Magneto-Optics of the Weyl Semimetal TaAs in the THz and IR Regions

Claudia Felser; Hiroshi Watanabe; J\"org Sichelschmidt; Marcus Schmidt; Shin-ichi Kimura; Vicky S\"u\ss; Yuki Nakajima; Yuko Yokoyama

REVIEW 4 major objections 5 minor 19 references

Magneto-Optics of the Weyl Semimetal TaAs in the THz and IR Regions

T0 review · 4 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Magnetic-field optical spectra reveal a Dirac-to-parabolic band crossover in TaAs at about 17 meV.

desk verdict A plausible, useful magneto-optical study of TaAs with a genuinely new scaling claim, but the quantitative support is thinner than the abstract suggests—worth refereeing with a request for error bars and a check on the Kramers-Kronig extrapolation. read the letter →

arxiv 1908.09994 v1 pith:V6NDAA5Y submitted 2019-08-27 cond-mat.str-el

Shin-ichi Kimura , Yuko Yokoyama , Yuki Nakajima , Hiroshi Watanabe , Jörg Sichelschmidt , Vicky Süss , Marcus Schmidt , Claudia Felser This is my paper · ORCID

classification cond-mat.str-el

keywords WeylsemimetalTaAsmagneto-opticsopticalconductivityLandaulevelsterahertzinfraredspectroscopybanddispersion

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

Using magnetic-field-dependent reflectivity of the type-I Weyl semimetal TaAs, a material whose low-energy electrons mimic massless Weyl fermions, the paper reconstructs the optical conductivity at 10 K and reads the band shape from how Landau-level absorption peaks move with field. In the THz range, a broad absorption peak shifts as $\sqrt{B}$ while its amplitude falls as $1/\sqrt{B}$, the predicted signature of optical transitions in linearly dispersing Weyl bands; the spectra collapse onto a single curve under that scaling. In the infrared range above about 17 meV, reflectivity peaks move linearly in $B$, the signature of parabolic free-electron-like bands. The paper concludes that TaAs's band dispersion crosses over from Dirac-like near the Fermi level to free-electron-like near the saddle points, with the crossover around 17 meV, and reports the intensity scaling as an experimental first for Weyl semimetals.

What carries the argument

The engine of the argument is optical absorption between magnetic-field-induced Landau levels, detected as reflectivity changes and converted to optical conductivity by Kramers-Kronig analysis. In a linear band, inter-Landau-level transition energies scale as $\sqrt{B}$ and the absorption strength as $1/\sqrt{B}$; in a parabolic band, the transition energies scale as $B$. The paper uses those two scaling laws as a dispersion meter: the field dependence of each peak labels which kind of band produces it, and the crossover energy labels where the Weyl band ceases to be linear.

What would settle it

Measure the low-energy optical conductivity of TaAs directly, for example by time-domain THz transmission, at 10 K in fields from 0 to 6 T, and compare the peak position and intensity with the Kramers-Kronig-reconstructed spectra; if the apparent peak near 5 meV at 4 T does not move as $\sqrt{B}$ with amplitude proportional to $1/\sqrt{B}$, the central claim fails. Equally decisive would be a band-structure calculation of the field-dependent inter-Landau-level absorption: if no transition with the reported scaling appears near the quoted energies, the interpretation is wrong.

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Extended reading notes

Core claim

The central claim is that in TaAs the conduction band changes dispersion character with energy: near the Fermi level it is linear, so the inter-Landau-level optical peak in the THz region moves as $\hbar\omega_{\mathrm{peak}} = a\sqrt{B}$ with $a = 2.65\,\mathrm{meV}/\mathrm{T}^{1/2}$ and its spectral weight shrinks as $1/\sqrt{B}$; above roughly 17 meV the bands are parabolic, so the infrared Landau-level peaks move linearly in $B$ and extrapolate to about 17 meV at zero field. That extrapolation point is identified with the saddle points between the Weyl points, and the crossover between the two field dependencies is offered as evidence that the linearly dispersing Weyl bands become free-electron-like away from the Weyl points. The simultaneous collapse of energy and intensity scaling is the paper's main experimental result.

Load-bearing premise

The central claim rests on the assumption that the reflectivity below the measured spectral range is correctly reconstructed by the chosen piecewise extrapolation rules in the Kramers-Kronig transform; if that reconstruction is off, the peak positions and intensities that produce the reported $\sqrt{B}$ and $B$ scalings could shift.

Editorial extensions

If this is right

The conduction band of TaAs changes from linear Dirac to parabolic around 17 meV, so magneto-optical Landau-level spectroscopy can map band dispersion directly.
The $\sqrt{B}$ energy scaling paired with the $1/\sqrt{B}$ intensity scaling gives a concrete experimental fingerprint for identifying Weyl-band Landau levels in other materials.
The suppression of the Drude spectral weight with field ties the optical response to the giant magnetoresistance of TaAs.
Extrapolating the infrared peaks to zero field places the saddle-point energy near 17 meV, connecting the optical measurements to the underlying band structure.

Reading between the lines

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

Extended to higher fields, the same measurement could track the crossover continuously and yield a dispersion curve rather than a single crossover energy.
A low-energy measurement that avoids Kramers-Kronig reconstruction, such as time-domain THz transmission, could independently test the $\sqrt{B}$ peak shift and $1/\sqrt{B}$ intensity collapse.
If the same scaling analysis were applied to other type-I Weyl semimetals, each would be expected to show its own crossover energy set by its saddle-point position, making the method a general probe of band shape.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The paper’s real news is the first experimental report of the predicted 1/sqrt(B) intensity scaling for inter-Landau-level absorption in a Weyl semimetal, and it is the same material in which the authors see both sqrt(B) and B-linear regimes. That is a nice, clean result to put on the record. The THz data, the comparison to Ashby and Carbotte, and the identification of the 17 meV crossover to the saddle point are all coherent. The self-citation for that energy is not a problem; the earlier paper did the band-structure work.

The soft spots are in the quantitative backing. The Kramers-Kronig extrapolation changes at the 2–4 T boundary: Hagen-Rubens below, constant above. The 2 T peak at ~4 meV sits right in that window, so the intermediate-field peak positions and intensities could be systematically biased. The paper gives no error bars on the peak energies or on the fitted a = 2.65 meV/T^1/2, and the scaling collapse in Fig. 2c is judged by eye. The IR peaks are read from R(B)/R(0) ratios with changes below 2% and no uncertainty estimate, and the B-linear lines are guides to the eye. The extrapolation of those IR peaks to ~17 meV rests on a few points. These are addressable, and none of them clearly kills the core claim—the sqrt(B) scaling is consistent with prior Dirac-material work, and the intensity scaling is a new observation that fits theory. But as it stands the strongest claim is suggestive, not demonstrated.

The reader’s circularity concern is fair but minor: using the fitted peak positions to normalize the horizontal axis of the collapse makes the energy collapse partly a restatement of the fit. The intensity collapse is less affected. A clean test would show scaled traces with residuals and a stated procedure for peak picking.

Who gets value from this: experimentalists working on Weyl and Dirac semimetal magneto-optics, and theorists who want a data point for the Ashby-Carbotte scaling. It deserves a serious referee—conditional acceptance with a request for error analysis, a validation of the extrapolation scheme, and quantitative collapse metrics. I would probably cite it as the first report of the intensity scaling, with a cautious qualifier pending the revision.

Referee Report

4 major / 5 minor

Summary. The paper reports magneto-optical reflectivity and optical conductivity measurements of the type-I Weyl semimetal TaAs at 10 K in magnetic fields up to 6 T, covering the THz and IR ranges (3 meV to 54 meV, with B=0 data to 30 eV for Kramers-Kronig analysis). The central claim is that the THz optical conductivity develops a gap-like peak whose energy grows as sqrt(B) with intensity scaling as 1/sqrt(B), consistent with the Ashby–Carbotte theory of Landau-level transitions in linear (Dirac) bands, while IR reflectivity peaks show a linear-B energy dependence, interpreted as transitions in parabolic (free-electron-like) bands. The authors conclude that the two behaviors signal a crossover from Dirac to free-electron-like dispersion at about 17 meV.

Significance. If the evidence is accepted, the paper would provide one of the first experimental demonstrations of the 1/sqrt(B) intensity scaling predicted for Landau-level optical absorption in Weyl semimetals, and a rare observation of a field-dependent crossover in the effective band dispersion. The measurement strategy, combining THz and IR reflectivity with Kramers-Kronig analysis over a very wide range, is appropriate and the comparison with Ashby–Carbotte theory is explicit and falsifiable. However, the quantitative support for the key scaling laws is incomplete, and the central claim is therefore not yet fully established.

major comments (4)

[Section 2 and Fig. 2a] The Kramers-Kronig extrapolation changes from a Hagen-Rubens function for B <= 2 T to a constant for B >= 4 T. The THz sigma(omega) below about 5 meV is largely determined by this choice, and the peak assigned at 2 T sits at about 4 meV, i.e., exactly in the regime where the extrapolation scheme changes. This could systematically bias the peak positions and amplitudes in Fig. 2a. The authors should validate the extrapolation, for example by comparing the low-energy conductivity with an independent measurement or by reporting the sensitivity of the extracted peak energy and intensity to alternative low-energy extrapolations.
[Fig. 2b, Fig. 3b] No uncertainties are reported for the peak positions or for the fitted exponent a = 2.65 meV/T^1/2 in Fig. 2b. The IR peaks in Fig. 3a are extracted from reflectivity ratios with changes below 2%, and Fig. 3b shows points with no error bars and only guide lines for the B-linear dependence. The paper should provide error estimates propagated from spectral noise and from the extrapolation ambiguity, fit the IR slopes quantitatively, and test whether the data are statistically consistent with B-linear versus other functional forms.
[Fig. 2c] The scaling collapse in Fig. 2c is judged visually. Because the horizontal axis is normalized by sqrt(B) using the very peak positions that establish the sqrt(B) law, the energy-axis collapse is partly a restatement of the fitted scaling. A quantitative residual analysis of the collapsed curves is needed, and the 1/sqrt(B) intensity scaling should be tested independently of the peak-energy normalization. This is a correctness-risk concern, not a claim that the theory is circular: the theory is taken from the external reference [11].
[Fig. 3a and Section 3] The IR peaks are identified as down arrows in Fig. 3a, but the paper gives no criterion for peak selection or uncertainty in locating them. With spectral changes below 2%, the assignment would be considerably strengthened by fitting the line shapes, by reproducing the peaks in sigma(omega) rather than only R(omega)/R(0), and by checking stability against the 0 T reference spectrum.

minor comments (5)

[Fig. 2 caption] The caption contains an incomplete sentence and typos: "spectrm" should be "spectrum" and the phrase "with the Ha" is cut off.
[Section 2] The description "appropriate extrapolations" is vague; the authors should specify the exact extrapolation functions used at low and high energy (beyond 30 eV) in the Kramers-Kronig analysis.
[Section 3] The term "W2 points" is introduced without definition; it should be defined or accompanied by a reference to the earlier band-structure discussion in Ref. [8].
[Abstract] The phrase "could be scaled not only in the energy scale by sqrt(B) but also in the intensity by 1/sqrt(B)" is grammatically awkward; "the intensity was scaled" would be clearer.
[References] Reference [14] is cited as an arXiv preprint (arXiv:1503.02630); if a published version exists, it should be cited instead.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: the B-scaling claims are data fits tested against external theory, with only a non-load-bearing self-citation for the 17 meV crossover energy.

full rationale

The paper's central claims are experimental observations compared against an external theory, Ashby and Carbotte [11]. The sqrt(B) peak-energy dependence is obtained by fitting the measured THz sigma(omega) peak positions (Fig. 2b, a = 2.65 meV/T^1/2), and the 1/sqrt(B) intensity scaling is tested by directly rescaling the measured spectra in Fig. 2c. The subsequent collapse plot is not a 'prediction' derived from a fitted parameter: the horizontal normalization by sqrt(B) is a standard way to display a scaling law already suggested by the data and theory, and the additional intensity normalization by 1/sqrt(B), the peak asymmetry, and overall spectral shape are independent content that is not forced by the energy fit. The IR region claim of B-linear peak energies is based on peak positions read from R(B)/R(0) spectra (Fig. 3b), not on an equation imported from the authors' prior work. The only self-citation is Ref. [8] for the ~17 meV saddle-point energy used to interpret the extrapolated IR peak energies; however, the extrapolation to ~17 meV is presented from the present data independently, and the core comparison of sqrt(B) vs B scaling does not reduce to that citation. The Kramers-Kronig extrapolation caveat (Hagen-Rubens below 2 T, constant above 4 T) is an experimental uncertainty, not a circular step, because the scaling conclusions are not built into those extrapolations. Overall, the derivation chain is self-contained: measured reflectivity -> KKA -> sigma(omega) -> peak tracking -> scaling comparison, with the tested scaling form coming from an external theory. No equation is defined in terms of the claim, and no fitted input is renamed as a prediction.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The central claim relies on a single fitted parameter, the sqrt(B) prefactor a, and on four background assumptions: Kramers-Kronig validity, the Landau level assignment, the applicability of external theory, and the safety of the extrapolation choices. No new physical entities are introduced.

free parameters (1)

a in ℏω_peak = a√B = 2.65 meV/T^1/2
Fitted to the THz peak energies in Fig. 2b. This value is used to normalize the horizontal axis in the scaling plot Fig. 2c.

assumptions (4)

standard math Kramers-Kronig relations with the stated extrapolations yield an accurate σ(ω) spectrum.
Used throughout Section 2 to convert measured R(ω,B) into σ(ω,B). The validity of the low-energy extrapolation is assumed without independent verification.
domain assumption The E ⊥ B || c configuration probes inter-Landau-level transitions of the Weyl bands near the Fermi level.
The paper assumes the observed peaks originate from Landau levels of the Weyl bands and not from other carrier pockets or magneto-plasmon effects.
domain assumption The Ashby-Carbotte theory for the optical conductivity of Weyl semimetals applies to TaAs.
The sqrt(B) and 1/sqrt(B) scalings are taken from Ref. 11 and used to identify the THz peaks as inter-Landau-level transitions.
ad hoc to paper The chosen extrapolation functions (Hagen-Rubens for B <= 2 T, constant for B >= 4 T) do not distort the peak positions or intensity scaling.
The extrapolation scheme changes at B = 2-4 T and is not justified beyond 'appropriate extrapolations'; this could affect the low-energy σ(ω) used for the scaling analysis.

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Cite this review

Pith. "Pith review of Magneto-Optics of the Weyl Semimetal TaAs in the THz and IR Regions." pith.science (2026). https://pith.science/paper/V6NDAA5Y

@misc{pith2026190809994,
  author       = {Pith},
  title        = {Pith review of: Magneto-Optics of the Weyl Semimetal TaAs in the THz and IR Regions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/V6NDAA5Y}},
  note         = {Machine review of arXiv:1908.09994}
}

abstract

The magnetic-field dependence of optical reflectivity [$R(\omega)$] and optical conductivity [$\sigma(\omega)$] spectra of the ideal type-I Weyl semimetal TaAs has been investigated at the temperature of 10 K in the terahertz (THz) and infrared (IR) regions. The obtained $\sigma(\omega)$ spectrum in the THz region of $\hbar\omega\leq15$ meV is strongly affected by the applied magnetic field ($B$): The Drude spectral weight is rapidly suppressed and an energy gap originating from the optical transition in the lowest Landau levels appears with a gap size that increases in proportion to $\sqrt{B}$, which suggests linear band dispersions. The obtained THz $\sigma(\omega)$ spectra could be scaled not only in the energy scale by $\sqrt{B}$ but also in the intensity by $1/\sqrt{B}$ as predicted theoretically. In the IR region for $\hbar\omega\geq17$ meV, on the other hand, the observed $R(\omega)$ peaks originating from the optical transitions in higher Landau levels are proportional to linear-$B$ suggesting parabolic bands. The different band dispersions originate from the crossover from the Dirac to the free-electron bands.

Figures

Figures reproduced from arXiv: 1908.09994 by the authors.

**Figure 1.** Magnetic-field (B) dependence of reflectivity [R(ω)] spectrum of TaAs in the energy range of ~ω ≤ 25 meV at the temperature of 10 K. R(ω) spectrum for ~ω ≥ 25 meV was taken only at B = 0 T. In this paper, we report the magnetic-field dependence of the electronic structure of an ideal Weyl semimetal TaAs by using σ(ω) spectra in the terahertz (THz) and infrared (IR) regions at the temperature of 10 K. As a result, th… view at source ↗

**Figure 2.** (a) Magnetic-field dependence of optical conductivity [σ(ω, B)] spectrum of TaAs in the THz region at the temperature of 10 K. The spectrm of B = 0 T below 3 meV is in the extrapolation region with the Ha (b) Energy of the broad peak in (a) as a function of magnetic field. The dashed line is the fitted function of ~ωpeak = a √ B, where a = 2.65 [meV/T 1/2 ]. (c) Same as (a), but the horizontal and vertical axes are … view at source ↗

**Figure 3.** (a) R(ω) spectra of TaAs under magnetic field divided by the spectrum at 0 T. The spectra are shifted by 2 % upwards by equal intervals. (b) Peak energies observed in Figs. 2a and 3a as a function of magnetic field. The dashed lines are guides for the eyes. in the THz region (same as Fig. 2b) are also plotted. A B-linear dependence of the peak energy in the IR region is clearly observed, which is different from the … view at source ↗

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [11]

P . E. C. Ashby and J. P . Carbotte, Phys. Rev. B 87, 245131 (2013)

work page 2013

[2] [1]

B. A. Bernevig, Nat. Phys. 11, 698 (2015)

2015

[3] [2]

Jia, S.-Y

S. Jia, S.-Y . Xu, and M. Z. Hasan, Nat. Mat. 15, 1140 (2016)

work page 2016

[4] [3]

B. Q. Lv, N. Xu, 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, Nat. Phys. 11, 724 (2015)

work page 2015

[5] [4]

N. Xu, H. M. Weng, B. Q. Lv, C. E. Matt, J. Park, F. Bisti, V . N . Strocov, D. Gawryluk, E. Pomjakushina, K. Conder, N. C. Plumb, M. Radovic, G. Aute` s, O. V . Y azyev, Z.Fang, X. Dai, T. Qian, J. Mesot, H. Ding, and M. Shi, Nat. Commun. 7, 11006 (2016)

work page 2016

[6] [5]

B. Xu, Y . M. Dai, L. X. Zhao, K. Wang, R. Y ang, W . Zhang, J. Y . Liu, H. Xiao, G. F. Chen, A. J. Taylor, D. A. Y arotski, R. P . Prasankumar, and X. G. Qiu, Phys. Rev. B 93, 121110(R) (2016)

work page 2016

[7] [6]

Neubauer, A

D. Neubauer, A. Y aresko, W . Li, A. L¨ ohle, R. H¨ ubner, M. B. Schilling, C. Shekhar, C. Felser, M. Dressel, and A. V . Pronin, Phys. Rev. B 98, 195203 (2018)

work page 2018

[8] [7]

Y asuoka, T

H. Y asuoka, T. Kubo, Y . Kishimoto, D. Kasinathan, M. Schm idt, B. Y an, Y . Zhang, H. Tou, C. Felser, A. P . Mackenzie, and M. Baenitz, Phys. Rev. Lett. 118, 236403 (2017)

work page 2017