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Prediction of three-fold fermions in a nearly-ideal Dirac semimetal BaAgAs

T0 review · 3 major / 3 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read BaAgAs is predicted to be a nearly ideal Dirac semimetal whose symmetry-protected Dirac points split into clean three-fold fermions when inversion symmetry is broken by phosphorus alloying.

desk verdict Solid Dirac semimetal prediction for BaAgAs; the alloy triple-point claim is a symmetry story that the evidence doesn't yet back for a real disordered solid. read the letter →

arxiv 1908.01336 v1 pith:B6XTZNPB submitted 2019-08-04 cond-mat.mtrl-sci cond-mat.mes-hall

Sougata Mardanya , Bahadur Singh , Shin-Ming Huang , Tay-Rong Chang , Chenliang Su , Hsin Lin , Amit Agarwal , Arun Bansil This is my paper · ORCID
classification cond-mat.mtrl-scicond-mat.mes-hall
keywords three-foldfermionstriple-pointsemimetalDiracBaAgAsfirst-principlescalculationsk.pmodelsymmetry-protectednodalpointstopologicalphasetransition
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 a material family in which three-fold fermions appear cleanly at the Fermi level. With spin-orbit coupling, BaAgAs is a nearly ideal Dirac semimetal: a pair of symmetry-protected Dirac points sits on the C3 rotation axis with no competing trivial bands nearby. Breaking inversion symmetry, by alloying arsenic with phosphorus in BaAgAs1−xPx, splits each Dirac point into a pair of three-fold fermion points, giving a tunable triple-point semimetal. Because three-fold fermions sit conceptually between Weyl and Dirac fermions and are expected to produce unusual surface and transport responses, the value lies in having a concrete, already-synthesized parent compound in which to realize and tune them.

What carries the argument

The central mechanism is symmetry reduction along the $C_3$ rotation axis. Along $\Gamma$–$A$, the $C_{6v}$ point group (equal to $C_2\otimes C_{3v}$) allows one singly degenerate band (a one-dimensional irreducible representation, $A_1$) and one doubly degenerate band (a two-dimensional irreducible representation, $E_1$) to invert without hybridizing because they belong to different representations. In the absence of spin-orbit coupling this gives a stable threefold crossing; including spin-orbit coupling makes each band Kramers doubly degenerate, and the resulting $\Delta_7$ and $\Delta_9$ states remain protected by their different $C_3$ rotation eigenvalues, so the crossing becomes a fourfold Dirac point. Removing inversion removes the $C_2$ factor, reducing the group to $C_{3v}$; the formerly fourfold point then splits into two threefold points. The paper's minimal low-energy description is a four-band $\mathbf{k}\cdot\mathbf{p}$ Hamiltonian whose inversion-breaking perturbation $\Delta H = h(1\otimes\sigma_y)$ shifts the two members of the split pair to $k_{\mathrm{TP}}=(0,0,\pm h/(B_1-B_2))$.

What would settle it

Measure the bulk dispersion of a synthesized BaAgAs$_{0.5}$P$_{0.5}$ crystal along the $\Gamma$–$A$ ($C_3$) axis with angle-resolved photoemission: the central claim fails if no gapless triply-degenerate crossing appears near the Fermi level at the predicted $k_z$ (near the parent Dirac point at $0.159\,\frac{2\pi}{c}$). A complementary test is an ab initio calculation over a realistically disordered supercell ensemble; if configurational disorder opens a gap at the triple point, the clean three-fold fermion phase is not realized.

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Extended reading notes

Core claim

BaAgAs in the hexagonal space group $P6_3/mmc$ has $C_{6v}$ symmetry along the $\Gamma$–$A$ line. Without spin-orbit coupling, a doubly degenerate $E_1$ band (As $p$ states) crosses a singly degenerate $A_1$ band (Ag $s$ states) at two points at $(0,0,\pm 0.146\,\frac{2\pi}{c})$, forming spinless triple points connected by one nodal line (a type-A triple-point semimetal). With spin-orbit coupling, time-reversal and inversion make each band Kramers-degenerate, and the $\Delta_7$ and $\Delta_9$ representations, which carry different $C_3$ eigenvalues, cross stably at $(0,0,\pm 0.159\,\frac{2\pi}{c})$ near the Fermi level, giving a nearly ideal Dirac semimetal with $Z_2$ invariants 1 and 0 on the $k_z=0$ and $k_z=\pi/c$ planes. In an ordered BaAgAs$_{0.5}$P$_{0.5}$ supercell, inversion is broken and the symmetry along the axis reduces from $C_{6v}$ to $C_{3v}$; each Dirac point then splits into a pair of triple points. A four-band $\mathbf{k}\cdot\mathbf{p}$ Hamiltonian with an added inversion-breaking term $\Delta H = h(1\otimes\sigma_y)$ reproduces the split, placing the triple points at $k_{\mathrm{TP}}=(0,0,\pm h/(B_1-B_2))$.

Load-bearing premise

The calculations model the alloy BaAgAs$_{0.5}$P$_{0.5}$ as a single ordered repeating cell, and assume this stands in for the real disordered mixture without destroying the threefold rotational symmetry along the $C_3$ axis.

Editorial extensions

If this is right

  • Angle-resolved photoemission on BaAgAs should reveal a topological surface Dirac cone and closed Fermi arcs connecting the two projected Dirac points.
  • In BaAgAs$_{1-x}$P$_x$, increasing phosphorus content moves the material from the Dirac semimetal through a gap-closing transition near $x = 0.56$ to the trivial insulator BaAgP, giving a concentration-tuned topological phase transition.
  • The alloy at $x = 0.5$ should show a clean triple-point semimetal with surface Fermi arcs that touch at a doubly degenerate band, distinct from nonsymmorphic triple-point materials.
  • Because the predicted topological features sit near the Fermi level with no trivial band background, both ARPES and scanning tunneling spectroscopy can test them directly.
  • The k.p Hamiltonian shows that a single inversion-breaking parameter $h$ controls the Dirac-to-triple-point splitting, so the mechanism is captured by a minimal low-energy model.

Reading between the lines

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

  • The same symmetry-reduction recipe could be applied to other $C_{6v}$ Dirac semimetals: any perturbation that removes the $C_2$ rotation, such as strain, an electric field, or a surface termination, should also split Dirac points into triple points without requiring phosphorus alloying.
  • If the real alloy's disorder is weak along the $C_3$ axis, the triple points may survive as broadened crossings; a supercell ensemble calculation could map how much local disorder the $C_{3v}$ protection tolerates.
  • The touching Fermi surfaces that the paper notes could drive magnetic breakdown in quantum oscillations, offering a transport signature testable in high-field measurements on the alloy.
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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

3 major / 3 minor

Summary. The manuscript combines first-principles DFT calculations (GGA, with a hybrid-functional cross-check) and a low-energy k.p model to study the electronic structure of hexagonal BaAgAs. It reports that, in the absence of SOC, BaAgAs hosts a pair of spinless triple-point crossings on the C3 rotation axis; with SOC, these evolve into a nearly-ideal Dirac semimetal with a pair of Dirac points near the Fermi level. The paper further claims that breaking inversion symmetry via alloying in BaAgAs1−xPx, modeled with the virtual crystal approximation and one ordered supercell at x=0.5, yields a clean and tunable three-fold fermion semimetal. Surface-state calculations for the Dirac phase show topological surface states, and a symmetry-based k.p Hamiltonian is used to describe the Dirac-to-triple-point evolution.

Significance. If the central alloy prediction holds, the BaAgAs family would be a valuable tunable platform for triple-point fermion physics. The pure-material Dirac semimetal result is supported by standard DFT methodology and a hybrid-functional check, and the k.p model provides a useful symmetry framework. The predicted surface Fermi arcs and band features are falsifiable by ARPES/STS. The principal weakness is that the alloy claim rests on the crude VCA and a single ordered supercell, with the paper itself acknowledging that no sophisticated disorder treatment was attempted; given the very small inversion-breaking scale in the k.p model, the 'clean and tunable' assertion in the abstract is not yet supported.

major comments (3)
  1. [Triple point semimetal state; Fig. 4] The central claim of a clean three-fold fermion semimetal in random BaAgAs1−xPx is not established. The evidence consists of the VCA and a single ordered supercell at x=0.5; VCA artificially preserves the C3v symmetry that protects the TPs, while a random alloy has no exact C3v in any particular configuration. The paper itself notes that a more sophisticated treatment of disorder effects is possible but was not attempted. Using the parameters below Eq. (1) with h = -0.00022 eV, the two TPs are separated by about 2h/(B1-B2) ~ 1.7×10^-4 Å^-1 in kz, an energy scale of order 0.2 meV, which is plausibly smaller than substitutional As/P disorder broadening. Please either provide disorder-aware calculations (e.g., several random supercells or a CPA treatment) or revise the claim to refer specifically to the ordered BaAgAs0.5P0.5 supercell.
  2. [Model Hamiltonian] The inversion-breaking parameter h in the k.p Hamiltonian is introduced as an input ('with h = -0.00022 eV') rather than derived from the supercell DFT band structure. Since the TP separation and hence the central alloy prediction depend directly on h, the manuscript should state how h is obtained and show a quantitative comparison between the k.p model and the DFT bands of the ordered supercell. As written, the tunability claim is not a first-principles prediction.
  3. [Abstract and Summary] The title and abstract present three-fold fermions as a property of BaAgAs, but in the physical (SOC-included) case BaAgAs is a Dirac semimetal; the three-fold fermions appear only after inversion breaking, which is modeled via alloying. Given the concerns above about the alloy modeling, the manuscript should either soften the abstract's claim or clearly separate the robust pure-BaAgAs results from the alloy prediction.
minor comments (3)
  1. [Triple point semimetal state] The ordered supercell used at x = 0.5 is not described; please specify its size, the As/P arrangement, and the resulting space group, and state whether the structure preserves the C3v symmetry on the Γ-A line after relaxation.
  2. [Crystal structure and methodology] Reference [48] is incomplete; please provide the journal name and volume for M. Albrecht's work.
  3. [Model Hamiltonian] In the sentence defining ΔH = h (1⊗σ_y), the notation should be made explicit: which two of the four basis states does σ_y act on, and what is the ordering of the 4×4 matrix in the basis given for Eq. (1)?

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central Dirac and triple-point claims come from first-principles DFT; the k.p model is a post hoc fit.

full rationale

The paper's central claims are that BaAgAs without spin-orbit coupling hosts spinless triple points, that BaAgAs with spin-orbit coupling becomes a nearly-ideal Dirac semimetal with a pair of Dirac nodes, and that an ordered BaAgAs0.5P0.5 supercell with broken inversion symmetry hosts clean triple points. All of these are obtained from first-principles DFT band structures, symmetry/irrep analysis, and surface-state calculations, and none of them is derived from the fitted k.p parameters. The k.p Hamiltonian is explicitly presented as a low-energy model to better understand the DFT result, and its material-dependent parameters are stated to be obtained by fitting to the first-principles bands. The inversion-breaking term h is added to describe the same triple-point state already shown in the supercell DFT calculation, so the k.p model is a post hoc rationalization rather than the source of the prediction. The paper itself acknowledges that VCA is a simple description and that a more sophisticated disorder treatment is possible, but that limitation concerns the robustness of the alloy prediction, not circularity. No load-bearing self-citation chain appears: references to prior triple-point classification schemes are used only to identify the type of crossing, not to prove BaAgAs-specific results. In short, the derivation chain is self-contained with respect to its DFT inputs and the k.p model is an interpretive fit, not a forced restatement of the prediction.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central prediction rests on DFT calculations with standard approximations; the k.p model adds a hand-set inversion-breaking scale h and material parameters fitted to DFT, but these do not feed back into the DFT result. The most significant unverified inputs are the alloy-modeling assumptions.

free parameters (2)
  • Inversion-breaking perturbation strength h = -0.00022 eV
    Added to the k.p Hamiltonian to model inversion breaking in the alloy; chosen by hand, not derived from the supercell calculation.
  • k.p parameters (A1, A2, B1, B2, C, D, D') = A1=-17.78 eV·Å², A2=77.26 eV·Å², B1=1.67 eV·Å, B2=-0.85 eV·Å, C=-0.08 eV·Å², D=4.11 eV·Å, D'=0.75 eV·Å²
    Fitted to the DFT band structure around the Dirac point; used to illustrate the model but not needed for the central DFT claim.
assumptions (4)
  • domain assumption GGA-PBE exchange-correlation functional adequately describes the band ordering and topological properties of BaAgAs.
    The prediction of Dirac/triple points depends on the DFT band structure; GGA may underestimate gaps, though a hybrid functional check is provided.
  • domain assumption The virtual crystal approximation is a valid description of BaAgAs1−xPx solid solutions.
    Used to model the alloy band structure as a function of P concentration; VCA is approximate and may miss disorder effects.
  • domain assumption The ordered BaAgAs0.5P0.5 supercell with a specific As/P arrangement is representative of the disordered alloy and preserves the C3v symmetry along the C3 axis.
    The supercell breaks inversion in a particular way; real disorder may behave differently.
  • standard math Standard group theory and theory of invariants for the C6v and C3v point groups.
    Used to construct the k.p Hamiltonian and classify band crossings.

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Pith. "Pith review of Prediction of three-fold fermions in a nearly-ideal Dirac semimetal BaAgAs." pith.science (2026). https://pith.science/paper/B6XTZNPB

@misc{pith2026190801336,
  author       = {Pith},
  title        = {Pith review of: Prediction of three-fold fermions in a nearly-ideal Dirac semimetal BaAgAs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/B6XTZNPB}},
  note         = {Machine review of arXiv:1908.01336}
}
abstract

Materials with triply-degenerate nodal points in their low-energy electronic spectrum produce crystalline-symmetry-enforced three-fold fermions, which conceptually lie between the two-fold Weyl and four-fold Dirac fermions. Here we show how a silver-based Dirac semimetal BaAgAs realizes three-fold fermions through our first-principles calculations combined with a low-energy effective $\mathbf{k.p}$ model Hamiltonian analysis. BaAgAs is shown to harbor triply-degenerate nodal points, which lie on its $C_{3}$ rotation axis, and are protected by the $C_{6v}$($C_2\otimes C_{3v}$) point-group symmetry in the absence of spin-orbit coupling (SOC) effects. When the SOC is turned on, BaAgAs transitions into a nearly-ideal Dirac semimetal state with a pair of Dirac nodes lying on the $C_{3}$ rotation axis. We show that breaking inversion symmetry in the BaAgAs$_{1-x}$P$_x$ alloy yields a clean and tunable three-fold fermion semimetal. Systematic relaxation of other symmetries in BaAgAs generates a series of other topological phases. BaAgAs materials thus provide an ideal platform for exploring tunable topological properties associated with a variety of different fermionic excitations.

Figures

Figures reproduced from arXiv: 1908.01336 by the authors.

Figure 1
Figure 1. FIG. 1: (a)-(d) Schematic evolution of the band struc [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: (a) Bulk band structure of BaAgAs (without SOC). [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. FIG. 4: Bulk band structure of BaAgAs [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

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Works this paper leans on

58 extracted references · 39 canonical work pages

  1. [1]

    Bansil, H

    A. Bansil, H. Lin, and T. Das, Rev. Mod. Phys. 88, 021004 (2016)

    2016

  2. [2]

    N. P. Armitage, E. J. Mele, and A. Vishwanath, Rev. Mod. Phys. 90, 015001 (2018)

    2018

  3. [3]

    Kong and Y

    D. Kong and Y. Cui, Nat. Chem. 3, 845 (2011)

    work page 2011

  4. [4]

    S. M. Young, S. Zaheer, J. C. Y. Teo, C. L. Kane, E. J. Mele, and A. M. Rappe, Phys. Rev. Lett. 108, 140405 (2012)

    2012

  5. [5]

    Z. Wang, Y. Sun, X.-Q. Chen, C. Franchini, G. Xu, H. Weng, X. Dai, and Z. Fang, Phys. Rev. B 85, 195320 (2012)

    2012

  6. [6]

    Z. K. Liu, B. Zhou, Y. Zhang, Z. J. Wang, H. M. Weng, D. Prabhakaran, S.-K. Mo, Z. X. Shen, Z. Fang, X. Dai, Z. Hussain, and Y. L. Chen, Science 343, 864 (2014)

    2014

  7. [7]

    Z. K. Liu, J. Jiang, B. Zhou, Z. J. Wang, Y. Zhang, H. M. Weng, D. Prabhakaran, S.-K. Mo, H. Peng, P. Dudin, T. Kim, M. Hoesch, Z. Fang, X. Dai, Z. X. Shen, D. L. Feng, Z. Hussain, and Y. L. Chen, Nat. Mater. 13, 677 (2014)

    2014

  8. [8]

    Neupane, S.-Y

    M. Neupane, S.-Y. Xu, R. Sankar, N. Alidoust, G. Bian, C. Liu, I. Belopolski, T.-R. Chang, H.-T. Jeng, H. Lin, A. Bansil, F. Chou, and M. Z. Hasan, Nat. Commun. 5, 3786 (2014)

    work page 2014

Show all 58 references
  1. [9]

    Borisenko, Q

    S. Borisenko, Q. Gibson, D. Evtushinsky, V. Zabolotnyy, B. B¨ uchner, and R. J. Cava, Phys. Rev. Lett.113, 027603 (2014)

    2014

  2. [10]

    Chang, S.-Y

    T.-R. Chang, S.-Y. Xu, D. S. Sanchez, W.-F. Tsai, S.-M. Huang, G. Chang, C.-H. Hsu, G. Bian, I. Belopolski, Z.- M. Yu, S. A. Yang, T. Neupert, H.-T. Jeng, H. Lin, and M. Z. Hasan, Phys. Rev. Lett. 119, 026404 (2017)

    2017

  3. [11]

    Singh, S

    B. Singh, S. Mardanya, C. Su, H. Lin, A. Agarwal, and A. Bansil, Phys. Rev. B 98, 085122 (2018)

    2018

  4. [12]

    Singh, B

    B. Singh, B. Ghosh, C. Su, H. Lin, A. Agarwal, and A. Bansil, Phys. Rev. Lett. 121, 226401 (2018)

    2018

  5. [13]

    Chang, S.-Y

    G. Chang, S.-Y. Xu, X. Zhou, S.-M. Huang, B. Singh, B. Wang, I. Belopolski, J. Yin, S. Zhang, A. Bansil, H. Lin, and M. Z. Hasan, Phys. Rev. Lett. 119, 156401 (2017)

    2017

  6. [14]

    S.-Y. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, G. Chang, Z. Yuan, C.-C. 6 Lee, S.-M. Huang, H. Zheng, J. Ma, D. S. Sanchez, B. Wang, A. Bansil, F. Chou, P. P. Shibayev, H. Lin, S. Jia, and M. Z. Hasan, Science 349, 613 (2015)

    2015

  7. [15]

    Huang, S.-Y

    S.-M. Huang, S.-Y. Xu, I. Belopolski, C.-C. Lee, G. Chang, B. Wang, N. Alidoust, G. Bian, M. Neupane, C. Zhang, S. Jia, A. Bansil, H. Lin, and M. Z. Hasan, Nat. Commun. 6, 7373 (2015)

    2015

  8. [16]

    B. Q. Lv, H. M. Weng, B. B. Fu, X. P. Wang, H. Miao, J. Ma, P. Richard, X. C. Huang, L. X. Zhao, G. F. Chen, Z. Fang, X. Dai, T. Qian, and H. Ding, Phys. Rev. X 5, 031013 (2015)

    2015

  9. [17]

    S.-Y. Xu, N. Alidoust, I. Belopolski, Z. Yuan, G. Bian, T.-R. Chang, H. Zheng, V. N. Strocov, D. S. Sanchez, G. Chang, C. Zhang, D. Mou, Y. Wu, L. Huang, C.-C. Lee, S.-M. Huang, B. Wang, A. Bansil, H.-T. Jeng, T. Neu- pert, A. Kaminski, H. Lin, S. Jia, and M. Zahid Hasan, Nat....

    2015

  10. [18]

    C. Fang, M. J. Gilbert, X. Dai, and B. A. Bernevig, Phys. Rev. Lett. 108, 266802 (2012)

    2012

  11. [19]

    Singh, A

    B. Singh, A. Sharma, H. Lin, M. Z. Hasan, R. Prasad, and A. Bansil, Phys. Rev. B 86, 115208 (2012)

    2012

  12. [20]

    B. J. Wieder, Y. Kim, A. M. Rappe, and C. L. Kane, Phys. Rev. Lett. 116, 186402 (2016)

    2016

  13. [21]

    Bradlyn, J

    B. Bradlyn, J. Cano, Z. Wang, M. G. Vergniory, C. Felser, R. J. Cava, and B. A. Bernevig, Science353, 6299 (2016)

    2016

  14. [22]

    Chang, S.-Y

    G. Chang, S.-Y. Xu, B. J. Wieder, D. S. Sanchez, S.-M. Huang, I. Belopolski, T.-R. Chang, S. Zhang, A. Bansil, H. Lin, and M. Z. Hasan, Phys. Rev. Lett. 119, 206401 (2017)

    2017

  15. [23]

    P. Tang, Q. Zhou, and S.-C. Zhang, Phys. Rev. Lett. 119, 206402 (2017)

    2017

  16. [24]

    Di Sante, A

    D. Di Sante, A. Hausoel, P. Barone, J. M. Tomczak, G. Sangiovanni, and R. Thomale, Phys. Rev. B 96, 121106 (2017)

    2017

  17. [25]

    Z. Zhu, G. W. Winkler, Q. Wu, J. Li, and A. A. Soluyanov, Phys. Rev. X 6, 031003 (2016)

    2016

  18. [26]

    Chang, S.-Y

    G. Chang, S.-Y. Xu, S.-M. Huang, D. S. Sanchez, C.- H. Hsu, G. Bian, Z.-M. Yu, I. Belopolski, N. Alidoust, H. Zheng, T.-R. Chang, H.-T. Jeng, S. A. Yang, T. Neupert, H. Lin, and M. Z. Hasan, Sci. Rep. 7, 1688 (2017)

    2017

  19. [27]

    H. Weng, C. Fang, Z. Fang, and X. Dai, Phys. Rev. B 93, 241202 (2016)

    2016

  20. [28]

    H. Weng, C. Fang, Z. Fang, and X. Dai, Phys. Rev. B 94, 165201 (2016)

    2016

  21. [29]

    J. B. He, D. Chen, W. L. Zhu, S. Zhang, L. X. Zhao, Z. A. Ren, and G. F. Chen, Phys. Rev. B 95, 195165 (2017)

    2017

  22. [30]

    Xu and L.-M

    Y. Xu and L.-M. Duan, Phys. Rev. B 96, 155301 (2017)

    2017

  23. [31]

    J. Yu, B. Yan, and C.-X. Liu, Phys. Rev. B 95, 235158 (2017)

    2017

  24. [32]

    Xia and G

    Y. Xia and G. Li, Phys. Rev. B 96, 241204 (2017)

    2017

  25. [33]

    J. Wang, X. Sui, W. Shi, J. Pan, S. Zhang, F. Liu, S.- H. Wei, Q. Yan, and B. Huang, Phys. Rev. Lett. 119, 256402 (2017)

    2017

  26. [34]

    H. Yang, J. Yu, S. S. P. Parkin, C. Felser, C.-X. Liu, and B. Yan, Phys. Rev. Lett. 119, 136401 (2017)

    2017

  27. [35]

    W. Gao, X. Zhu, F. Zheng, M. Wu, J. Zhang, C. Xi, P. Zhang, Y. Zhang, N. Hao, W. Ning, and M. Tian, Nat. Commun. 9, 3249 (2018)

    2018

  28. [36]

    Huang, K.-H

    H. Huang, K.-H. Jin, and F. Liu, Phys. Rev. Lett. 120, 136403 (2018)

    2018

  29. [37]

    Kim, H.-S

    J. Kim, H.-S. Kim, and D. Vanderbilt, Phys. Rev. B 98, 155122 (2018)

    2018

  30. [38]

    Z.-G. Song, C. Felser, and Y. Sun, Phys. Rev. B 98, 165131 (2018)

    2018

  31. [39]

    R. C. Xiao, C. H. Cheung, P. L. Gong, W. J. Lu, J. G. Si, and Y. P. Sun, J. Phys. Condens. Matter 30, 245502 (2018)

    2018

  32. [40]

    J. Z. Ma, J. B. He, Y. F. Xu, B. Q. Lv, D. Chen, W. L. Zhu, S. Zhang, L. Y. Kong, X. Gao, L. Y. Rong, Y. B. Huang, P. Richard, C. Y. Xi, E. S. Choi, Y. Shao, Y. L. Wang, H. J. Gao, X. Dai, C. Fang, H. M. Weng, G. F. Chen, T. Qian, and H. Ding, Nat. Phys. 14, 349 (2018)

    2018

  33. [41]

    B. Q. Lv, Z. L. Feng, Q. N. Xu, X. Gao, J. Z. Ma, L. Y. Kong, P. Richard, Y. B. Huang, V. N. Strocov, C. Fang, H. M. Weng, Y. G. Shi, T. Qian, and H. Ding, Nature 546, 627 (2017)

    2017

  34. [42]

    Hohenberg and W

    P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964)

    1964

  35. [43]

    Kresse and D

    G. Kresse and D. Joubert, Phys. Rev. B 59, 1758 (1999)

    1999

  36. [44]

    Kresse and J

    G. Kresse and J. Furthm¨ uller, Phys. Rev. B 54, 11169 (1996)

    1996

  37. [45]

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

    1996

  38. [46]

    Marzari and D

    N. Marzari and D. Vanderbilt, Phys. Rev. B 56, 12847 (1997)

    1997

  39. [47]

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

    2018

  40. [48]

    Albrecht, 34, 1373 (1979)

    M. Albrecht, 34, 1373 (1979)

    1979

  41. [49]

    S.-Y. Xu, Y. Xia, L. A. Wray, S. Jia, F. Meier, J. H. Dil, J. Osterwalder, B. Slomski, A. Bansil, H. Lin, R. J. Cava, and M. Z. Hasan, Science 332, 560 (2011)

    2011

  42. [50]

    T. Sato, K. Segawa, K. Kosaka, S. Souma, K. Nakayama, K. Eto, T. Minami, Y. Ando, and T. Takahashi, Nat. Phys. 7, 840 (2011)

    2011

  43. [51]

    Bansil, Phys

    A. Bansil, Phys. Rev. B 20, 4025 (1979)

    1979

  44. [52]

    Bansil, Z

    A. Bansil, Z. Naturforsch. A 48, 165 (1993)

    1993

  45. [53]

    Bansil, Phys

    A. Bansil, Phys. Rev. B 20, 4035 (1979)

    1979

  46. [54]

    Bansil, S

    A. Bansil, S. Kaprzyk, P. E. Mijnarends, and J. Tobo la, Phys. Rev. B 60, 13396 (1999)

    1999

  47. [55]

    Bansil, R

    A. Bansil, R. S. Rao, P. E. Mijnarends, and L. Schwartz, Phys. Rev. B 23, 3608 (1981)

    1981

  48. [56]

    See Supplemental Material at http://link.aps.org/supplemental/ 10.1103/PhysRevMa- terials.3.071201 for further details

    doi

  49. [57]

    [25] and [26]

    Note that the mechanism for the emergence of TPs in BaAgAs0.5P0.5 is similar to that proposed in Refs. [25] and [26]

  50. [58]

    These features are distinct from those of other known semimetals and can lead, for example, to mag- netic tunneling/breakdown in quantum oscillations

    The TPs in BaAgAs 0.5P0.5 are connected by a doubly- degenerate nodal line in sharp contrast to the case of a non-symmorphic TPS [21], and support unique Fermi surfaces which essentially touch at the doubly-degenerate band. These features are distinct from those of other known...

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