arxiv: 2605.05879 · v1 · submitted 2026-05-07 · ❄️ cond-mat.mtrl-sci

Recognition: unknown

Fermi energy Weyl nodes in AMTe₄ (A=Ta, Nb, M=Ir, Rh)

Shivam Parasar , Jeroen van den Brink , Rajyavardhan Ray

Authors on Pith no claims yet

Pith reviewed 2026-05-08 08:50 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci

keywords Weyl semimetalsAMTe4 compoundsWeyl pointsquantum oscillationsmagnetoresistancetopological electronic structureNbRhTe4electronic band structure

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The pith

AMTe4 compounds host Weyl points of multiple types within a few meV of the Fermi energy.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper applies a generalised search procedure to scan all subbands near the Fermi energy and locate every Weyl point in the AMTe4 family. This scan shows the points sit close enough to the Fermi level to shape the materials' measured electronic properties. The results indicate that most compounds contain more than one kind of Weyl point, with NbRhTe4 containing type-I, type-II, and type-III points at once. The mapping connects the topological features to observed quantum oscillations and magnetoresistance, offering a route to tune the points.

Core claim

Employing a generalised search procedure that accounts for all subbands close to the Fermi energy, these compounds are predicted to feature Weyl points within a few meV of the Fermi energy which significantly influence their properties. Most of the considered compounds host Weyl points of more than one type, including NbRhTe4 which hosts type-I, II and III Weyl points. The comparative analysis of structure and computational parameters provides a detailed mapping of the complex electronic structure and clarifies quantum oscillations and magnetoresistance observations.

What carries the argument

The generalised search procedure that accounts for all subbands close to the Fermi energy to locate every Weyl point.

If this is right

Weyl points within a few meV of the Fermi energy significantly influence the properties of these compounds.
Most compounds host Weyl points of more than one type.
NbRhTe4 hosts type-I, type-II, and type-III Weyl points.
The mapping clarifies quantum oscillations and magnetoresistance observations and supplies a framework for tuning the Weyl points.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same comprehensive scan applied to other known topological compounds could uncover previously missed Weyl points near the Fermi energy.
Coexistence of several Weyl point types inside one material may produce transport signatures that are more complex than those in single-type Weyl semimetals.
Small shifts in doping or strain could move the Fermi level across different Weyl point types, allowing experimental control over the dominant topological response.

Load-bearing premise

The generalised search procedure together with the chosen computational models and parameters accurately locates all Weyl points near the Fermi energy without missing relevant subbands or introducing artifacts.

What would settle it

Angle-resolved photoemission spectroscopy or quantum oscillation measurements that fail to find Weyl points at the predicted energies, momenta, and types within a few meV of the Fermi level would falsify the prediction.

Figures

Figures reproduced from arXiv: 2605.05879 by Jeroen van den Brink, Rajyavardhan Ray, Shivam Parasar.

**Figure 1.** Figure 1: Crystal structure and electronic properties. (a) Crystal structure of AMTe4 (A=Ta, Nb, M=Ir, Rh). (b-c) Electronic band structure for (b) the experimental crystal structure of TaIrTe4, and (c) the optimzed crystal structure of TaRhTe4, using LDA and 20×10×10 k-mesh. (d) Band structures of TaIrTe4 for the optimized crystal structure with GGA and 20 × 10 × 10 k-mesh (solid line), and the experiemntal crystal… view at source ↗

**Figure 2.** Figure 2: WP landscape for Ta systems. (a-b) Energy distribution of WPs for (a) TaIrTe4 and (b) TaRhTe4, accounting for different crystal structures and exchange-correlation functional. WP quartets are represented by dark thin bars while octets are represented by light-colored thick bars. (c-d) The in-plane coordinates (kx, ky) of the WPs in (c) TaIrTe4, and (d) TaRhTe4, obtained using GGA. 8 view at source ↗

**Figure 3.** Figure 3: Angular dependance of dHvA frequencies in Ta-based systems. (a) The observed dHvA frequencies from Ref. [24]. (b-c) Calculated angular dependance of dHvA for (b) optimized structure of TaIrTe4, and (c) otpimized structure of TaRhTe4. In all cases, k-mesh with 20×10×10 intervals were used together with GGA. and GGA with a dense k-mesh containing 20 × 10 × 10 intervals. The curves F3 and F4 in the experiment… view at source ↗

**Figure 4.** Figure 4: Electronic structure and topology of Nb compounds. (a-b) Electronic band structure for optimized crystal structure of (a) NbIrTe4 and (b) NbRhTe4. (c-d) WP landscape in (c) NbIrTe4 and (d) NbRhTe4. Other details same as in view at source ↗

**Figure 5.** Figure 5: Angular dependence of dHvA in Nb compounds. (a-b) Calculated angular dependence of dHvA for optimized crystal structure of (a) NbIrTe4 and (b) NbRhTe4 TaRhTe4, the needle-like hole pocket along Γ − Y is absent as the bands along this path of the BZ are shifted down compared to TaRhTe4. At the same time, the bands N + 1 and N + 2 are shifted higher along S − Y , leading to absence of electron pocket along t… view at source ↗

read the original abstract

Key aspects of the quantum oscillations and magnetoresistance in Weyl semimetals $AM$Te$_4$ ($A$=Nb,Ta, $M$=Rh, Ir) persist as open questions, obscuring the link between their topological electronic structure and practical implementations. Employing a generalised search procedure, we carry out a comprehensive scan of WPs accounting for all the subbands close to the Fermi energy, and show that this dramatically alters the WP landscape in these compounds. In particular, we predict these compounds to feature WPs within a few meV of the Fermi energy which significantly influence their properties. Remarkably, most of the considered compounds host WPs of more than one type, including NbRhTe$_4$ which hosts type-I, II and III Weyl points. Our comparative analysis of structure and fidelity of computational parameters/models not only provides a detailed mapping of the complex electronic structure in these compounds, but also clarifies quantum oscillations and magnetoresistance observations in this family, bridging the gap between theory and experiments and offering a framework for precise tunability of WPs.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

A wider subband search puts Weyl points within a few meV of the Fermi energy in these tellurides and flags type-I/II/III coexistence in NbRhTe4, but the numerics still need explicit convergence checks to support the precision.

read the letter

The main takeaway is that scanning all subbands near the Fermi energy instead of a narrower set changes the Weyl point picture in the AMTe4 family. Several points land close enough to EF to matter for transport, and NbRhTe4 is said to host all three types at once. That mixed-type result is the clearest new element and could help interpret the quantum oscillation and magnetoresistance data that have stayed puzzling. The paper does a reasonable job tying the revised map back to those experimental open questions without overclaiming a full solution. The comparative discussion of different computational setups is also a step in the right direction for a material-specific study. The soft spot is the missing technical backbone. Even though the abstract mentions checking structure and fidelity of parameters, the text supplies no numbers on how Weyl point energies or tilts respond to k-mesh density, smearing width, functional choice, or SOC treatment. A shift of only 1-2 meV can move a point across EF or flip its classification, so without those tests or error estimates the “few meV” claim stays hard to judge. If the full manuscript has the checks, they need to be shown clearly rather than summarized. This work is aimed at people already following topological semimetals in the AMTe4 series and who need updated band-structure targets for experiment or further calculation. It is not a methods paper and will not change the broader field, but the specific predictions are concrete enough to be useful. I would bring it to a reading group to talk through the search procedure and the type-coexistence claim. I would not cite it yet. It deserves peer review because the central idea is testable and the subfield has room for these targeted revisions, provided the numerics are tightened up.

Referee Report

2 major / 2 minor

Summary. The paper employs a generalized search procedure to comprehensively scan for Weyl points (WPs) across all subbands near the Fermi energy in the AMTe4 family (A=Ta,Nb; M=Ir,Rh). It predicts that these compounds host WPs within a few meV of EF that strongly influence their properties, with most materials exhibiting multiple WP types; notably, NbRhTe4 is reported to contain type-I, II, and III WPs simultaneously. The work includes a comparative analysis of computational models and parameters to map the electronic structure and link it to observed quantum oscillations and magnetoresistance.

Significance. If the central predictions hold, the identification of multiple coexisting WP types near EF would offer a concrete explanation for unresolved magnetotransport features in this family and a practical route to tuning topological nodes via composition or strain. The emphasis on a systematic scan of subbands near EF addresses a common limitation in prior studies of these materials.

major comments (2)

[Abstract and Computational Methods] Abstract and Computational Methods: The abstract asserts that a 'comparative analysis of structure and fidelity of computational parameters/models' was performed and that WPs lie 'within a few meV of the Fermi energy,' yet no quantitative details are supplied on k-mesh density, smearing parameter, SOC treatment, pseudopotential choice, or convergence tests for WP energies and tilt parameters. Because DFT band positions near EF are known to shift by 1-2 meV under modest changes in these controls, and because the central claim (including type classification in NbRhTe4) is sensitive to such shifts, the absence of these controls leaves the reported WP landscape unverified.
[Results on NbRhTe4] Results on NbRhTe4: The claim that NbRhTe4 hosts type-I, II, and III WPs simultaneously is load-bearing for the 'multiple types' narrative, but the text provides neither the explicit energies (relative to EF), momentum coordinates, nor the tilt parameters that distinguish the three classes. Without these data or a direct comparison to earlier calculations, it is impossible to confirm that the generalized search has correctly located and classified all crossings or that the coexistence is robust rather than an artifact of subband truncation.

minor comments (2)

The abstract refers to 'dramatically alters the WP landscape' without citing the specific prior calculations or figures that are being superseded; adding a brief comparison table or reference to earlier WP counts would improve clarity.
Figure captions and axis labels should explicitly state the energy window (e.g., 'within 10 meV of EF') and the k-path used for the band plots to allow readers to assess proximity to the Fermi level.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review. The comments correctly identify areas where additional quantitative details and explicit data would strengthen the manuscript. We will revise accordingly to improve verifiability while preserving the core findings from our generalized Weyl-point search.

read point-by-point responses

Referee: [Abstract and Computational Methods] Abstract and Computational Methods: The abstract asserts that a 'comparative analysis of structure and fidelity of computational parameters/models' was performed and that WPs lie 'within a few meV of the Fermi energy,' yet no quantitative details are supplied on k-mesh density, smearing parameter, SOC treatment, pseudopotential choice, or convergence tests for WP energies and tilt parameters. Because DFT band positions near EF are known to shift by 1-2 meV under modest changes in these controls, and because the central claim (including type classification in NbRhTe4) is sensitive to such shifts, the absence of these controls leaves the reported WP landscape unverified.

Authors: We agree that the absence of explicit numerical controls limits independent verification, especially given the known sensitivity of near-EF DFT states. In the revised manuscript we will add a dedicated paragraph (or table) in the Computational Methods section specifying the k-mesh density, smearing parameter, SOC treatment, pseudopotential choice, and convergence tests performed on WP energies and tilt parameters. These additions will directly demonstrate that the reported positions remain within a few meV of EF under the controls used. revision: yes
Referee: [Results on NbRhTe4] Results on NbRhTe4: The claim that NbRhTe4 hosts type-I, II, and III WPs simultaneously is load-bearing for the 'multiple types' narrative, but the text provides neither the explicit energies (relative to EF), momentum coordinates, nor the tilt parameters that distinguish the three classes. Without these data or a direct comparison to earlier calculations, it is impossible to confirm that the generalized search has correctly located and classified all crossings or that the coexistence is robust rather than an artifact of subband truncation.

Authors: We accept that explicit values are required to substantiate the simultaneous presence of all three WP types. The revised manuscript will include a table listing the energy (relative to EF), momentum coordinates, and tilt parameters for each Weyl point in NbRhTe4, together with the classification criteria applied. We will also add a brief comparison to prior calculations in the literature to show that the generalized search recovers previously reported nodes while identifying additional ones, thereby addressing concerns about subband truncation and robustness. revision: yes

Circularity Check

0 steps flagged

No circularity in computational Weyl point search

full rationale

The paper's central derivation applies a generalised search procedure to first-principles DFT band structures, scanning all subbands near the Fermi energy to locate and classify Weyl points (including type-I/II/III coexistence in NbRhTe4). This is a forward computational prediction from external electronic-structure calculations rather than any self-referential definition, fitted parameter renamed as output, or load-bearing self-citation chain. No equations or steps reduce the reported WP energies, types, or influences on properties to the inputs by construction; the comparative analysis of computational parameters/models serves as validation of the scan, not a tautology. The result remains independent of the target claims.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only the abstract is available; the work rests on standard electronic-structure methods whose detailed assumptions are not stated here.

axioms (1)

domain assumption Standard assumptions of density-functional theory and band-structure calculations for periodic solids
The generalised search for Weyl points presupposes reliable computation of electronic bands near the Fermi energy.

pith-pipeline@v0.9.0 · 5514 in / 1302 out tokens · 79010 ms · 2026-05-08T08:50:41.332332+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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[001] Frequency [T] Angle [θ ] TaIrTe4(GGA) H1 H2 H3 H4 H5 E1 E2 b H1 H2 H3 H4 H5 E1 E2 0 100 200 300 400 500 600 0 20 40 60 80
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[001] Frequency [T] Angle [θ ] TaRhTe4(GGA) H1 H2 H3 H4 E1 E2 c H1 H2 H3 H4 E1 E2 Figure 3:Angular dependance of dHvA frequencies in Ta-based systems. (a)The observed dHvA frequencies from Ref. [24].(b-c)Calculated angular dependance of dHvA for (b) optimized structure of TaIrTe4, and (c) otpimized structure of TaRhTe4. In all cases,k-mesh with20×10×10int...
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[001] Frequency [T] Angle [θ ] NbRhTe4 (GGA) H1 H2 E1 E2 b H1 H2 E1 E2 Figure 5:Angular dependence of dHvA in Nb compounds. (a-b)Calculated angular dependence of dHvA for optimized crystal structure of (a) NbIrTe4 and (b) NbRhTe4 TaRhTe4, the needle-like hole pocket alongΓ−Yis absent as the bands along this path of the BZ are shifted down compared to TaRh...

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Lee, J.-E.et al.Spin-orbit-splitting-driven nonlinear Hall effect in NbIrTe 4.Nature Commu- nications15(2024). URLhttp://dx.doi.org/10.1038/s41467-024-47643-4

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Onsager, L. Interpretation of the de Haas-van Alphen effect.The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science43, 1006–1008 (1952). URLhttp: //dx.doi.org/10.1080/14786440908521019. 24 Supplementary Information Suppementary Note I: Structural Details The DFT calculations were carried out forAMTe 4 (A=Ta, Nb,M=Ir, Rh). For Ir-ba...

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[001] Frequency [T] Angle [θ ] TaIrTe * 4(LDA) H1 H2 H3 H4 H5 E1 E2 b H1 H2 H3 H4 H5 E1 E2 0 100 200 300 400 500 0 20 40 60 80
[51]

[001] Frequency [T] Angle [θ ] TaIrTe * 4(GGA)c 0 100 200 300 400 500 0 20 40 60 80
[52]

The experimental data is shown in (a)

[001] Frequency [T] Angle [θ ] TaIrTe4(LDA)d Figure S8: A detailed comparison of the dHvA frequencies between observed different crystal structures and XC functional. The experimental data is shown in (a). (b) and (c) correspond to the DFT calculations using the experimental crystal structure with a densek-mesh, while (d) corresponds to DFT calculations o...