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REVIEW 4 major objections 5 minor 86 references

Phonon-based determination of elastic coefficients in the Weyl semimetal TaAs

T0 review · 4 major / 5 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read Sound speeds yield all six elastic constants of the Weyl semimetal TaAs

desk verdict A solid, clearly-written methods paper that reproduces known elastic constants for TaAs via a standard phonon-to-elastic inversion; the main issues are an equation typo, an unspecified fitting window, and scatter among symmetry-equivalent velocities that is averaged over without error bars. read the letter →

arxiv 2608.03903 v1 pith:T6BRP7FQ submitted 2026-08-04 cond-mat.mtrl-sci

Fabián Jofré-Parra , Debankita Ghosh , Enrique Muñoz This is my paper · ORCID
classification cond-mat.mtrl-sci
keywords WeylsemimetalTaAselasticconstantsphonondispersionsoundvelocitydensityfunctionalperturbationtheoryspin-orbitcouplingcontinuumelasticity
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 establish that the complete set of six independent elastic coefficients of TaAs can be obtained from the low-frequency acoustic phonon branches, without applying any shear stress. Using DFPT phonon spectra that include spin-orbit coupling, the authors extract sound velocities along high-symmetry directions and invert the elastic dynamical matrix for a body-centered tetragonal crystal. The resulting moduli agree with prior DFT calculations to within about 10% for most coefficients, with larger deviations of roughly 20% for the off-diagonal couplings C12 and C13. From these coefficients they derive bulk, shear, and Young's moduli, plus a Poisson ratio near 0.497. This matters because direct experimental elastic constants for TaAs are still missing, and the phonon route offers a check against Raman and Brillouin scattering experiments.

What carries the argument

The central object is the C4v elastic dynamical matrix M(q) for the body-centered tetragonal lattice, built from the six Voigt stiffness coefficients. Diagonalizing this matrix along [001], [100], [110], and [101] yields relations (B13)–(B16) between sound velocities and elastic moduli, an overdetermined system that the paper inverts to express each Cij in terms of measured phonon slopes. The non-obvious piece is the definition of C44 as an average of three transverse velocities (z,t1; x,t1; xy,t2) that should be equal by symmetry but differ in the computed spectrum; the average is introduced to suppress numerical dispersion.

What would settle it

Recompute the acoustic branches with a much denser q-mesh and shrink the fitting window toward the Γ point; if the three velocities that should all give C44 (from v_z,t1, v_x,t1, and v_xy,t2) do not converge to a single value, then the Eq. (4) average is hiding a systematic error that propagates into every derived elastic modulus.

Watch

Extended reading notes

Core claim

On its own terms, the paper claims that sound velocities fitted from the acoustic branches near the Γ point are sufficient data to fix all six independent elastic stiffness coefficients of body-centered tetragonal TaAs. The PBE phonon-derived set is C11 = 272.26 GPa, C33 = 250.53 GPa, C12 = 122.08 GPa, C13 = 102.76 GPa, C44 = 95.00 GPa, C66 = 184.60 GPa, with PBEsol values somewhat higher; all satisfy the mechanical stability criteria. The claim is not that these values are exact, but that they reproduce prior first-principles elastic constants within about 10% for most coefficients, that the derived bulk, shear, Young's moduli, and Poisson ratio follow consistently, and that the method work

Load-bearing premise

The slopes of the acoustic phonon branches near zero wave vector are treated as unbiased sound speeds, so the scatter among symmetry-equivalent branches is harmless numerical dispersion that averaging removes rather than a systematic bias from the fitting window.

Editorial extensions

If this is right

  • The full stiffness tensor of TaAs is obtained without applying shear strain, avoiding large supercells and Pulay stress corrections tied to shear deformations.
  • The six derived moduli satisfy the tetragonal mechanical stability criteria, confirming linear-elastic stability of TaAs.
  • The derived polycrystalline descriptors place TaAs near the brittle–malleable boundary on the B/G criterion and give a Poisson ratio close to the central-force upper bound of 0.5.
  • The same phonon-based inversion provides a direct comparison point for Raman, Brillouin–Mandelstam, and ultrafast X-ray measurements of acoustic modes in Weyl semimetals.
  • Because the velocity–modulus system is overdetermined, the method carries internal consistency checks: discrepancies among symmetry-equivalent velocities flag which acoustic branches are least reliable.

Reading between the lines

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

  • If the phonon-slope inversion is as transferable as the paper suggests, it should apply to the isostructural Weyl semimetals TaP, NbAs, and NbP, whose elastic constants are also experimentally unmeasured; a multi-material test would sharpen the comparison.
  • The near-10% agreement with prior DFT values does not by itself validate the method, because prior DFT shear calculations share the same exchange-correlation functional and similar pseudopotential errors; the decisive test is experimental sound-velocity input.
  • The very high Poisson ratio near 0.497 is extremely sensitive to C12 and C13, the two coefficients with the largest deviations; it should be read as a derived quantity whose accuracy is contingent on pinning down those off-diagonal couplings.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. This paper combines DFPT phonon calculations (PBE and PBEsol, with SOC) with a continuum elasticity model to extract the six independent elastic constants of body-centered tetragonal TaAs from acoustic sound velocities near the Γ point. The authors report C11=272.26, C33=250.53, C12=122.08, C13=102.76, C44=95.00, C66=184.60 GPa at the PBE level, compare these with earlier DFT values, and derive polycrystalline bulk, shear, and Young moduli and Poisson's ratio. The intended contribution is a shear-free, phonon-based route to the full stiffness tensor.

Significance. The methodological core is standard and potentially useful: DFPT acoustic branches in the long-wavelength limit are connected to elastic coefficients through the Christoffel equations, and the paper avoids explicit shear strains. The use of two functionals (PBE, PBEsol) and the comparison with an experimental sound velocity for v_xy,t2 are positives. The extraction is not circular: no parameter is fitted to the target elastic constants, and the underlying relations are textbook elasticity. However, the current manuscript contains a wrong printed formula for C13, an internally inconsistent Poisson ratio in Table V, and no convergence or uncertainty analysis for the linear fits that feed all extracted constants. These issues are load-bearing for the central claim, so the paper cannot be accepted in its present form.

major comments (4)
  1. [§II.B, Eq. (3) and Appendix B] Eq. (3) is not the expression for C13 as written. Combining the diagonalization results in Eq. (B16), ρ(v_xz,l^2 − v_xz,t1^2) = Δ2/2, and the square root in Eq. (3) reduces to (C13 + C44)/ρ, not C13/ρ. A numerical check with the PBE velocities in Table III gives a value of approximately 198 GPa for the square-root term; subtracting C44 = 95 GPa gives about 103 GPa, matching the reported C13. The printed formula is therefore missing a '− C44' term and must be corrected, or the derivation in Appendix B must be revised to justify the expression actually used.
  2. [§III.C, Table V] The reported Poisson ratio ν = 0.497 is inconsistent with the same table's B and E values. Using Eq. (13) with the PBE rows, B = 160.75 GPa and E = 250.33 GPa gives ν = (3B−E)/(6B) ≈ 0.240, not 0.497. The literature-average values in Table V give ν ≈ 0.277, not 0.4975. This is not a small typo: the cited B/G ratios around 1.6–1.9 correspond to ν ≈ 0.24–0.28, so the brittle/malleable and Poisson-ratio discussion built on ν ≈ 0.497 is invalid. The entire set of derived quantities in Table V must be recomputed and cross-checked.
  3. [§II.B and §III.B] The linear-fit window for extracting sound velocities is never specified. This is a substantive issue, not just a presentation gap. The three transverse velocities that should all equal sqrt(C44/ρ) differ by about 25%: v_z,t1 = 2.57, v_x,t1 = 2.95, v_xy,t2 = 2.86 km/s imply C44 values of roughly 80, 106, and 99 GPa. Eq. (4) averages these, but averaging removes scatter only if the deviations are random; if the deviations are a window-dependent numerical dispersion, the bias propagates into C12 and C13, which already deviate about 20% from literature. The conclusion acknowledges 'numerical dispersion in the extracted sound velocities.' A convergence test over the fitting window and q-point sampling is required to support the quantitative claim.
  4. [Tables III–V] None of the present results carry error bars or uncertainty estimates. Given the 25% spread among symmetry-equivalent velocities, reporting Cij to five significant figures without uncertainties prevents a meaningful quantitative comparison with the literature. The authors should propagate uncertainties from the linear fits and, ideally, from the finite q-grid, at least for the constants that rely on differences or averages (C12, C13, C44).
minor comments (5)
  1. [Appendix B, Eq. (B11)] The eigenvalue equation writes (M(q) − ρω) Δx(q,ω) = 0, but the preceding text uses ρω². The dispersion relation below then refers to ρω_α(q), which should be ρω_α²(q). This appears to be a typographical slip, but it is confusing in a derivation-heavy appendix.
  2. [Appendix B, Eq. (B10)] The last term is printed as '+ C^2_33 ∂^2_z'; it should be '+ C33 ∂^2_z' (no square), consistent with the dynamical matrix in Eq. (B12).
  3. [§III.C] The text says 'we compute the sound velocities from DFTP'; this should read 'DFPT'. In the same paragraph, 'our comparison relays only' should be 'relies only.'
  4. [Appendix A] The phrase 'elastic propertied' should be 'elastic properties.'
  5. [§III.B] The statement that all sound-velocity deviations are 'below 10^{-1}' is vague; the maximum relative deviation should be stated explicitly, and the individual deviations are better shown in a table or figure.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: elastic constants are obtained from first-principles sound velocities via textbook continuum relations, with no parameter fitted to the target values.

full rationale

The derivation chain is linear: DFPT phonon dispersions are computed from first principles; acoustic branches are linearly fitted near Γ to yield sound velocities (Table III); the C4v elastic continuum relations (Appendix B, Eqs. (B13)-(B16), used in Eqs. (1)-(5)) convert those velocities to Cij; and the resulting constants are compared with independent DFT strain-stress values and literature (Table IV). None of the Cij are used to fit sound velocities; the inversion relations are parameter-free textbook elasticity. The C44 estimator in Eq. (4) is an average of three symmetry-equivalent transverse velocities; averaging redundant ab initio estimates is an estimator, not a fit to a target. Self-citations (Refs. 10-13, 77, 78) concern Weyl-semitismetal transport and phonon physics and do not carry the elastic derivation. The paper's own caveat that the approach 'can be affected by numerical dispersion in the extracted sound velocities' is an accuracy/convergence limitation, not a circular reduction. A possible algebraic typo in Eq. (3) (it appears to yield C13+C44 from the stated B16 relations) is a correctness/reproducibility concern, but it does not make the method circular. No load-bearing step is equivalent by construction to its inputs.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

No free parameters are fitted to the target values. The inversion from sound velocities to Cij is parameter-free, but the unreported fit window and the hand-chosen C44 average act as by-hand parameters. The central claim rests on standard continuum elasticity, standard DFT functionals, and the assumption that the DFPT acoustic branches are converged and linear near Γ.

free parameters (2)
  • Linear-fit window for acoustic sound velocities near Γ = not reported
    Sec. II.A states only "in the vicinity of the Γ point." The extracted velocities are sensitive to this window (symmetry-equivalent modes disagree by up to 25% in implied C44), so the window choice is an unreported, by-hand parameter.
  • C44 estimator (arithmetic mean of three transverse velocities) = PBE: ρ(2.57²+2.95²+2.86²)/3 = 95.1 GPa
    Eq. (4) averages three velocities that should be identical by symmetry. The individual estimates (about 80, 106, and 99 GPa for PBE) span a wide range, so the averaging scheme is a hand-chosen estimator that determines the reported C44.
assumptions (5)
  • standard math TaAs has C4v point-group symmetry, so the stiffness tensor has exactly six independent coefficients with the Voigt form of Eqs. (B3)-(B5) and all other components zero.
    Invoked in Sec. II.B and Appendix B; standard crystallographic reduction used to write the dynamical matrix (B12).
  • domain assumption In the long-wavelength limit the acoustic phonon slopes equal the continuum sound velocities satisfying the eigenvalue problem (B11) with ρv² as eigenvalues of M(q).
    Used to write Eqs. (B13)-(B16) and invert them as Eqs. (1)-(5). Standard continuum elasticity, but its validity at the finite q points of the 5×5×5 DFPT mesh is assumed.
  • domain assumption DFPT with PBE or PBEsol, PAW pseudopotentials, and SOC yields accurate acoustic phonon branches for TaAs.
    The velocities are extracted from these branches; the paper does not provide pseudopotential identifiers, so the accuracy claim rests on the stated QE settings and on agreement with prior phonon work.
  • domain assumption The strain-stress DFT calculations of C11, C33, C12, C13 stay inside the linear elastic regime.
    Fig. 6 shows stress versus strain; the linear fit range and absence of higher-order terms are assumed, and the paper notes the elastic regime "must be carefully monitored."
  • domain assumption The relaxed PBE (PBEsol) lattice parameters provide the correct density ρ for the Cij = ρv² conversion.
    Table I: ρ = 12.147 g/cm³ (PBE) and 12.477 g/cm³ (PBEsol) are used in Eqs. (1)-(5); experimental density is 12.2±0.3 g/cm³.

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Pith. "Pith review of Phonon-based determination of elastic coefficients in the Weyl semimetal TaAs." pith.science (2026). https://pith.science/paper/T6BRP7FQ

@misc{pith2026260803903,
  author       = {Pith},
  title        = {Pith review of: Phonon-based determination of elastic coefficients in the Weyl semimetal TaAs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/T6BRP7FQ}},
  note         = {Machine review of arXiv:2608.03903}
}
read the original abstract

Reliable determination of elastic properties in topological semimetals is essential for understanding strain-related effects, but is often hindered by methodological and computational limitations. In this work, we combine first-principles phonon calculations with an elastic continuum model to determine the elastic properties of Weyl semimetal TaAs. The sound velocities extracted from the acoustic phonon branches are used to obtain the full set of elastic moduli, which show good agreement with previously reported values in the literature. From these results, we derive standard elastic parameters such as bulk, shear, and Young's moduli, and the Poisson ratio. This approach highlights a computationally efficient alternative to conventional strain-based methods, avoiding the need for large supercells when shear is applied, and thus possible strain-induced inconsistencies in the electronic basis, while providing a possibility to connect with experimental characterizations (e.g. Raman or Brillouin-Mandelstam scattering) of the lattice dynamics in Weyl semimetals.

Figures

Figures reproduced from arXiv: 2608.03903 by the authors.

Figure 1
Figure 1. FIG. 1: Primitive (left) and conventional (right) unit cells. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Electronic band structure computed with (red, solid [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Fermi surface in the first Brillouin zone. Red dots [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: FIG. 4: Phonon dispersion and DOS, based on the PBE. [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: Acoustic modes extracted from the phonon [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: Stress as a function of the applied strain. [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7: Phonon dispersion obtained with PBEsol functional. [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]

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