Revisiting the Topological Nature of TaIrTe4, SrSi2, and Cu2XY3: An ab-initio Investigation

Prakash Pandey; Sudhir K. Pandey

REVIEW 6 major objections 6 minor 1 cited by

Revisiting the Topological Nature of TaIrTe4, SrSi2, and Cu2XY3: An ab-initio Investigation

T0 review · 6 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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

Pith's one-line read Direct DFT node searches correct published Weyl-node counts in TaIrTe4, SrSi2, and the Cu2XY3 family.

desk verdict A useful corrective study whose headline node counts are undercut by an unstated band-pair restriction; worth refereeing, but the completeness claims need reining in. read the letter →

arxiv 2505.24359 v1 pith:CTRDAIMF submitted 2025-05-30 cond-mat.mtrl-sci

Prakash Pandey , Sudhir K. Pandey This is my paper

classification cond-mat.mtrl-sci

keywords Weylsemimetalnodallinesringsfirst-principlesDFTtight-bindingmodelTaIrTe4SrSi2Cu2XY3

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 direct density-functional-theory node searches rather than Wannier-function-based tight-binding models, this paper re-examines three families of predicted topological semimetals and finds that published node counts change. It reports sixteen Weyl nodes and two nodal lines in TaIrTe4 (four nodes more than earlier studies), a previously missing set of twelve Weyl pairs in SrSi2, and no Weyl points or nodal rings in Cu2SnTe3, contrary to a recent tight-binding prediction. The paper argues that such differences help explain why experimental checks of topological-phase catalogs sometimes come up empty, because small changes in lattice parameters, atomic positions, or the exchange-correlation functional can move or destroy the nodes. A sympathetic reader would take the central claim to be that direct first-principles band-touching searches are the more reliable benchmark for these materials.

What carries the argument

The load-bearing tool is a direct first-principles search for band-touching points (the paper's PY-NODE code) that uses Nelder-Mead minimization on DFT bands to find where the topmost valence band and the bottommost conduction band touch across the full Brillouin zone, with chiralities checked by a Wilson-loop calculation. The comparison target is the maximally localized Wannier-function tight-binding model used in prior studies. The argument works by showing that the direct search finds nodes the tight-binding model misses, or finds none where the model predicted nodes, and by showing that the result is sensitive to lattice constants, atomic positions, and the exchange-correlation functional.

What would settle it

Repeat the node search on the same compounds while scanning lower valence and higher conduction bands; finding additional Weyl nodes in Cu2SnTe3, or more than sixteen in TaIrTe4, would falsify the paper's stated counts. A simpler check is to reproduce the TaIrTe4 and Cu2SnTe3 counts with an independent all-electron DFT code and successively denser k-meshes.

Watch

Extended reading notes

Core claim

The central discovery is a set of corrected topological node counts obtained by searching directly on DFT band structure instead of on a fitted tight-binding model. In TaIrTe4, the direct search finds sixteen Weyl points and two nodal lines, with four of the Weyl points absent from earlier studies. In SrSi2, the same approach yields three distinct sets of Weyl points, W1, W2, and W3, where the W2 set (twelve pairs) was not reported in prior work. In the Cu2XY3 family, the paper finds four small nodal rings in Cu2SiTe3, eight Weyl points in Cu2GeTe3, eight Weyl points in Cu2GeSe3, and no Weyl points or nodal rings in Cu2SnTe3, each differing from published tight-binding results. The paper further shows that the SrSi2 gap depends sensitively on the functional and lattice constant, and that in Cu2SnS3 small atomic displacements can drive the Weyl phase into a nodal-arc phase.

Load-bearing premise

The search is limited to the touching point between the topmost valence band and the bottommost conduction band, so any Weyl point or nodal line involving other bands would be missed, even though the paper reports its node counts as complete.

Editorial extensions

If this is right

Published tight-binding counts for TaIrTe4, SrSi2, and the Cu2XY3 family should be treated with caution until confirmed by direct DFT node searches.
Corrected counts: TaIrTe4 hosts sixteen Weyl points and two nodal lines; SrSi2 has an additional twelve-pair Weyl set W2; Cu2SnTe3 is not a Weyl semimetal.
SrSi2 sits near a topological transition: at the experimental lattice constant it is metallic within PBE, gapped within TB-mBJ, and develops Weyl nodes under roughly 1.5% compression, so samples with slightly different lattice constants can appear semimetallic or semiconducting.
In Cu2SnS3, atomic displacements of order 0.01 to 0.03 can switch the system from a Weyl phase to a nodal-arc phase, so local strain in real samples can wash out predicted topological signatures.

Reading between the lines

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

Because the search only examines the topmost valence and bottommost conduction bands, the corrected counts may still be incomplete; a full all-band search could reveal additional nodes deeper in the band structure.
The same direct-search re-benchmarking could be applied to other materials whose topological status rests on Wannier-function tight-binding models, and would likely yield different counts for some of them.
The sensitivity of node existence to lattice constants and functionals suggests that topological-phase maps should be published as phase diagrams over strain and band filling, not as single-lattice verdicts.
A testable extension would be to check whether the newly found W2 nodes in SrSi2 and the extra four nodes in TaIrTe4 produce surface Fermi-arc signatures distinct from the previously known nodes.

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.

Desk Editor's Note

read the letter

Short version: the paper reports concrete, checkable corrections to published topological counts for three material families using direct DFT searches rather than Wannier tight-binding. That is a genuinely useful exercise, and the authors do some things well: they list coordinates and energies for nodes, check chirality with WloopPHI, test multiple functionals and lattice parameters for SrSi2, and include a sensible robustness study for Cu2SnS3. The central idea—that structural sensitivity and exchange-correlation choice can explain theory-experiment mismatches—is plausible.

The soft spot is real and it is not minor. The PY-NODE search is explicitly limited to the touching point between the topmost valence band and the bottommost conduction band, in every material section. The text then presents "sixteen Weyl nodes" for TaIrTe4, "24 nodes" for SrSi2, and "no Weyl points" for Cu2SnTe3 as if they were complete counts of the material's topology. They are not. Other band pairs can cross in a multi-band semimetal, and the paper provides no argument that the relevant physics lives only in that one pair. So the headline corrections are, at best, statements about one band pair. That does not destroy the paper's value, but it changes the claim from "the earlier TBM predictions are wrong" to "the earlier predictions are not reproduced for this specific pair with these settings." That is still worth publishing, but the abstract and conclusions need to say it.

Other issues: no k-mesh or smearing convergence analysis, no error bars on node energies, and the TaIrTe4 table appears incomplete relative to the text—it lists only W1/W2/W3 rather than all 16 nodes. The reliance on the authors' own PY-NODE code, without convergence data in this paper, is a related weakness; citing your own earlier benchmarks is fine, but here the benchmark citations are doing work that a convergence section should do. None of this sinks the project, but it matters for how confident the reader can be in the numbers.

Who is this for? People who work on these specific materials, and anyone using TBM-derived topological catalogs. A serious referee should see it, mainly to enforce the band-pair restriction and ask for convergence data. If I were the editor, I would send it out.

Referee Report

6 major / 6 minor

Summary. The manuscript revisits the topological classification of TaIrTe4, SrSi2, and the Cu2XY3 family (X=Si, Ge, Sn; Y=S, Se, Te) using direct DFT-based searches for band crossings with the PY-NODE code and chirality checks with WloopPHI. The authors report additional Weyl points in TaIrTe4 and SrSi2 relative to earlier tight-binding studies, and a null result for Weyl points in Cu2SnTe3, and they argue that MLWF-based tight-binding models are unreliable. They also study the sensitivity of the Cu2SnS3 topological phase to atomic displacements. The central claims are presented as corrections to published topological assignments.

Significance. If the reported node counts were established as exhaustive, the paper would provide an important cautionary result for the use of Wannier-interpolated tight-binding models in topological materials discovery. The use of a full-potential DFT search with explicit chirality verification is a methodological strength, and the node coordinates and energies in Tables I and II are falsifiable predictions. However, the exhaustiveness of the node search and the internal consistency of the Cu2XY3 results must be resolved before the conclusions can be accepted.

major comments (6)

[Topological nature of TaIrTe4; Verification of topological phase of Cu2XY3] The PY-NODE search is explicitly restricted to the touching point between the topmost valence band and the bottommost conduction band. Consequently, the reported counts—'sixteen Weyl nodes' for TaIrTe4, '24 node points' for SrSi2, and 'did not find any Weyl points' for Cu2SnTe3—are at most lower bounds for a single band pair, not exhaustive counts of all Weyl nodes in the material. Because the paper uses these counts to overturn earlier full-band-structure tight-binding predictions, either the search must be extended to all band pairs or the claims must be rephrased as pair-restricted results.
[Verification of topological phase of Cu2XY3] The text contains a direct contradiction: it first states that 'the materials Cu2GeSe3, Cu2GeTe3, and Cu2SnSe3 host eight, eight, and four Weyl points, respectively,' and then states that 'In the case of Cu2SnSe3 and Cu2SnTe3, we did not find any Weyl points or nodal rings.' The abstract only claims the null result for Cu2SnTe3, so at least one of these statements is erroneous. Please correct the text and ensure the SM tables are consistent.
[Abstract; Verification of topological phase of Cu2XY3] The topological assignments for the Cu2XY3 family differ between the abstract and the main text. The abstract assigns 'four small nodal rings, eight Weyl points, and eight nodal arcs, respectively' to Cu2SiTe3, Cu2GeTe3, and Cu2GeSe3, whereas the main text gives eight Weyl points to Cu2GeSe3 and assigns the eight nodal arcs to Cu2GeS3 (introduced parenthetically). These conflicting assignments must be reconciled before the paper can be understood consistently.
[Introduction; Topological nature of TaIrTe4] The attribution of the differences to 'inaccuracy of the constructed TBM' or 'limitations in the Wannierization procedure' is not supported by the evidence presented, because the authors do not control for differences in DFT code, lattice constants, XC functional, or other numerical settings between their calculations and those of Refs. [14,17,47]. A controlled comparison, such as constructing Wannier functions from the same DFT calculation, is needed before concluding that Wannierization is the source of the discrepancies.
[Computational details; Tables I and II] No convergence analysis is reported for the PY-NODE search with respect to k-mesh, smearing width, or number of bands, and no error estimates are given for the node coordinates and energies in Tables I and II. The Introduction itself stresses the need for such convergence; without it, the quantitative node positions and energies are not yet established to the standard the paper advocates.
[Topological nature of SrSi2; Abstract] The newly identified W2 nodes in SrSi2 are obtained only with the PBE/PBEsol functionals; the same section reports that with TB-mBJ at the near-experimental lattice constant (6.5106 Å) a gap of 11.14 meV opens, so no Weyl nodes exist at that level of theory. The abstract's unqualified statement that additional Weyl points were found in SrSi2 therefore overstates the case; the sensitivity to the XC functional and lattice constant should be reflected in the abstract.

minor comments (6)

[Topological nature of SrSi2] The text states a 1% reduction of the optimized lattice parameter gives ≈6.5106 Å; however, 6.5698 Å × 0.99 = 6.5041 Å, so the stated percentage and value are inconsistent. Please correct the percentage or the numerical value.
[Verification of topological phase of Cu2XY3] The sentence 'Cu2SiTe3 (Cu2GeS3) hosts four small nodal rings (eight nodal-arcs)' is ambiguous; please spell out the assignment for each material separately.
[Topological nature of SrSi2; Verification of topological phase of Cu2XY3] The SM is cited for 'Table IV' in two different contexts (band gaps for SrSi2 and nodal features for Cu2XY3), which suggests a table-numbering conflict in the supplementary material; please verify the SM numbering.
[Topological nature of SrSi2] The statement that at 6.5106 Å 'the topmost valence band crosses the Fermi level' is followed immediately by 'within this potential, there is a band gap of 11.14 meV' for the same lattice constant; please clarify which functional each statement refers to.
[Table I] Table I lists only the three representative sets W1–W3; since the claim is sixteen Weyl nodes, please state the multiplicities explicitly (e.g., number of points per set) or list all sixteen points.
[Throughout] There are minor typos, such as 'materail' in the last paragraph of the SrSi2 section, and inconsistent use of 'nodal arcs' versus 'nodal rings' between the abstract and the main text.

Circularity Check

0 steps flagged · score 0.0 of 10

No fitted-to-target reduction: the Weyl-node counts are direct DFT search outputs; the restricted two-band search and same-group PY-NODE citations are scope and self-citation issues, not circular derivations.

full rationale

The derivation chain is not circular in the sense defined here. The claimed node counts (16 for TaIrTe4, 24 for SrSi2, zero for Cu2SnTe3, etc.) are produced by PY-NODE, which minimizes the DFT band-energy difference between the selected bands, and the chiralities are computed independently with WloopPHI; these are outputs of the calculation, not inputs that are then re-labeled as predictions. No parameter is fitted to a subset of the data and then used to predict a closely related quantity. The paper's statement that PY-NODE 'provides better results for various materials [43,45,46]' is a same-group citation, since reference [43] shares author S. K. Pandey and references [45,46] are by the present authors or their group. However, those citations describe independent, code-reproduced benchmarks on other materials with stated first-principles assumptions; they do not contain the target node counts of this paper, so they are real evidence rather than a circular premise. The more substantive issue is a scope limitation: the text explicitly restricts the search to 'the touching point between the topmost valence band and the bottommost conduction band' (TaIrTe4 section) and to touching points 'between the topmost valence band and the bottommost conduction band' (Cu2XY3 section). Thus the reported totals are complete for that one band pair, not proven to be exhaustive over all possible multi-band crossings. This undercuts the strength of the comparison with tight-binding predictions, but it does not make the result equal to its input by definition; the coordinates, energies, and chiralities are new, physically meaningful outputs. Accordingly, no circular step is identified.

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

No new entities or fitted constants are introduced. The only manual parameter is the SrSi2 lattice compression. Four assumptions carry the argument: DFT faithfulness, completeness of a two-band search, reliability of the authors' own node-search code, and equivalence of structures between this work and the prior Wannier studies.

free parameters (1)

SrSi2 lattice compression for node search = 1.5% compression (a=6.4712 Å) plus 1% compression (a=6.5106 Å)
Chosen by hand to approximate the experimental lattice and to test gap closure; the reported 12-node semimetal state appears only at the 1.5% compression.

assumptions (4)

domain assumption PBE/PBEsol DFT band structures faithfully represent the band topology used for all node counts
No experimental or many-body benchmark is used for the disputed features; all Weyl and nodal claims are read off Kohn-Sham bands.
domain assumption Searching only the topmost valence and bottommost conduction band pair finds every relevant Weyl point or nodal arc
This is stated before Fig. 1 and repeated in the Cu2XY3 section; the completeness of the counts depends on there being no crossings between other bands.
domain assumption PY-NODE root-finding and WloopPHI chirality results are numerically reliable for these materials
Both codes are cited from the authors' own prior work, and no convergence data with respect to k-mesh, smearing, or search parameters are provided in this preprint.
ad hoc to paper Differences from refs [14,17,47] are caused by Wannierization inaccuracy rather than by different structures, functionals, or numerical settings
The central conclusion about TBM inaccuracy presumes the compared calculations are otherwise equivalent; this equivalence is not demonstrated.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Revisiting the Topological Nature of TaIrTe4, SrSi2, and Cu2XY3: An ab-initio Investigation." pith.science (2026). https://pith.science/paper/CTRDAIMF

@misc{pith2026250524359,
  author       = {Pith},
  title        = {Pith review of: Revisiting the Topological Nature of TaIrTe4, SrSi2, and Cu2XY3: An ab-initio Investigation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CTRDAIMF}},
  note         = {Machine review of arXiv:2505.24359}
}

abstract

Several topological electronic materials have been theoretically predicted, leading to a comprehensive catalog systematically characterized by their band crossings. Researchers have attempted to experimentally verify the topological nature of some materials from the present catalogs, but not all efforts have yielded positive results. Here, we introduce a possible reason for the discrepancies between theoretical and experimental results. In this direction, firstly we have revisited the nature of the well-known topological materials TaIrTe$_4$ and SrSi$_2$ using \textit{state-of-the-art ab-initio} calculations, and found additional Weyl points in both materials that were missing in previously reported studies. Then we have verified the recently predicted topological states of the \textit{Imm2}-phase of Cu$_2$XY$_3$ (X=Si, Ge, Sn \& Y=S, Se, Te). Contrary to previously reported results, we did not find any Weyl points or nodal arcs in Cu$_2$SnTe$_3$. Notably, our theoretical results reveal that Cu$_2$SiTe$_3$, Cu$_2$GeTe$_3$ and Cu$_2$GeSe$_3$ each host four small nodal rings, eight Weyl points, and eight nodal arcs, respectively, which differ from previous studies. Considering Cu$_2$SnS$_3$ as an example, we have also investigated the robustness of the topological phase against local strain. Our study provides insights into the inconsistencies between theoretical predictions and experimental results, and demonstrates how the topological phase is sensitive to changes in lattice parameters, atomic positions, and exchange-correlation functionals.

Figures

Figures reproduced from arXiv: 2505.24359 by the authors.

**Figure 2.** FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_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

Strain-tunable type-II to type-III & Gimbal nodal line transition in Imm2-phase of Cu$_2$SnS$_3$: An ab-initio study
cond-mat.mtrl-sci 2025-07 reject novelty 4.0 of 10

Strain drives Cu2SnS3 through nodal-line phases with one, three, five, or seven loops, including 'gimbal' intersecting loops, in the authors' DFT calculations.

Reference graph

Works this paper leans on

63 extracted references · 52 canonical work pages · cited by 1 Pith paper

[1]

We found a total of six- teen Weyl nodes and two nodal lines

PY-NODE code suc- cessfully identiﬁed the touching point between the top- most valence band and the bottommost conduction band across the full Brillouin zone. We found a total of six- teen Weyl nodes and two nodal lines. Notably, four ad- ditional Weyl points found in our analysis were absent in previous studies [ 17]. The coordinates and correspond- ing ...

work page
[2]

Zhang, Y

T. Zhang, Y. Jiang, Z. Song, H. Huang, Y. He, Z. Fang, H. Weng, and C. Fang, Nature 566, 475 (2019)

2019
[3]

Bradlyn, L

B. Bradlyn, L. Elcoro, J. Cano, M. G. Vergniory, Z. Wang, C. Felser, M. I. Aroyo, and B. A. Bernevig, Nature 547, 298 (2017)

2017
[4]

Bradlyn, J

B. Bradlyn, J. Cano, Z. Wang, M. G. Vergniory, C. Felser, R. J. Cava, and B. A. Bernevig, Science 353, aaf5037 (2016)

2016
[5]

Claussen, B

N. Claussen, B. A. Bernevig, and N. Regnault, Phys. Rev. B 101, 245117 (2020)

work page 2020
[6]

R. Y. Chen, Z. G. Chen, X.-Y. Song, J. A. Schneeloch, G. D. Gu, F. Wang, and N. L. Wang, Phys. Rev. Lett. 115, 176404 (2015)

work page 2015
[7]

R. Y. Chen, S. J. Zhang, J. A. Schneeloch, C. Zhang, Q. Li, G. D. Gu, and N. L. Wang, Phys. Rev. B 92, 075107 (2015)

work page 2015
[8]

Y. Zhou, J. Wu, W. Ning, N. Li, Y. Du, X. Chen, R. Zhang, Z. Chi, X. Wang, X. Zhu, P. Lu, C. Ji, X. Wan, Z. Yang, J. Sun, W. Yang, M. Tian, Y. Zhang, and H. kwang Mao, Proc. Natl. Acad. Sci. U.S.A 113, 2904 (2016)

work page 2016

Show all 63 references

[9]

Li, W.-K

X.-B. Li, W.-K. Huang, Y.-Y. Lv, K.-W. Zhang, C.-L. Yang, B.-B. Zhang, Y. B. Chen, S.-H. Yao, J. Zhou, M.-H. Lu, L. Sheng, S.-C. Li, J.- F. Jia, Q.-K. Xue, Y.-F. Chen, and D.-Y. Xing, Phys. Rev. Lett. 116, 176803 (2016)

2016
[10]

Wu, J.-Z

R. Wu, J.-Z. Ma, S.-M. Nie, L.-X. Zhao, X. Huang, J.-X. Yin, B.-B. Fu, P. Richard, G.-F. Chen, Z. Fang, X. Dai, H.-M. Weng, T. Qian, H. Ding, and S. H. Pan, Phys. Rev. X 6, 021017 (2016)

2016
[11]

Manzoni, L

G. Manzoni, L. Gragnaniello, G. Aut` es, T. Kuhn, A. Sterzi, F. Cilento, M. Zacchigna, V. Enenkel, I. Vobornik, L. Barba, F. Bisti, P. Bugnon, A. Magrez, V. N. Strocov, H. Berger, O. V. Yazyev, M. Fonin, F. Parmigiani, and A. Crepaldi, Phys. Rev. Lett. 117, 237601 (2016)

2016
[12]

Hartstein, H

M. Hartstein, H. Liu, Y.-T. Hsu, B. S. Tan, M. Ciomaga Hatnean, G. Balakrishnan, and S. E. Sebastian, iScience 23, 101632 (2020)

2020
[13]

Iraola, I

M. Iraola, I. n. Robredo, T. Neupert, J. L. Ma˜ nes, R. Valent ´ ı, and M. G. Vergniory, Phys. Rev. Res. 6, 033195 (2024)

2024
[14]

Thunstr¨ om and K

P. Thunstr¨ om and K. Held, Phys. Rev. B 104, 075131 (2021)

2021
[15]

Koepernik, D

K. Koepernik, D. Kasinathan, D. V. Efremov, S. Khim, S. Borisenko, B. B¨ uchner, and J. van den Brink, Phys. Rev. B 93, 201101 (2016)

2016
[16]

Haubold, K

E. Haubold, K. Koepernik, D. Efremov, S. Khim, A. Fe- dorov, Y. Kushnirenko, J. van den Brink, S. Wurmehl, 6 B. B¨ uchner, T. K. Kim, M. Hoesch, K. Sumida, K. Taguchi, T. Yoshikawa, A. Kimura, T. Okuda, and S. V. Borisenko, Phys. Rev. B 95, 241108 (2017)

2017
[17]

Belopolski, P

I. Belopolski, P. Yu, D. S. Sanchez, Y. Ishida, T.-R. Chang, S. S. Zhang, S.-Y. Xu, H. Zheng, G. Chang, G. Bian, et al. , Nat. Commun. 8, 942 (2017)

2017
[18]

X. Zhou, Q. Liu, Q. Wu, T. Nummy, H. Li, J. Griﬃth, S. Parham, J. Waugh, E. Emmanouili- dou, B. Shen, O. V. Yazyev, N. Ni, and D. Dessau, Phys. Rev. B 97, 241102 (2018)

2018
[19]

M. Zeng, C. Fang, G. Chang, Y.-A. Chen, T. Hsieh, A. Bansil, H. Lin, and L. Fu, arXiv preprint arXiv:1504.03492 (2015)

2015 arXiv
[20]

L.-K. Zeng, R. Lou, D.-S. Wu, Q. N. Xu, P.-J. Guo, L.- Y. Kong, Y.-G. Zhong, J.-Z. Ma, B.-B. Fu, P. Richard, P. Wang, G. T. Liu, L. Lu, Y.-B. Huang, C. Fang, S.-S. Sun, Q. Wang, L. Wang, Y.-G. Shi, H. M. Weng, H.-C. Lei, K. Liu, S.-C. Wang, T. Qian, J.-L. Luo, and H. Ding, Phy...

2016
[21]

X. H. Niu, D. F. Xu, Y. H. Bai, Q. Song, X. P. Shen, B. P. Xie, Z. Sun, Y. B. Huang, D. C. Peets, and D. L. Feng, Phys. Rev. B 94, 165163 (2016)

2016
[22]

Oinuma, S

H. Oinuma, S. Souma, D. Takane, T. Nakamura, K. Nakayama, T. Mitsuhashi, K. Horiba, H. Kumi- gashira, M. Yoshida, A. Ochiai, T. Takahashi, and T. Sato, Phys. Rev. B 96, 041120 (2017)

2017
[23]

Guo, H.-C

P.-J. Guo, H.-C. Yang, B.-J. Zhang, K. Liu, and Z.-Y. Lu, Phys. Rev. B 93, 235142 (2016)

2016
[24]

U. Dey, M. Chakraborty, A. Taraphder, and S. Tewari, Sci. Rep 8, 14867 (2018)

2018
[25]

Z. Wang, P. Zhang, G. Xu, L. K. Zeng, H. Miao, X. Xu, T. Qian, H. Weng, P. Richard, A. V. Fedorov, H. Ding, X. Dai, and Z. Fang, Phys. Rev. B 92, 115119 (2015)

2015
[26]

Zhang, K

P. Zhang, K. Yaji, T. Hashimoto, Y. Ota, T. Kondo, K. Okazaki, Z. Wang, J. Wen, G. D. Gu, H. Ding, and S. Shin, Science 360, 182 (2018)

2018
[27]

Zhang, Z

P. Zhang, Z. Wang, X. Wu, K. Yaji, Y. Ishida, Y. Ko- hama, G. Dai, Y. Sun, C. Bareille, K. Kuroda, et al. , Nature Physics 15, 41 (2019)

2019
[28]

Borisenko, V

S. Borisenko, V. Bezguba, A. Fedorov, Y. Kushnirenko, V. Voroshnin, M. Sturza, S. Aswartham, and A. Yaresko, npj Quantum Mater. 5, 67 (2020)

2020
[29]

Li, S.-D

Y.-F. Li, S.-D. Chen, M. Garc ´ ıa-D ´ ıez, M. I. Iraola, H. Pfau, Y.-L. Zhu, Z.-Q. Mao, T. Chen, M. Yi, P.-C. Dai, J. A. Sobota, M. Hashimoto, M. G. Vergniory, D.- H. Lu, and Z.-X. Shen, Phys. Rev. X 14, 021043 (2024)

2024
[30]

Gibney, Nature 560, 151 (2018)

E. Gibney, Nature 560, 151 (2018)

2018
[31]

N. C. Frey, M. K. Horton, J. M. Munro, S. M. Griﬃn, K. A. Persson, and V. B. Shenoy, Sci. adv. 6, eabd1076 (2020)

2020
[32]

Andrejevic, J

N. Andrejevic, J. Andrejevic, B. A. Bernevig, N. Regnault, F. Han, G. Fabbris, T. Nguyen, N. C. Drucker, C. H. Rycroft, and M. Li, Adv. Mater. 34, 2204113 (2022)

2022
[33]

Regnault, Y

N. Regnault, Y. Xu, M.-R. Li, D.-S. Ma, M. Jovanovic, A. Yazdani, S. S. Parkin, C. Felser, L. M. Schoop, N. P. Ong, et al. , Nature 603, 824 (2022)

2022
[34]

Rasul, M

A. Rasul, M. S. Hossain, A. G. Dastider, H. Roy, M. Z. Hasan, and Q. D. Khosru, Sci. Rep 14, 31564 (2024)

2024
[35]

Marrazzo, S

A. Marrazzo, S. Beck, E. R. Margine, N. Marzari, A. A. Mostoﬁ, J. Qiao, I. Souza, S. S. Tsirkin, J. R. Yates, and G. Pizzi, Rev. Mod. Phys. 96, 045008 (2024)

2024
[36]

Marzari, A

N. Marzari, A. A. Mostoﬁ, J. R. Yates, I. Souza, and D. Vanderbilt, Rev. Mod. Phys. 84, 1419 (2012)

2012
[37]

Q. Wu, S. Zhang, H.-F. Song, M. Troyer, and A. A. Soluyanov, Comput. Phys. Comm. 224, 405 (2018)

2018
[38]

C. S. Lue, S. F. Wong, J. Y. Huang, H. L. Hsieh, H. Y. Liao, B. Ramachandran, and Y. K. Kuo, J. Appl. Phys. 113, 013710 (2013)

2013
[39]

Y.-K. Kuo, B. Ramachandran, and C.-S. Lue, Front. Chem. 2, 106 (2014)

2014
[40]

M.-Y. Yao, J. Noky, Q.-G. Mu, K. Manna, N. Kumar, V. N. Strocov, C. Shekhar, S. Medvedev, Y. Sun, and C. Felser, Phys. Rev. B 110, 224514 (2024)

2024
[41]

Singh, G

B. Singh, G. Chang, T.-R. Chang, S.-M. Huang, C. Su, M.-C. Lin, H. Lin, and A. Bansil, Sci. Rep. 8, 10540 (2018)

2018
[42]

Y. Shao, Z. Sun, Y. Wang, C. Xu, R. Sankar, A. J. Brein- del, C. Cao, M. M. Fogler, A. J. Millis, F. Chou, et al. , Proc. Natl. Acad. Sci. U.S.A. 116, 1168 (2019)

2019
[43]

Mele, Proc

E. Mele, Proc. Natl. Acad. Sci. U.S.A. 116, 1084 (2019)

2019
[44]

Pandey and S

V. Pandey and S. K. Pandey, Comput. Phys. Comm. 283, 108570 (2023)

2023
[45]

Pandey, A

V. Pandey, A. Sihi, and S. K. Pandey, J. Phys.: Condens. Matter 33, 475503 (2021)

2021
[46]

Pandey and S

P. Pandey and S. K. Pandey, arXiv preprint arXiv:2502.12722 (2025)

2025
[47]

Pandey and S

V. Pandey and S. K. Pandey, J. Phys.: Condens. Matter 35, 455501 (2023)

2023
[48]

L. Zhou, Y. Qian, C. Yue, Y. Jiang, Z. Fang, W. Zhang, C. Fang, and H. Weng, Phys. Rev. Res. 4, 033067 (2022)

2022
[49]

Blaha, K

P. Blaha, K. Schwarz, F. Tran, R. Laskowski, G. K. Madsen, and L. D. Marks, J. Chem. Phys. 152, 074101 (2020)

2020
[50]

J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996)

1996
[51]

See supplementary material at this link
[52]

J. A. Nelder and R. Mead, Comput. J. 7, 308 (1965)

1965
[53]

Pandey and S

P. Pandey and S. K. Pandey, Comput. Phys. Comm. 303, 109281 (2024)

2024
[54]

Saini, M

H. Saini, M. Laurien, P. Blaha, and O. Rubel, Comput. Phys. Comm. 270, 108147 (2022)

2022
[55]

Pringle, Structural Science 28, 2326 (1972)

G. Pringle, Structural Science 28, 2326 (1972)

1972
[56]

M. Imai, T. Naka, T. Furubayashi, H. Abe, T. Nakama, and K. Yagasaki, Appl. Phys. Lett 86 (2005)

2005
[57]

Tran and P

F. Tran and P. Blaha, Phys. Rev. B 83, 235118 (2011)

2011
[58]

W. Li, C. F. Walther, A. Kuc, and T. Heine, J. Chem. Theory Comput. 9, 2950 (2013)

2013
[59]

Zimmermann, P

R. Zimmermann, P. Steiner, R. Claessen, F. Reinert, S. H¨ ufner, P. Blaha, and P. Dufek, J. Phys.: Condens. Matter 11, 1657 (1999)

1999
[60]

S. F. Cogan, N. M. Nguyen, S. J. Perrotti, and R. D. Rauh, J. Appl. Phys. 66, 1333 (1989)

1989
[61]

Enesca, L

A. Enesca, L. Andronic, A. Duta, and S. Manolache, Rom. J. Inf. Sci. Technol. 10, 269 (2007)

2007
[62]

Y. Qiu, M. Yang, H. Fan, Y. Zuo, Y. Shao, Y. Xu, X. Yang, and S. Yang, CrystEngComm 13, 1843 (2011)

2011
[63]

Kam and B

K. Kam and B. Parkinson, J. Phys. Chem. 86, 463 (1982)

1982

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

We found a total of six- teen Weyl nodes and two nodal lines

PY-NODE code suc- cessfully identiﬁed the touching point between the top- most valence band and the bottommost conduction band across the full Brillouin zone. We found a total of six- teen Weyl nodes and two nodal lines. Notably, four ad- ditional Weyl points found in our analysis were absent in previous studies [ 17]. The coordinates and correspond- ing ...

work page

[2] [2]

Zhang, Y

T. Zhang, Y. Jiang, Z. Song, H. Huang, Y. He, Z. Fang, H. Weng, and C. Fang, Nature 566, 475 (2019)

2019

[3] [3]

Bradlyn, L

B. Bradlyn, L. Elcoro, J. Cano, M. G. Vergniory, Z. Wang, C. Felser, M. I. Aroyo, and B. A. Bernevig, Nature 547, 298 (2017)

2017

[4] [4]

Bradlyn, J

B. Bradlyn, J. Cano, Z. Wang, M. G. Vergniory, C. Felser, R. J. Cava, and B. A. Bernevig, Science 353, aaf5037 (2016)

2016

[5] [5]

Claussen, B

N. Claussen, B. A. Bernevig, and N. Regnault, Phys. Rev. B 101, 245117 (2020)

work page 2020

[6] [6]

R. Y. Chen, Z. G. Chen, X.-Y. Song, J. A. Schneeloch, G. D. Gu, F. Wang, and N. L. Wang, Phys. Rev. Lett. 115, 176404 (2015)

work page 2015

[7] [7]

R. Y. Chen, S. J. Zhang, J. A. Schneeloch, C. Zhang, Q. Li, G. D. Gu, and N. L. Wang, Phys. Rev. B 92, 075107 (2015)

work page 2015

[8] [8]

Y. Zhou, J. Wu, W. Ning, N. Li, Y. Du, X. Chen, R. Zhang, Z. Chi, X. Wang, X. Zhu, P. Lu, C. Ji, X. Wan, Z. Yang, J. Sun, W. Yang, M. Tian, Y. Zhang, and H. kwang Mao, Proc. Natl. Acad. Sci. U.S.A 113, 2904 (2016)

work page 2016