strength is that the calculation is not a perturbative expansion but an exact solution of the modified Maxwell equations, with no fitted parameters, and the gauge invariance of the integrated energy flux is addressed explicitly. However, the physical significance of the headline threshold-free prediction depends on the choice of energy-momentum tensor, and several load-bearing algebraic steps are asserted rather than shown.

major comments (5)
  1. [Sec. 2, Eq. (3); Sec. 3, Eq. (16)] The central physical prediction, including the threshold-free ν = − radiation for β < 1/n, is computed using the modified Poynting vector in Eq. (3). The manuscript does not derive Eq. (3) from the CFJ Lagrangian, nor does it prove that this is the unique locally conserved energy-momentum tensor compatible with the field equations. The gauge-invariance proof in Eqs. (14)–(15) shows only that the integrated flux is gauge invariant for this particular flux; it does not show that this flux is the observable energy loss of the moving charge. Alternative conserved energy flux definitions are used in the literature, notably in Refs. [63,64], and they lead to different conclusions about vacuum Cherenkov losses. The field-level checks in Table 1 and the Appendix compare E and B, not the energy flux, so they cannot validate the flux convention. The claim that Eν is 'the' spectral energy distribution is therefore a statement about a chosen EMT, and the claimed resolution of the [63,64] vs [67,70] controversy is not fully established.
  2. [Sec. 2, after Eq. (13)] The coefficients X± are asserted without derivation: the text states that 'imposing the boundary conditions at ρ → 0 we obtain' X+ = −iωΓQ+/c and X− = iωΓQ−/c, but no matching calculation is shown. These coefficients set the absolute normalization of all fields and therefore determine the magnitude of the spectral energy distribution in Eq. (18). Without this derivation, the central quantitative result cannot be independently verified.
  3. [Sec. 3, before Eq. (18)] The exact cancellation of the interference term E(+,−) is a load-bearing assumption: it is what allows the total spectrum to be written as E = E+ + E− and what gives each polarization an independent physical meaning. The manuscript states only that 'Surprisingly, the interference term yields exactly zero,' with no algebra. If this cancellation failed, Eq. (18) would not be the per-mode spectrum and the positivity argument for each Eν would lose its meaning. Given that the fields are superpositions of Bessel functions with different arguments, the vanishing of all cross terms in Eq. (16) is nontrivial and needs to be demonstrated.
  4. [Sec. 3, Eq. (18)] The derivation of Eq. (18) from Eq. (16) is described as 'simple but tedious' and is not shown. Since Eq. (18) is the central quantitative result of the paper, and since it involves products of fields and potentials with different polarization indices, the omission of intermediate steps prevents the reader from checking the algebra. At minimum, an appendix with the key steps leading to Eq. (18) is required.
  5. [Sec. 3 and Appendix, Table 1 and Eq. (30)] The comparison with Refs. [63,64] is presented as a validation of the exact solution, but it checks only near-zone fields (e.g., B(0,1) ∼ sinθ/R^2) and uses a power-series expansion in σ at fixed frequency and fixed ρ. For the subluminal threshold-free window, ω ≤ σβ/(1 − n^2β^2), the radial wavenumber of the radiating mode is q− = O(σ^2) from Eq. (17), so the oscillatory asymptotic behavior of K1(−i√q−ρ) sets in only at ρ ∼ 1/σ. The fixed-order expansion in Eq. (30) is not uniform in this regime and does not capture the radiating sector of the exact solution. Consequently, the Appendix comparison does not demonstrate that the radiative part of the field, which carries the headline prediction, agrees with previous results.
minor comments (4)
  1. [Eq. (16)] The notation E is used both for the total energy and for the spectral distribution d^2E/dωdz; please define the per-unit-length, per-unit-frequency quantity explicitly and use a distinct symbol, such as E_ω, to avoid confusion.
  2. [Table 1] The superscripts (0,1), (1,1), (2,1), and (2,2) in the first column are never explained; the reader must infer that they refer to the order of the σ-expansion and to field components. Please state this explicitly.
  3. [Abstract and Sec. 4] The term 'threshold-free Cherenkov radiation' should be qualified: the radiation occurs in a finite frequency window 0 < ω < σβ/(1 − n^2β^2), so there is no velocity threshold, but there is a frequency cutoff. This distinction is clear in the main text but could be stated in the abstract.
  4. [Appendix] The sentence 'Lack of space prevent us for showing the expansion for each polarization mode' contains grammatical errors and should be rewritten; more importantly, showing the per-mode expansion would strengthen the validation of the exact solution.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the derivation is a self-contained solution of the CFJ field equations with no fitted parameters and no load-bearing self-citations.

full rationale

The paper's central result, Eq. (18), is obtained by solving Maxwell's equations for CFJ electrodynamics in the space-frequency domain, imposing source boundary conditions at ρ→0 and outgoing-wave causality at ρ→∞, and then computing the time-integrated flux of the energy-momentum tensor introduced in Eq. (3). This is a direct derivation rather than a fit: no parameter is adjusted to data, and no prior result of the same authors is invoked to force the conclusion. The gauge-invariance proof for the total radiated energy is carried out explicitly in Eqs. (14)–(15), and the positivity of each polarization channel follows algebraically from Eqs. (19)–(23). The comparisons with Refs. [63,64] are external validations, not inputs, and the manuscript explicitly checks its own series expansion against those independent iterative calculations. The only debatable point is the physical choice of the energy-momentum tensor in Eq. (3), since CFJ electrodynamics admits more than one locally conserved stress tensor. That is an underdetermination or modeling concern about which observable corresponds to radiated energy, not a circularity: the paper does not define the radiation to be the EMI flux and then present that definition as a prediction; it computes the flux of a specified conserved tensor and proves the relevant integrated quantity is gauge invariant. Therefore no circular step is exhibited, and the circularity score is 0.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

No new particles, forces, or dimensions are introduced. The two circular polarization modes are normal modes of the established CFJ model, not invented entities. The model parameters sigma, n, and beta are inputs from the physical setup, not fitted to data. The main external inputs are the CFJ Lagrangian and the choice of the energy-momentum tensor defining the radiated energy.

assumptions (5)
  • domain assumption The medium is described by CFJ electrodynamics with constant epsilon, mu = 1, and magnetoelectric coefficient sigma (Eqs. 1-2).
    The entire calculation uses this model; real chiral matter has frequency-dependent responses, and the paper assumes epsilon and sigma are constant in a finite frequency range.
  • domain assumption The local energy density and Poynting vector are given by Eq. (3), derived from a specific conserved energy-momentum tensor.
    Different choices of the energy-momentum tensor could yield different radiated energy; the paper argues this one is the canonical conserved tensor, but the physical identification is a load-bearing premise.
  • domain assumption Fields are decomposed as E_phi = X K1(Q rho), E_rho = Y K1(Q rho) (Eq. 9), with the I1 solution rejected by boundary conditions.
    This ansatz is standard for the homogeneous equations, but the justification that the source only fixes the singular part and that the outgoing-wave condition selects the correct branch is not fully derived in the text.
  • ad hoc to paper The interference term between polarization modes vanishes exactly.
    Stated without proof in Section 3; this claim is crucial for the independent-mode interpretation of the spectral energy distribution.
  • standard math Gauge invariance of the total radiated energy holds assuming boundary terms (delta Lambda B) vanish at t = +/- infinity.
    Standard integration by parts in the gauge-invariance proof; requires decay assumptions on the gauge function and fields at infinity.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Cherenkov radiation in isotropic chiral matter: the space-frequency domain." pith.science (2026). https://pith.science/paper/DKGAQMHX

@misc{pith2026250706369,
  author       = {Pith},
  title        = {Pith review of: Cherenkov radiation in isotropic chiral matter: the space-frequency domain},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DKGAQMHX}},
  note         = {Machine review of arXiv:2507.06369}
}
read the original abstract

The electromagnetic response of isotropic chiral matter, as described by Carroll-Field-Jackiw electrodynamics, arises in distinct physical contexts ranging from condensed matter systems to Lorentz-violating extensions of high-energy physics. Here, we derive exact expressions for the circularly polarized electromagnetic fields that contribute independently to Cherenkov radiation in isotropic chiral matter. Each spectral energy distribution is gauge-invariant and positive, yielding radiation that emerges at a characteristic angle, akin to the standard case. Furthermore, we identify specific frequency ranges that permit zero, one, or two Cherenkov cones for a given setup. Remarkably, one sector of the model allows for the existence of threshold-free Cherenkov radiation arising from slowly-moving charges.

Figures

Figures reproduced from arXiv: 2507.06369 by the authors.

Figure 1
Figure 1. Left panel: Emission angles as a function of the fre [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. The function Ω(ω) for the charge velocities β1 = 0.01, β2 = 0.10 and β3 = 0.25. In other words, the strongest variations of η˜−1 arise from the amplifying factor 1/(γ − 1) as schematically shown in [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗

Discussion (0). Sign in to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Anomalous increasing super reflectance in chiral matter

    cond-mat.other 2025-07 conditional novelty 5.0 of 10

    A chiral medium with oppositely signed magnetic and Hall conductivities is derived to reflect more light than it receives, with reflectance increasing with frequency inside the absorption band.

Reference graph

Works this paper leans on

84 extracted references · 42 canonical work pages · cited by 1 Pith paper

  1. [2]

    Vavilov, Cr acad, sci

    S. Vavilov, Cr acad, sci. ussr 2, 457 (1934), in: Dokl. Aka d. Nauk SSSR, Vol. 2, 1934, p. 457

    1934

  2. [3]

    I. M. Frank, I. E. Tamm, Coherent visible radiation of fas t electrons pass- ing through matter, Compt. Rend. Acad. Sci. URSS 14 (3) (1937 ) 109–114. doi:10.3367/UFNr.0093.196710o.0388

    work page arXiv 1937

  3. [4]

    Ypsilantis, J

    T. Ypsilantis, J. Seguinot, Theory of ring imaging Chere nkov counters, Nucl. Instrum. Meth. A 343 (1994) 30–51. doi:10.1016/0168-9002(94)90532-0. 12

    doi:10.1016/0168-9002(94)90532-0 1994

  4. [5]

    J. J. Aubert, et al., Experimental Observation of a Heavy Particle J, Phys. Rev. Lett. 33 (1974) 1404–1406. doi:10.1103/PhysRevLett.33.1404

    doi:10.1103/physrevlett.33.1404 1974

  5. [6]

    Amenomori, et al., First Detection of sub-PeV Diffuse G amma Rays from the Galactic Disk: Evidence for Ubiquitous Galactic Cosmic Rays beyond P eV Energies, Phys

    M. Amenomori, et al., First Detection of sub-PeV Diffuse G amma Rays from the Galactic Disk: Evidence for Ubiquitous Galactic Cosmic Rays beyond P eV Energies, Phys. Rev. Lett. 126 (14) (2021) 141101. arXiv:2104.05181, doi:10.1103/PhysRevLett.126.141101

    arXiv 2021

  6. [7]

    Adamo, K

    G. Adamo, K. F. MacDonald, Y. Fu, C. Wang, D. Tsai, F. J. Gar cía de Abajo, N. Zheludev, Light well: a tunable free-electron light source on a chip, P hysical review letters 103 (11) (2009) 113901. doi:doi.org/10.1103/PhysRevLett.103.113901

    work page doi:10.1103/physrevlett.103.113901 2009

  7. [8]

    S. Liu, P. Zhang, W. Liu, S. Gong, R. Zhong, Y. Zhang, M. Hu, Surface polari- ton cherenkov light radiation source, Physical review lett ers 109 (15) (2012) 153902. doi:doi.org/10.1103/PhysRevLett.109.153902

    work page doi:10.1103/physrevlett.109.153902 2012

  8. [9]

    F. Liu, L. Xiao, Y. Ye, M. Wang, K. Cui, X. Feng, W. Zhang, Y. Huang, Integrated cherenkov radiation emitter eliminating the electron velocity thres hold, Nature Photonics 11 (5) (2017) 289–292. doi:doi.org/10.1038/nphoton.2017.45

    work page doi:10.1038/nphoton.2017.45 2017

Show all 84 references
  1. [10]

    Hachadorian, P

    R. Hachadorian, P. Bruza, M. Jermyn, D. Gladstone, B. Po gue, L. Jarvis, Imaging radiation dose in breast radiotherapy by x-ray ct calibration of chere nkov light, Nature communications 11 (1) (2020) 2298. doi:doi.org/10.1038/s41467-020-16031-z

    2020 doi

  2. [11]

    D. A. Alexander, A. Nomezine, L. A. Jarvis, D. J. Gladsto ne, B. W. Pogue, P. Bruza, Color cherenkov imaging of clinical radiation therapy, Light: Sc ience & Applications 10 (1) (2021)

    2021

  3. [12]

    T. M. Shaffer, E. C. Pratt, J. Grimm, Utilizing the power o f cerenkov light with nanotechnol- ogy, Nature nanotechnology 12 (2) (2017) 106–117. doi:doi.org/10.1038/nnano.2016.301

    2017 doi

  4. [13]

    X. Wang, L. Li, J. Li, P. Wang, J. Lang, Y. Yang, Cherenkov luminescence in tu- mor diagnosis and treatment: A review, in: Photonics, Vol. 9 , MDPI, 2022, p. 390. doi:10.3390/photonics9060390

    2022 doi

  5. [14]

    Kotagiri, G

    N. Kotagiri, G. P. Sudlow, W. J. Akers, S. Achilefu, Brea king the depth dependency of pho- totherapy with cerenkov radiation and low-radiance-respo nsive nanophotosensitizers, Nature nanotechnology 10 (4) (2015) 370–379. doi:10.1038/nnano.2015.17

    2015 doi

  6. [15]

    Kamkaew, L

    A. Kamkaew, L. Cheng, S. Goel, H. F. Valdovinos, T. E. Bar nhart, Z. Liu, W. Cai, Cerenkov radiation induced photodynamic therapy using chl orin e6-loaded hollow meso- porous silica nanoparticles, ACS applied materials & inter faces 8 (40) (2016) 26630–26637. doi:10.1021/acsam...

    2016 doi

  7. [16]

    V. P. Zrelov, Cherenkov radiation in high-energy physi cs : [by] V. P. Zrelov. Translated from Russian [by Y. Oren. Edited by Benny Baruch]., U.S. Atomic En ergy Commission. AEC- tr-7099, Jerusalem, Israel Program for Scientific Translat ions; [available for U.S. Dept. of Comme...

    1970

  8. [17]

    H. Hu, X. Lin, Y. Luo, Free-electron radiation engineer ing via structured environments, arXiv preprint arXiv:2108.06149 (2021). doi:10.2528/PIER21081303

    2021 arXiv

  9. [18]

    Zhang, X

    T. Zhang, X. Zhang, Z. Zhang, X. Xu, Y. Wang, Z. Duan, Y. We i, Y. Gong, S. Liu, M. Hu, et al., Tunable optical topological transition of cherenko v radiation, Photonics Research 10 (7) (2022) 1650–1660. doi:10.1109/IRMMW-THz50927.2022.9895651

    2022

  10. [19]

    H. Hu, X. Lin, J. Zhang, D. Liu, P. Genevet, B. Zhang, Y. Lu o, Nonlocal- ity induced cherenkov threshold, Laser & Photonics Reviews 14 (10) (2020) 2000149. doi:10.1002/lpor.202000149

    2020 doi

  11. [20]

    Z. Gong, J. Chen, R. Chen, X. Zhu, C. Wang, X. Zhang, H. Hu, Y. Yang, B. Zhang, H. Chen, et al., Interfacial cherenkov radiation from ultralow-ene rgy electrons, Proceedings of the Na- tional Academy of Sciences 120 (38) (2023) e2306601120. doi:10.1073/pnas.2306601120

    2023 doi

  12. [21]

    Skryabin, Y

    D. Skryabin, Y. Kartashov, O. Egorov, M. Sich, J. Chana, L. Tapia Rodriguez, P. Walker, E. Clarke, B. Royall, M. Skolnick, et al., Backward cherenko v radiation emitted by polariton solitons in a microcavity wire, Nature communica tions 8 (1) (2017) 1554. doi:10.1038/s41467-01...

    2017 doi

  13. [22]

    Genevet, D

    P. Genevet, D. Wintz, A. Ambrosio, A. She, R. Blanchard, F. Capasso, Controlled steering of cherenkov surface plasmon wakes with a one-dimensional m etamaterial, Nature Nanotech- nology 10 (9) (2015) 804–809. doi:10.1038/nnano.2015.137

    2015 doi

  14. [23]

    S. N. Galyamin, A. V. Tyukhtin, A. Kanareykin, P. Schoes sow, Reversed cherenkov-transition radiation by a charge crossing a left-handed medium boundar y, Physical review letters 103 (19) (2009) 194802. doi:10.1103/PhysRevLett.103.194802

    2009 doi

  15. [24]

    Veselago, The electrodynamics of substances with si multaneously negative values of ǫ and µ, Usp

    V. Veselago, The electrodynamics of substances with si multaneously negative values of ǫ and µ, Usp. fiz. nauk 92 (3) (1967) 517–526. doi:10.1070/PU1968v010n04ABEH003699

    1967 doi

  16. [25]

    R. A. Shelby, D. R. Smith, S. Schultz, Experimental veri fication of a negative index of refrac- tion, science 292 (5514) (2001) 77–79. doi:10.1126/science.1058847

    2001 doi

  17. [26]

    S. Xi, H. Chen, T. Jiang, L. Ran, J. Huangfu, B.-I. Wu, . f. J. A. Kong, M. Chen, Experimen- tal verification of reversed cherenkov radiation in left-ha nded metamaterial, Physical review letters 103 (19) (2009) 194801. doi:10.1103/PhysRevLett.103.194801

    2009 doi

  18. [27]

    Zhang, X

    S. Zhang, X. Zhang, Flipping a photonic shock wave, Phys ics 2 (2009) 91

    2009

  19. [28]

    X. Lu, M. A. Shapiro, I. Mastovsky, R. J. Temkin, M. Conde , J. G. Power, J. Shao, E. E. Wisniewski, C. Jing, Generation of high-power, revers ed-cherenkov wakefield ra- diation in a metamaterial structure, Physical review lette rs 122 (1) (2019) 014801. doi:10.1103/PhysRevLett...

    2019 doi

  20. [29]

    Z. Duan, X. Tang, Z. Wang, Y. Zhang, X. Chen, M. Chen, Y. Go ng, Observa- tion of the reversed cherenkov radiation, Nature Communica tions 8 (1) (2017) 14901. doi:10.1038/ncomms14901. 14

    2017 doi

  21. [30]

    O. J. Franca, L. F. Urrutia, O. Rodríguez-Tzompantzi, R eversed electromagnetic Vavilov- Čerenkov radiation in naturally existing magnetoelectric media, Phys. Rev. D 99 (11) (2019) 116020. arXiv:1905.12088, doi:10.1103/PhysRevD.99.116020

    2019 arXiv

  22. [31]

    R. Chen, Z. Gong, Z. Wang, X. Xi, B. Zhang, Y. Yang, B. Zhan g, I. Kaminer, H. Chen, X. Lin, A gain route to reversed cherenkov radiation, Science Advan ces 11 (14) (2025) eads5113. doi:10.1126/sciadv.ads5113

    2025 doi

  23. [32]

    S. M. Carroll, G. B. Field, R. Jackiw, Limits on a Lorentz and Parity Violating Modification of Electrodynamics, Phys. Rev. D 41 (1990) 1231. doi:10.1103/PhysRevD.41.1231

    1990 doi

  24. [33]

    Sikivie, Experimental Tests of the Invisible Axion, Phys

    P. Sikivie, Experimental Tests of the Invisible Axion, Phys. Rev. Lett. 51 (1983) 1415–1417, [Erratum: Phys.Rev.Lett. 52, 695 (1984)]. doi:10.1103/PhysRevLett.51.1415

    1983 doi

  25. [34]

    Wilczek, Two Applications of Axion Electrodynamics , Phys

    F. Wilczek, Two Applications of Axion Electrodynamics , Phys. Rev. Lett. 58 (1987) 1799. doi:10.1103/PhysRevLett.58.1799

    1987 doi

  26. [35]

    C. Adam, F. R. Klinkhamer, Causality and CPT violation f rom an Abelian Chern- Simons like term, Nucl. Phys. B 607 (2001) 247–267. arXiv:hep-ph/0101087, doi:10.1016/S0550-3213(01)00161-4

    2001 arXiv

  27. [36]

    V. A. Kostelecky, A. G. M. Pickering, Vacuum photon spli tting in Lorentz violating quantum electrodynamics, Phys. Rev. Lett. 91 (2003) 031801 . arXiv:hep-ph/0212382, doi:10.1103/PhysRevLett.91.031801

    2003 arXiv

  28. [37]

    Lehnert, R

    R. Lehnert, R. Potting, Vacuum Cerenkov radiation, Phy s. Rev. Lett. 93 (2004) 110402. arXiv:hep-ph/0406128, doi:10.1103/PhysRevLett.93.110402

    2004 arXiv

  29. [38]

    Lehnert, R

    R. Lehnert, R. Potting, The Cerenkov effect in Lorentz-v iolating vacua, Phys. Rev. D 70 (2004) 125010, [Erratum: Phys.Rev.D 70, 129906 (2004)]. arXiv:hep-ph/0408285, doi:10.1103/PhysRevD.70.129906

    2004 arXiv

  30. [39]

    Kaufhold, F

    C. Kaufhold, F. R. Klinkhamer, Vacuum Cherenkov radiat ion and photon triple-splitting in a Lorentz-noninvariant extension of quantum electrodynami cs, Nucl. Phys. B 734 (2006) 1–23. arXiv:hep-th/0508074, doi:10.1016/j.nuclphysb.2005.11.001

    2006 arXiv

  31. [40]

    Colladay, P

    D. Colladay, P. McDonald, R. Potting, Cherenkov Radiat ion with Massive, CPT- violating Photons, Phys. Rev. D 93 (12) (2016) 125007. arXiv:1603.00308, doi:10.1103/PhysRevD.93.125007

    2016 arXiv

  32. [41]

    Schreck, Vacuum Cherenkov radiation for Lorentz-vi olating fermions, Phys

    M. Schreck, Vacuum Cherenkov radiation for Lorentz-vi olating fermions, Phys. Rev. D 96 (9) (2017) 095026. arXiv:1702.03171, doi:10.1103/PhysRevD.96.095026

    2017 arXiv

  33. [42]

    Lisboa-Santos, J

    L. Lisboa-Santos, J. a. A. A. S. Reis, M. Schreck, M. M. Fe rreira, Jr., Planar electrodynamics modified by higher-derivative terms, Phys. Rev. D 108 (11) (2023) 115032. arXiv:2309.16839, doi:10.1103/PhysRevD.108.115032

    2023 arXiv

  34. [43]

    O’Connor, B

    J. O’Connor, B. Altschul, Radiation from an oscillatin g dipole in the presence of photon- sector CPT and Lorentz violation, Phys. Rev. D 109 (4) (2024) 045005. arXiv:2309.05648, doi:10.1103/PhysRevD.109.045005. 15

    2024 arXiv

  35. [44]

    P. D. S. Silva, M. M. Ferreira, M. Schreck, L. F. Urrutia, Magnetic-conductivity effects on electromagnetic propagation in dispersive matter, Phys . Rev. D 102 (7) (2020) 076001. arXiv:2006.02022, doi:10.1103/PhysRevD.102.076001

    2020 arXiv

  36. [45]

    P. D. S. Silva, L. Lisboa-Santos, M. M. Ferreira, Jr., M. Schreck, Effects of CPT-odd terms of dimensions three and five on electromagnetic propagation in continuous matter, Phys. Rev. D 104 (11) (2021) 116023. arXiv:2109.04659, doi:10.1103/PhysRevD.104.116023

    2021 arXiv

  37. [46]

    O. J. Franca, S. Y. Buhmann, Modification of transition r adiation by three-dimensional topological insulators, Phys. Rev. B 105 (15) (2022) 155120 . arXiv:2110.08369, doi:10.1103/PhysRevB.105.155120

    2022 arXiv

  38. [47]

    O. J. Franca, L. F. Urrutia, Radiation from a dipole perp endicular to the interface be- tween two planar semi-infinite magnetoelectric media, Rev. Mex. Fis. 68 (6) (2022) 060701. arXiv:2107.06824, doi:10.31349/RevMexFis.68.060701

    2022 arXiv

  39. [48]

    Barredo-Alamilla, L

    E. Barredo-Alamilla, L. F. Urrutia, M. M. Ferreira, Jr. , Electromagnetic radiation in chiral matter: The Cherenkov case, Phys. Rev. D 107 (9) (2023) 09602 4. arXiv:2305.07963, doi:10.1103/PhysRevD.107.096024

    2023 arXiv

  40. [49]

    P. D. S. Silva, M. J. Neves, M. M. Ferreira, Jr., Optical p roperties and energy propagation in a dielectric medium supporting magnetic current, Phys. R ev. B 109 (18) (2024) 184439. arXiv:2305.08153, doi:10.1103/PhysRevB.109.184439

    2024 arXiv

  41. [50]

    O. J. Franca, S. Y. Buhmann, Vavilov-Cherenkov radiati on for parallel motion in three- dimensional topological insulators, Phys. Rev. B 110 (19) ( 2024) 195150. arXiv:2405.15906, doi:10.1103/PhysRevB.110.195150

    2024 arXiv

  42. [51]

    Lindell, A

    I. Lindell, A. Sihvola, S. Tretyakov, A. J. Viitanen, El ectromagnetic waves in chiral and bi-isotropic media, Artech House, 1994

    1994

  43. [52]

    Serdyukov, I

    A. Serdyukov, I. Semchenko, S. Tretyakov, A. Sihvola, E lectromagnetics of bi-anisotropic materials: Theory and applications (2001)

    2001

  44. [53]

    Fernandez-Corbaton, M

    I. Fernandez-Corbaton, M. Fruhnert, C. Rockstuhl, Obj ects of maximum electromagnetic chirality, Phys. Rev. X 6 (2016) 031013. doi:10.1103/PhysRevX.6.031013

    2016 doi

  45. [54]

    K. V. Voronin, A. N. Toksumakov, G. A. Ermolaev, A. S. Sla vich, M. K. Tatmyshevskiy, S. M. Novikov, A. A. Vyshnevyy, A. V. Arsenin, K. S. Novoselov, D. A . Ghazaryan, et al., Chiral photonic super-crystals based on helical van der waals homo structures, Laser & Photonics Revi...

    2024

  46. [55]

    Toftul, P

    I. Toftul, P. Tonkaev, K. Koshelev, F. Lai, Q. Song, M. Go rkunov, Y. Kivshar, Chiral dichro- ism in resonant metasurfaces with monoclinic lattices, Phy s. Rev. Lett. 133 (2024) 216901. doi:10.1103/PhysRevLett.133.216901

    2024 doi

  47. [56]

    Z. Qiu, G. Cao, X.-G. Huang, Electrodynamics of chiral m atter, Physical Review D 95 (3) (2017) 036002. 16

    2017

  48. [57]

    Jaggard, H

    D. Jaggard, H. Kritikos, C. Papas, Recent Advances in El ectromagnetic Theory, Springer- Verlag, 1990

    1990

  49. [58]

    Shaposhnikov, E

    L. Shaposhnikov, E. Barredo-Alamilla, F. Wilczek, M. A . Gorlach, Probing ultrafast magnetization dynamics via synthetic axion fields, Phys. Re v. Lett. 134 (2025) 246702. doi:10.1103/2rrr-glyn

    2025 doi

  50. [59]

    A. A. Zyuzin, S. Wu, A. A. Burkov, Weyl semimetal with bro ken time reversal and inversion symmetries, Phys. Rev. B 85 (2012) 165110. doi:10.1103/PhysRevB.85.165110

    2012 doi

  51. [60]

    A. A. Zyuzin, A. A. Burkov, Topological response in weyl semimetals and the chiral anomaly, Phys. Rev. B 86 (2012) 115133. doi:10.1103/PhysRevB.86.115133

    2012 doi

  52. [61]

    Fukushima, D

    K. Fukushima, D. E. Kharzeev, H. J. Warringa, Chiral mag netic effect, Phys. Rev. D 78 (2008) 074033. doi:10.1103/PhysRevD.78.074033

    2008 doi

  53. [62]

    D. K. Hong, S. H. Im, K. S. Jeong, D.-h. Yeom, Detecting ax ion dark matter with chiral magnetic effects, Phys. Rev. D 110 (2024) 055036. doi:10.1103/PhysRevD.110.055036

    2024 doi

  54. [63]

    Altschul, Absence of Long-Wavelength Cerenkov Radi ation With Isotropic Lorentz and CPT Violation, Phys

    B. Altschul, Absence of Long-Wavelength Cerenkov Radi ation With Isotropic Lorentz and CPT Violation, Phys. Rev. D 90 (2) (2014) 021701. arXiv:1405.6189, doi:10.1103/PhysRevD.90.021701

    2014 arXiv

  55. [64]

    Schober, B

    K. Schober, B. Altschul, No Vacuum Cerenkov Radiation L osses in the Timelike Lorentz- Violating Chern-Simons Theory, Phys. Rev. D 92 (12) (2015) 1 25016. arXiv:1510.05571, doi:10.1103/PhysRevD.92.125016

    2015 arXiv

  56. [65]

    Altschul, Why Cerenkov Radiation May Not Occur, Even When It Is Allowed by Lorentz- Violating Kinematics, Symmetry 9 (11) (2017) 250

    B. Altschul, Why Cerenkov Radiation May Not Occur, Even When It Is Allowed by Lorentz- Violating Kinematics, Symmetry 9 (11) (2017) 250. doi:10.3390/sym9110250

    2017 doi

  57. [66]

    DeCosta, B

    R. DeCosta, B. Altschul, Mode Analysis for Energetics o f a Moving Charge In Lorentz- and CPT-Violating Electrodynamics, Phys. Rev. D 97 (5) (2018) 0 55029. arXiv:1802.05838, doi:10.1103/PhysRevD.97.055029

    2018 arXiv

  58. [67]

    Tuchin, Radiative instability of quantum electrody namics in chiral matter, Phys

    K. Tuchin, Radiative instability of quantum electrody namics in chiral matter, Phys. Lett. B 786 (2018) 249–254. arXiv:1806.07340, doi:10.1016/j.physletb.2018.09.055

    2018 arXiv

  59. [68]

    Tuchin, Chiral Cherenkov and chiral transition radi ation in anisotropic matter, Phys

    K. Tuchin, Chiral Cherenkov and chiral transition radi ation in anisotropic matter, Phys. Rev. D 98 (11) (2018) 114026. arXiv:1809.08181, doi:10.1103/PhysRevD.98.114026

    2018 arXiv

  60. [69]

    Tuchin, Anomalous scattering and transport in chira l matter, Phys

    K. Tuchin, Anomalous scattering and transport in chira l matter, Phys. Lett. B 808 (2020) 135680. arXiv:2006.07950, doi:10.1016/j.physletb.2020.135680

    2020 arXiv

  61. [70]

    Hansen, K

    J. Hansen, K. Tuchin, Collisional energy loss and the ch iral magnetic effect, Phys. Rev. C 104 (3) (2021) 034903. arXiv:2012.06089, doi:10.1103/PhysRevC.104.034903

    2021 arXiv

  62. [71]

    Hansen, K

    J. Hansen, K. Tuchin, Electromagnetic bremsstrahlung and energy loss in chiral medium, Phys. Rev. D 108 (7) (2023) 076007. arXiv:2307.05761, doi:10.1103/PhysRevD.108.076007. 17

    2023 arXiv

  63. [72]

    J. D. Jackson, Classical Electrodynamics, Wiley, 1998

    1998

  64. [73]

    Schwinger, L

    J. Schwinger, L. L. DeRaad Jr, K. Milton, W.-y. Tsai, Cla ssical electrodynamics, CRC Press, 2019

    2019

  65. [74]

    Abramowitz, I

    M. Abramowitz, I. A. Stegun, Handbook of mathematical f unctions: with formulas, graphs, and mathematical tables, Vol. 55, Courier Corporation, 196 5

  66. [75]

    Chen, et al., Low-Velocity-Favored Transition Radi ation, Phys

    J. Chen, et al., Low-Velocity-Favored Transition Radi ation, Phys. Rev. Lett. 131 (11) (2023) 113002. arXiv:2212.13066, doi:10.1103/PhysRevLett.131.113002

    2023 arXiv

  67. [76]

    Borisenko, D

    S. Borisenko, D. Evtushinsky, Q. Gibson, A. Yaresko, K. Koepernik, T. Kim, M. Ali, J. van den Brink, M. Hoesch, A. Fedorov, et al., Time-reversal symmetr y breaking type-ii weyl state in ybmnbi2, Nature communications 10 (1) (2019) 3424. doi:10.1038/s41467-019-11393-5

    2019 doi

  68. [77]

    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 Ph ysics 11 (9) (2015) 724–727. doi:10.1038/nphys3426

    2015 doi

  69. [78]

    Grassano, O

    D. Grassano, O. Pulci, E. Cannuccia, F. Bechstedt, Influ ence of anisotropy, tilt and pairing of weyl nodes: the weyl semimetals taas, tap, nbas and nbp, Th e European Physical Journal B 93 (2020) 1–12. doi:10.1140/epjb/e2020-10110-x

    2020 doi

  70. [79]

    R. Zu, M. Gu, L. Min, C. Hu, N. Ni, Z. Mao, J. M. Rondinelli, V. Gopalan, Comprehensive anisotropic linear optical properties of the weyl semimeta ls taas and nbas, Physical Review B 103 (16) (2021) 165137. doi:10.1103/PhysRevB.103.165137

    2021 doi

  71. [80]

    B. M. Bolotovskii, O. S. Mergelyan, Theory of vavilov-c herenkov radiation in an isotopic optically active medium, Opt. Spectry. (USSR) (English Tra nsl.) Vol: 14 (03 1963)

    1963

  72. [81]

    Engheta, S

    N. Engheta, S. Bassiri, Čerenkov radiation in chiral me dia, Journal of applied physics 68 (9) (1990) 4393–4398

    1990

  73. [82]

    Barsukov, A

    K. Barsukov, A. Smirnova, Vavilov-cherenkov effect in a chiral waveguide, Technical Physics 44 (3) (1999) 328–330

    1999

  74. [83]

    S. N. Galyamin, A. A. Peshkov, A. V. Tyukhtin, Electroma gnetic field of a charge moving in a chiral isotropic medium, Phys. Rev. E 88 (2013) 013206. doi:10.1103/PhysRevE.88.013206

    2013 doi

  75. [84]

    S. N. Galyamin, A. V. Tyukhtin, A. A. Peshkov, Transitio n radiation at the boundary of a chiral isotropic medium, Phys. Rev. E 95 (2017) 032142. doi:10.1103/PhysRevE.95.032142. 18

    2017 doi

  76. [226]

    doi:10.1038/s41377-021-00660-0

    doi

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.