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REVIEW 2 major objections 6 minor 69 references

Electron and phonon topology in transition metal material TaSi

T0 review · 2 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read TaSi is predicted to be a chiral topological semimetal whose electrons and phonons both carry topological charges, with multifold fermions of Chern number +4 and chiral phonons of Chern number ±2.

desk verdict A plausible new chiral silicide, but the reported chirality accounting violates time-reversal symmetry, so the electronic topology claims need a full re-check before they can be trusted. read the letter →

arxiv 2507.11705 v1 pith:NPLFSABK submitted 2025-07-15 cond-mat.mtrl-sci

Saurabh Kumar Sen , Shivendra Kumar Gupta , Nagarjuna Patra , Ajit Singh Jhala , Poorva Singh This is my paper
classification cond-mat.mtrl-sci
keywords chiraltopologicalsemimetalmultifoldfermionsRarita-SchwingerfermionWeylphononsChernnumberspin-orbitcouplingTaSiphonontopology
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 predicts that the transition-metal silicide TaSi is a chiral topological semimetal whose electronic and phononic spectra both carry topological charges. In the electronic band structure with spin-orbit coupling, the calculation finds a fourfold spin-3/2 Rarita-Schwinger fermion at the Gamma point and a sixfold double-spin-1 fermion at the R point, each with Chern number +4, compensated by eight Weyl points with Chern number -1. In the phonon spectrum, chiral bosonic modes carry Chern numbers ±2 at Gamma and R. If correct, TaSi would be a single material hosting coexisting fermionic and bosonic topological excitations, a combination promising for transport and thermoelectric experiments.

What carries the argument

The argument rests on the non-symmorphic chiral symmetry of space group P2_13 (No. 198), specifically two anticommuting screw symmetries that square to -I and a threefold rotation. These symmetries force the fourfold and sixfold degeneracies at the TRIM points in the presence of SOC, and their representations determine the Chern numbers of the multifold fermions. The phonon topology is analysed with the same Berry-curvature machinery applied to the dynamical matrix, yielding chiral modes with Chern numbers ±2.

What would settle it

A direct check would be angle-resolved photoemission (ARPES) on single-crystal TaSi to look for the fourfold and sixfold crossings at Gamma and R with their predicted surface Fermi arcs, together with inelastic X-ray scattering to find the chiral phonon modes near 8-9 and 11.5-12.5 THz; observing no such crossings or arcs, or finding crossings at different energies than predicted, would falsify the claim. More cheaply, re-computing the band structure with a hybrid functional or GW quasiparticle corrections would show whether the crossings survive a change in exchange-correlation treatment.

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Extended reading notes

Core claim

The central claim is that TaSi, crystallizing in the chiral non-symmorphic space group P2_13 (No. 198), hosts multifold electronic fermions and topological phonons simultaneously. Under spin-orbit coupling, the Gamma point supports a fourfold spin-3/2 Rarita-Schwinger fermion and the R point a sixfold double-spin-1 fermion, each with chirality +4, while eight W1-type Weyl points of chirality -1 along Gamma-R balance the total chirality to zero. The phonon spectrum is dynamically stable and contains a spin-1 Weyl point at Gamma and a charge-2 Dirac point at R, with surface Fermi arcs connecting Gamma' and M' and Berry curvature showing Chern numbers ±2. The paper argues this coexistence is symmetry-protected by the screw rotations and threefold rotation of space group No. 198.

Load-bearing premise

The calculation assumes TaSi adopts the chiral P2_13 structure used here and that the PBE exchange-correlation approximation orders the bands and phonons correctly near the crossings; if the real structure differs or a more accurate functional shifts the band order, the predicted nodes could move, gap, or vanish.

Editorial extensions

If this is right

  • TaSi should be a dynamically stable chiral topological semimetal, since the computed phonon spectrum has no imaginary frequencies.
  • The total chirality of all electronic Weyl-like nodes cancels, so the material satisfies the Nielsen-Ninomiya constraint and is a genuine Weyl semimetal.
  • The (001) surface should show four Fermi arcs emanating from the Gamma point, consistent with the spin-3/2 Rarita-Schwinger fermion of chirality +4.
  • The phonon surface states should connect the projected Gamma and R points in two THz frequency windows, producing phononic Fermi arcs with Chern numbers ±2.
  • The coexistence of topological electrons and phonons in one crystal could enhance thermoelectric performance or unconventional superconductivity, as the paper argues for such materials.

Reading between the lines

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

  • If the predicted nodes sit close to the Fermi level as computed, transport measurements such as the anomalous Hall effect or chiral-anomaly magnetoresistance could reveal their topological charge without needing surface spectroscopy.
  • The same symmetry-based analysis could be applied to other transition-metal silicides in space group No. 198 to identify additional materials with both electronic and phononic Chern charges.
  • Recomputing the band structure with a hybrid functional or quasiparticle self-energy corrections would test whether the energy ordering and node positions survive beyond the PBE approximation; symmetry protection suggests the degeneracies would persist even if energies shift.
  • The phononic Chern number ±2 implies a chiral phonon edge mode that could, in principle, carry a thermal Hall signal, a consequence the paper does not quantify.
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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

2 major / 6 minor

Summary. This manuscript reports first-principles DFT and DFPT calculations for TaSi in the chiral non-symmorphic space group P2_13 (No. 198). The authors predict that the electronic band structure with spin-orbit coupling hosts a fourfold spin-3/2 Rarita-Schwinger fermion at Γ and a sixfold double-spin-1 fermion at R, both assigned Chern number +4, together with eight W1 Weyl points along Γ-R assigned Chern number -1. The phonon spectrum is reported to host chiral bosonic modes with Chern numbers ±2. The central claim is the coexistence of electronic and phononic topological quasiparticles in one material.

Significance. If the charge assignments were correct, TaSi would be a new example in the well-studied family of chiral topological semimetals crystallizing in space group 198, with the added feature of coexisting electronic and phononic chirality. The paper uses a standard and reproducible first-principles workflow: PAW-PBE DFT, Wannier interpolation, iterative Green's-function surface states, and DFPT phonons with a dynamical-stability check. The main advertised result, however, is not self-consistent under the time-reversal symmetry that the paper itself invokes, so the quantitative claims need to be re-derived before the coexistence conclusion can be accepted.

major comments (2)
  1. [Section III (chirality balance; Fig. 5)] The chirality accounting is inconsistent with the time-reversal symmetry stated in the paper. With SOC, TaSi is nonmagnetic and T^2 = -1, so the Berry curvature is odd under k -> -k. Consequently, a Weyl node at a non-TRIM point k0 has a partner at -k0 with opposite chirality. The W1 point lies on the Γ-R line, and its time-reversed partner is a distinct point on the same line. The eight W1 points must therefore form four pairs with charges +1 and -1; they cannot all carry chirality -1. This forces the W1 contribution to cancel on its own, and the total-chirality condition then requires C(Γ) and C(R) to have opposite signs. The reported '+4 at Γ, +4 at R, and eight times -1' are mutually inconsistent, independent of the exchange-correlation functional or structural stability. The abstract and Section III must be corrected, and the corrected integer charges should be reconciled with the known CoSi-type assignments for space group 198.
  2. [Section III, Fig. 5; Section IV, Figs. 7-9] The integer Chern numbers are asserted from qualitative Berry-curvature vector plots and Fermi-arc panels, but no numerical Chern numbers from an explicit flux calculation or Wilson-loop integration are reported for either the electronic or the phononic nodes. No k-mesh convergence information for the Chern numbers is given. Because the central claims depend on the exact integers |C| = 4, 1, and 2, please report the actual topological charge of each node, the numerical method used, and the convergence with respect to the k-mesh. This is needed not only to support the claims but also to resolve the sign inconsistency identified above.
minor comments (6)
  1. [Figure 3 and Section III] The text says fig. 3(c) shows the R point and fig. 3(d) the Γ point, while the caption says (c)-(d) are the Γ and R points, respectively; the same paragraph also swaps the assignments of (e) and (f). Please correct the mismatch so the reader can identify which panel contains each crossing.
  2. [References [51]-[53]] These three references do not form a coherent citation of the Nielsen-Ninomiya no-go theorem; in particular, reference [53] is a gravitational-collapse paper. Please replace them with a correct Nielsen-Ninomiya citation.
  3. [Abstract] There is a typo, 'possesess', and 'C = +-2' should be typeset as 'C = ±2'.
  4. [Section V] The sentence '1.5 times the default cut off energy(500 eV)' is ambiguous; please state the actual plane-wave cutoff and give convergence tests for the total energy, phonon frequencies, and the reported topological charges.
  5. [Section II and V] No structural parameters (lattice constant and internal coordinates) or comparison with experimental crystallographic data are given. Please include them so the calculations can be reproduced and the assumed P2_13 structure can be verified.
  6. [Section IV] The phononic surface-state path Y'-X'-Y''-X''-Y'-X'-Γ'-M' is not labeled in Fig. 2; a labeled surface Brillouin zone would make the surface analysis easier to follow.

Circularity Check

0 steps flagged · score 1.0 of 10

No circularity: topological charges are computed from first-principles wavefunctions; self-citations are contextual and not load-bearing.

full rationale

The paper's central claims are ab initio predictions for TaSi: multifold fermions with Chern numbers +4 (Γ, R) and −1 (W1 Weyl points) in the electronic band structure, and phononic modes with Chern numbers ±2. The derivation chain is: (i) PBE-GGA DFT band structure; (ii) a Wannier tight-binding Hamiltonian built from the DFT wavefunctions; (iii) Berry curvature and Fermi-arc calculations in WannierTools; (iv) DFPT phonons with phonopy and topological analysis via phonopyTB. No step fits a parameter to the claimed Chern numbers, and no step derives a charge from an ansatz that assumes the charge. The symmetry protection of the multifold degeneracies is justified by external, well-established classifications (Bradlyn et al., ref 32; Barman et al., ref 30), not by the present authors' own prior work. The only self-citations (refs 1, 46, 47) appear in the introduction as background examples of related topological materials and catalysis; none carries the load of the TaSi result, and none is invoked as an authority for the calculations. The stated chirality sum (+8 from Γ and R, −8 from eight W1 points, total zero by the Nielsen–Ninomiya theorem) is presented as a consistency check of the computed charges, not as a fitted input. The skeptic's concern about time-reversal symmetry (Γ and R both +4 while all eight W1 points share chirality −1) is a potential internal-consistency or correctness issue, not a circularity issue; under the review rules such concerns belong to a correctness pass, not to a circularity score. No quoted equation reduces to its own input by construction, and no load-bearing argument rests on a self-citation chain. The result is therefore self-contained against the input data, with only minor non-load-bearing self-citations.

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

The central claim imports the symmetry classification of multifold fermions from Bradlyn et al. (ref 32) and applies it to TaSi. No new particles or interactions are postulated; the analysis relies on standard DFT, Wannier, and DFPT approximations.

assumptions (4)
  • domain assumption TaSi crystallizes in space group P2_13 (No. 198) with a specific atomic arrangement and lattice constant.
    The entire calculation starts from this assumed structure; no experimental XRD or structural characterization is presented.
  • domain assumption The PBE-GGA exchange-correlation functional accurately describes the electronic structure and band ordering of TaSi.
    No comparison with hybrid functionals, GW, or experiment is provided; topological features depend on band ordering.
  • domain assumption The harmonic approximation and DFPT force constants accurately model the phonon dispersions of TaSi.
    Finite-temperature effects and anharmonicity are ignored; the topological classification of phonon crossings depends on the accuracy of the force constants.
  • domain assumption The maximally localized Wannier functions faithfully interpolate the DFT band structure and dynamical matrix.
    The Chern numbers and surface states are computed from the Wannier-interpolated Hamiltonians, which must reproduce the ab initio bands around the crossings.

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Cite this review

Pith. "Pith review of Electron and phonon topology in transition metal material TaSi." pith.science (2026). https://pith.science/paper/NPLFSABK

@misc{pith2026250711705,
  author       = {Pith},
  title        = {Pith review of: Electron and phonon topology in transition metal material TaSi},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NPLFSABK}},
  note         = {Machine review of arXiv:2507.11705}
}
read the original abstract

The plethora of multifold quasiparticles in topological materials has led to significant advancements in condensed matter physics, inspiring the investigation for materials that host both electronic and bosonic multifold excitations. In this work, we explore the electronic and phononic properties of TaSi, a non symmorphic chiral topological material crystallizing in space group P 2 1 3 (No. 198). This system exhibits multifold fermions, which are higher spin generalizations of Weyl fermions, protected by the unique crystalline symmetries of the structure. Using first principles calculations, we predict that electronic band possesses fourfold spin 3/2 Rarita Schwinger (RSW) fermions, sixfold excitations (double spin 1), all possessing large Chern numbers C = +4 and Weyl fermions of spin 1/2 with Chern no. -1 in the presence of spin orbit coupling (SOC). Additionally, the phononic band structure hosts chiral bosonic excitations characterized by Chern numbers C = +-2. The coexistence of chiral electronic and bosonic quasiparticles give rise to exotic transport phenomena, rendering the material as promising candidate for future applications in quantum materials, topological electronics, and spintronics.

Figures

Figures reproduced from arXiv: 2507.11705 by the authors.

Figure 2
Figure 2. FIG. 2. Crystal structure of TaSi [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 4
Figure 4. FIG. 4. Fermi arcs at the [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗
Figure 6
Figure 6. FIG. 6. Phonon dispersion curve showon in (a), The insets [PITH_FULL_IMAGE:figures/full_fig_p004_6.png] view at source ↗
Figures from the paper (3 more)
Figure 7
Figure 7. Figure 7: FIG. 7. Phononic surface states, (a)-(b) correspond to the [PITH_FULL_IMAGE:figures/full_fig_p004_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Fermi arcs projected along the (001) surface. (a)- [PITH_FULL_IMAGE:figures/full_fig_p005_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Berry curvature distribution (a) [PITH_FULL_IMAGE:figures/full_fig_p005_9.png]

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Pith tools

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