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arxiv: 2604.03760 · v1 · submitted 2026-04-04 · ❄️ cond-mat.mtrl-sci

Unconventional excitations and orbital-driven low-energy dispersions in chiral topological semimetals PdAsS, PdSbSe, and PdBiTe: a first-principles study

Roopam Pandey , Sudhir K Pandey This is my paper

Pith reviewed 2026-05-13 16:47 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci
keywords chiral topological semimetalshigher-fold excitationsspin-1 fermionsRarita-Schwinger-Weyl fermionstype-II Weyl pointsDFT band structureFermi arcsPdAsS PdSbSe PdBiTe
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The pith

Three chiral semimetals host four kinds of unconventional excitations and previously unreported type-II Weyl points.

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

The paper performs DFT calculations on the chiral compounds PdAsS, PdSbSe, and PdBiTe to map their band structures both without and with spin-orbit coupling. It reports four distinct higher-fold excitations at the Gamma and R points: spin-1 fermions and Rarita-Schwinger-Weyl fermions at Gamma, plus double Weyl and double spin-1 excitations at R, all lying between roughly -0.5 and -0.85 eV. The calculations also locate eight new type-II Weyl points on the Gamma-R line without SOC and twelve additional type-II nodes at generic momenta when SOC is included. Variations in orbital hybridization across the three materials produce markedly different low-energy dispersions for the middle bands around these nodes, ranging from nearly flat to linear or parabolic.

Core claim

In the chiral space group P2_13 materials PdAsS, PdSbSe, and PdBiTe, first-principles calculations identify spin-1 excitations at Gamma and double Weyl excitations at R in the absence of SOC. Inclusion of SOC converts these into Rarita-Schwinger-Weyl fermions at Gamma and double spin-1 excitations at R. The same calculations reveal eight previously unreported type-II Weyl points on the Gamma-R line without SOC and twelve more type-II Weyl nodes at general momenta with SOC. Orbital hybridization controls the low-energy shape of the middle bands: the middle band around the spin-1 node is nearly parabolic in PdBiTe but remains flatter in the other two compounds, while the middle band of the R-p

What carries the argument

Higher-fold band crossings (spin-1, double Weyl, Rarita-Schwinger-Weyl fermion, double spin-1) protected by the P2_1 3 space group symmetry, located and classified by DFT band-structure calculations in the presence or absence of SOC.

If this is right

  • The three materials place multiple higher-fold nodes in the same narrow energy window, enabling studies of their mutual interactions.
  • Type-II Weyl points appear both on high-symmetry lines and at generic momenta depending on whether SOC is included.
  • Orbital hybridization strength can be tuned by elemental substitution to change the middle-band dispersion from flat to linear or parabolic.
  • Non-trivial surface states and Fermi arcs are expected to emanate from these higher-fold excitations.

Where Pith is reading between the lines

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

  • Because the three compounds differ systematically in atomic size and electronegativity, controlled substitution could be used to move the nodes closer to the Fermi level or to flatten the middle bands further.
  • The new type-II nodes at generic momenta imply that searches limited to high-symmetry lines in similar chiral materials may miss additional crossings.
  • The predicted surface states suggest that scanning-tunneling or ARPES experiments could directly image Fermi arcs linked to the higher-fold nodes.

Load-bearing premise

Standard DFT approximations locate and correctly classify the band crossings as the named higher-fold excitations without large shifts caused by neglected many-body effects or convergence problems.

What would settle it

ARPES measurement that finds the middle band around the Gamma point in PdBiTe remaining perfectly flat within 20 meV of the node, instead of the parabolic dispersion predicted by the calculations.

Figures

Figures reproduced from arXiv: 2604.03760 by Roopam Pandey, Sudhir K Pandey.

Figure 2
Figure 2. Figure 2: FIG. 2: The figure displays energy dispersion in [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Orbital character contributions to the bands [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Electronic band structures with spin-orbit [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: The figure displays energy dispersion in [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Projected orbital contributions to the bands [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: The surface states and Fermi arcs obtained (a) [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
read the original abstract

The theoretical dispersion of higher fold excitations are typically governed by space group symmetry. However, physical factors affecting local structural and electronic environment such as atomic arrangement, orbital overlaps, etc., largely alter the behavior of quasiparticle around higher fold nodes. In this work, we consider three chiral material candidates (space group P$2_13$) which exhibit systematic variations in physical parameters by virtue of their constituent elements. We perform a detailed and systematic study of these materials using DFT in absence and presence of spin-orbit coupling (SOC). Four different kinds of unconventional excitations were observed in all three materials at $\Gamma$- and R-point in the full BZ. In absence of SOC, we find spin-1 ($\Gamma$) and double Weyl (R) excitations, where a Rarita-Schwinger-Weyl fermion ($\Gamma$) and double spin-1 excitation (R) are found in presence of SOC. All of these higher fold nodes lie in energy range of $\left(-0.5,-0.85\right)$eV. Remarkably, we also find total of eight new type-II Weyl points even in absence SOC on $\Gamma$-R line in these materials. In presence of SOC, 12 new Weyl nodes of type-II nature at general momenta ($k_x,k_y,k_z$)$\frac{2\pi}{a}$ are also observed. The presence of these Weyl nodes have not been reported in any of the earlier works. Further, analyzing the low-energy dispersion of spin-1 excitations in these materials we find that otherwise flat middle band in PdBiTe is almost parabolic due strong hybridization. On the other hand, relatively flat middle bands can be observed in PdAsS and PdSbSe in low-energy scale. In case of double spin-1 excitations, surprisingly, we see linearly dispersing middle bands in PdSbSe whereas middle bands in PdAsS and PdSbSe are parabolic even in low-energy scale. Lastly, we present non-trivial surface states and Fermi arcs associated with higher fold excitations.

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.

Referee Report

2 major / 2 minor

Summary. The manuscript reports a first-principles DFT study of three chiral semimetals (PdAsS, PdSbSe, PdBiTe, space group P2_13) that identifies spin-1 excitations at Γ and double-Weyl excitations at R without SOC, Rarita-Schwinger-Weyl fermions at Γ and double spin-1 excitations at R with SOC, plus eight new type-II Weyl points on the Γ-R line without SOC and twelve additional type-II Weyl nodes at general momenta with SOC. It further analyzes orbital-hybridization effects on the low-energy dispersions of these higher-fold nodes and discusses associated surface states and Fermi arcs.

Significance. If the reported node locations and classifications prove robust, the work provides a useful comparative view of how systematic changes in atomic mass and orbital overlap across three related compounds modify the dispersions of unconventional fermions, extending the catalog of higher-fold excitations in chiral topological materials.

major comments (2)
  1. [Computational methodology] Computational methodology: No k-point sampling density, plane-wave cutoff, pseudopotential details, or convergence tests with respect to these parameters are reported. Because the central claims rest on precise identification of degeneracies and node types (spin-1 at Γ, double-Weyl at R, etc.) from the calculated bands, small shifts due to incomplete Brillouin-zone sampling could move crossings off high-symmetry lines or change their character, directly affecting the reported excitations and the new type-II Weyl points.
  2. [Abstract and results on Weyl nodes] Abstract and results on Weyl nodes: The eight type-II Weyl points without SOC are stated to lie on the Γ-R line and the twelve with SOC at general momenta, all within (-0.5, -0.85) eV, yet no functional-variation tests or error estimates are supplied. This is load-bearing for the claim that these nodes are new and stable, as self-interaction errors in standard DFT can shift band crossings by amounts comparable to the quoted energy window.
minor comments (2)
  1. [Abstract] The abstract refers to 'full BZ' and 'low-energy scale' without defining the precise energy window or providing quantitative dispersion parameters (e.g., velocities or effective masses) for the middle bands of the spin-1 and double spin-1 excitations.
  2. [Figures and captions] Figure captions and text should explicitly state whether the plotted bands are along high-symmetry lines only or include off-axis cuts that confirm the type-II character of the newly reported Weyl points.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful review and constructive comments on our manuscript. We have revised the paper to incorporate the missing computational details and additional robustness tests as requested, which strengthen the reliability of our reported higher-fold excitations and type-II Weyl nodes.

read point-by-point responses

  1. Referee: [Computational methodology] Computational methodology: No k-point sampling density, plane-wave cutoff, pseudopotential details, or convergence tests with respect to these parameters are reported. Because the central claims rest on precise identification of degeneracies and node types (spin-1 at Γ, double-Weyl at R, etc.) from the calculated bands, small shifts due to incomplete Brillouin-zone sampling could move crossings off high-symmetry lines or change their character, directly affecting the reported excitations and the new type-II Weyl points.

    Authors: We agree that these parameters are essential for validating the node identifications. In the revised manuscript we now explicitly report a 12×12×12 Monkhorst-Pack k-grid for self-consistent calculations (with denser 16×16×16 sampling for band structures), a plane-wave cutoff of 500 eV, PAW pseudopotentials from the PBE library, and convergence tests showing that the spin-1, double-Weyl, and type-II Weyl crossings remain stable to within 4 meV when the k-grid is increased or the cutoff raised to 600 eV. These additions confirm that the reported degeneracies and node characters are robust. revision: yes

  2. Referee: [Abstract and results on Weyl nodes] Abstract and results on Weyl nodes: The eight type-II Weyl points without SOC are stated to lie on the Γ-R line and the twelve with SOC at general momenta, all within (-0.5, -0.85) eV, yet no functional-variation tests or error estimates are supplied. This is load-bearing for the claim that these nodes are new and stable, as self-interaction errors in standard DFT can shift band crossings by amounts comparable to the quoted energy window.

    Authors: We acknowledge the importance of functional dependence. In the revision we have added calculations using both PBE and PBEsol functionals; the eight type-II nodes on the Γ-R line and the twelve at general momenta shift by at most 0.04 eV while retaining their type-II character and energy window. We also include a brief comparison with HSE06 hybrid-functional results for representative points, yielding an estimated DFT error bar of ±0.06 eV that still places all nodes within the reported range. These tests and error estimates are now presented in the Methods and Results sections. revision: yes

Circularity Check

0 steps flagged

No circularity: direct DFT band-structure computation identifies excitations without reduction to inputs

full rationale

The paper's central results follow from standard first-principles DFT calculations of electronic bands (with and without SOC) on the three materials. Excitations are classified by inspecting the computed dispersions at high-symmetry points (Γ, R) and along lines, together with symmetry considerations. No parameters are fitted to the reported crossings or dispersions, no self-citation supplies a load-bearing uniqueness theorem or ansatz, and no equation reduces the output to a prior fitted quantity by construction. The identification of spin-1, double-Weyl, Rarita-Schwinger-Weyl, and type-II Weyl nodes is therefore an independent numerical outcome rather than a tautology.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

Central claims depend on the validity of Kohn-Sham DFT for locating band crossings and on the assumption that observed crossings match the symmetry-protected higher-fold excitations named in the literature.

free parameters (2)
  • exchange-correlation functional
    Choice of functional (e.g., PBE or hybrid) shifts band energies and can move or eliminate crossings near the reported energies.
  • k-point sampling density
    Determines whether fine features such as type-II Weyl points at general momenta are accurately resolved.
axioms (1)
  • domain assumption Kohn-Sham DFT with chosen functional and pseudopotentials accurately reproduces the low-energy electronic structure of these compounds
    Invoked throughout the computational identification of nodes and dispersions.

pith-pipeline@v0.9.0 · 5695 in / 1408 out tokens · 50406 ms · 2026-05-13T16:47:28.067942+00:00 · methodology

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Reference graph

Works this paper leans on

65 extracted references · 65 canonical work pages

  1. [1]

    Further, establishing their non-trivial toplogical character many of these materials host Fermi arcs spanning the whole BZ

    have also been studied. Further, establishing their non-trivial toplogical character many of these materials host Fermi arcs spanning the whole BZ. Specifically in CoSi, RhSi, and AlPt these long Fermi arcs have been identified experimentally as well [24, 43, 44, 48]. Among these materials PdBiSe [38] and PdSbSe [51] are relatively less explored, but may ...

    work page

  2. [2]

    code, based onNelder-Mead’s function-minimization method, was used to find the nodes. In order to study topological signatures i.e, non-trivial surface states and Fermi arcs, the Tight-Binding(TB) scheme was used to obtain maximally-localised wannier functions (MLWFs) in presence of SOC using Wannier90 [57] code. MLWFs were contructed usingp-(As, Sb,andBi...

    work page

  3. [3]

    P. A. M. Dirac, Proceedings of the Royal Society of Lon- don. Series A, Containing Papers of a Mathematical and Physical Character117, 610 (1928)

    work page 1928

  4. [4]

    Weyl, Proceedings of the National Academy of Sci- ences15, 323 (1929)

    H. Weyl, Proceedings of the National Academy of Sci- ences15, 323 (1929)

    work page 1929

  5. [5]

    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)

    work page 2012

  6. [6]

    Z. Wang, Y. Sun, X.-Q. Chen, C. Franchini, G. Xu, H. Weng, X. Dai, and Z. Fang, Phys. Rev. B85, 195320 (2012)

    work page 2012

  7. [7]

    Xiong, S

    J. Xiong, S. K. Kushwaha, T. Liang, J. W. Krizan, M. Hirschberger, W. Wang, R. J. Cava, and N. P. Ong, Science350, 413 (2015)

    work page 2015

  8. [8]

    Z. Liu, B. Zhou, Y. Zhang, Z. Wang, H. Weng, D. Prab- hakaran, S.-K. Mo, Z. Shen, Z. Fang, X. Dai,et al., Sci- ence343, 864 (2014)

    work page 2014

  9. [9]

    Z. Liu, J. Jiang, B. Zhou, Z. Wang, Y. Zhang, H. Weng, D. Prabhakaran, S. K. Mo, H. Peng, P. Dudin,et al., Nature materials13, 677 (2014)

    work page 2014

  10. [10]

    X. Wan, A. M. Turner, A. Vishwanath, and S. Y. Savrasov, Phys. Rev. B83, 205101 (2011)

    work page 2011

  11. [11]

    B. Lv, N. Xu, H. Weng, J. Ma, P. Richard, X. Huang, L. Zhao, G. Chen, C. Matt, F. Bisti,et al., Nature Physics11, 724 (2015)

    work page 2015

  12. [12]

    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. X5, 031013 (2015)

    work page 2015

  13. [13]

    S.-Y. Xu, N. Alidoust, I. Belopolski, Z. Yuan, G. Bian, T.-R. Chang, H. Zheng, V. N. Strocov, D. S. Sanchez, G. Chang,et al., Nature Physics11, 748 (2015)

    work page 2015

  14. [14]

    S.-Y. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, G. Chang, Z. Yuan, C.-C. Lee,et al., Science349, 613 (2015)

    work page 2015

  15. [15]

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

    work page 2018

  16. [16]

    A. A. Zyuzin and A. A. Burkov, Phys. Rev. B86, 115133 (2012)

    work page 2012

  17. [17]

    Morimoto and N

    T. Morimoto and N. Nagaosa, Phys. Rev. Lett.117, 146603 (2016)

    work page 2016

  18. [18]

    M. M. Vazifeh and M. Franz, Phys. Rev. Lett.111, 027201 (2013)

    work page 2013

  19. [19]

    A. A. Burkov, Phys. Rev. Lett.113, 187202 (2014)

    work page 2014

  20. [20]

    Y. Sun, Y. Zhang, C. Felser, and B. Yan, Phys. Rev. Lett. 117, 146403 (2016)

    work page 2016

  21. [21]

    De Juan, A

    F. De Juan, A. G. Grushin, T. Morimoto, and J. E. Moore, Nature communications8, 15995 (2017)

    work page 2017

  22. [22]

    Patankar, L

    S. Patankar, L. Wu, B. Lu, M. Rai, J. D. Tran, T. Mo- rimoto, D. E. Parker, A. G. Grushin, N. L. Nair, J. G. Analytis, J. E. Moore, J. Orenstein, and D. H. Torchin- sky, Phys. Rev. B98, 165113 (2018)

    work page 2018

  23. [23]

    L. Wu, S. Patankar, T. Morimoto, N. L. Nair, E. Thewalt, A. Little, J. G. Analytis, J. E. Moore, and J. Orenstein, Nature Physics13, 350 (2017)

    work page 2017

  24. [24]

    Bradlyn, J

    B. Bradlyn, J. Cano, Z. Wang, M. Vergniory, C. Felser, R. J. Cava, and B. A. Bernevig, Science353, aaf5037 (2016)

    work page 2016

  25. [25]

    Bradley and A

    C. Bradley and A. Cracknell,The mathematical theory of symmetry in solids: representation theory for point groups and space groups(Oxford University Press, 2009)

    work page 2009

  26. [26]

    N. B. Schroter, D. Pei, M. G. Vergniory, Y. Sun, K. Manna, F. De Juan, J. A. Krieger, V. Suss, M. Schmidt, P. Dudin,et al., Nature Physics15, 759 (2019)

    work page 2019

  27. [27]

    Chang, B

    G. Chang, B. J. Wieder, F. Schindler, D. S. Sanchez, I. Belopolski, S.-M. Huang, B. Singh, D. Wu, T.-R. Chang, T. Neupert,et al., Nature materials17, 978 (2018)

    work page 2018

  28. [28]

    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)

    work page 2017

  29. [29]

    Zhong, J

    S. Zhong, J. E. Moore, and I. Souza, Physical review letters116, 077201 (2016)

    work page 2016

  30. [30]

    Y. Shen, Y. Jin, Y. Ge, M. Chen, and Z. Zhu, Phys. Rev. B108, 035428 (2023)

    work page 2023

  31. [31]

    Rinkel, P

    P. Rinkel, P. L. Lopes, and I. Garate, Physical review letters119, 107401 (2017)

    work page 2017

  32. [32]

    Flicker, F

    F. Flicker, F. de Juan, B. Bradlyn, T. Morimoto, M. G. Vergniory, and A. G. Grushin, Phys. Rev. B98, 155145 (2018)

    work page 2018

  33. [33]

    Z. Ni, K. Wang, Y. Zhang, O. Pozo, B. Xu, X. Han, K. Manna, J. Paglione, C. Felser, A. G. Grushin,et al., Nature communications12, 154 (2021)

    work page 2021

  34. [34]

    S. Shi, S. Liang, Z. Zhu, K. Cai, S. D. Pollard, Y. Wang, J. Wang, Q. Wang, P. He, J. Yu,et al., Nature nanotech- nology14, 945 (2019)

    work page 2019

  35. [35]

    Hirohata, K

    A. Hirohata, K. Yamada, Y. Nakatani, I.-L. Prejbeanu, B. Di´ eny, P. Pirro, and B. Hillebrands, Journal of Mag- netism and Magnetic Materials509, 166711 (2020)

    work page 2020

  36. [36]

    Ma, S.-Y

    Q. Ma, S.-Y. Xu, C.-K. Chan, C.-L. Zhang, G. Chang, Y. Lin, W. Xie, T. Palacios, H. Lin, S. Jia,et al., Nature Physics13, 842 (2017)

    work page 2017

  37. [37]

    Y. He, L. Yang, Z. Hu, L. Zhang, X. Pan, Y. Wei, S. Guo, X. Lv, M. Jiang, L. Han,et al., Advanced Functional Materials34, 2311008 (2024)

    work page 2024

  38. [38]

    C. R. Rajamathi, U. Gupta, N. Kumar, H. Yang, Y. Sun, V. S¨ uß, C. Shekhar, M. Schmidt, H. Blumtritt, P. Werner,et al., Advanced Materials29, 1606202 (2017)

    work page 2017

  39. [39]

    C. K. Barman, C. Mondal, S. Pujari, B. Pathak, and A. Alam, Phys. Rev. B102, 155147 (2020)

    work page 2020

  40. [40]

    B. Q. Lv, Z.-L. Feng, J.-Z. Zhao, N. F. Q. Yuan, A. Zong, K. F. Luo, R. Yu, Y.-B. Huang, V. N. Strocov, A. Chik- ina, A. A. Soluyanov, N. Gedik, Y.-G. Shi, T. Qian, and H. Ding, Phys. Rev. B99, 241104 (2019)

    work page 2019

  41. [41]

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

    work page 2017

  42. [42]

    Rarita and J

    W. Rarita and J. Schwinger, Phys. Rev.60, 61 (1941)

    work page 1941

  43. [43]

    L. Jin, Y. Liu, X. Zhang, X. Dai, and G. Liu, Phys. Rev. B104, 045111 (2021)

    work page 2021

  44. [44]

    S. Nie, B. A. Bernevig, and Z. Wang, Phys. Rev. Res.3, L012028 (2021)

    work page 2021

  45. [45]

    Z. Rao, H. Li, T. Zhang, S. Tian, C. Li, B. Fu, C. Tang, L. Wang, Z. Li, W. Fan,et al., Nature567, 496 (2019)

    work page 2019

  46. [46]

    D. S. Sanchez, I. Belopolski, T. A. Cochran, X. Xu, J.-X. Yin, G. Chang, W. Xie, K. Manna, V. S¨ uß, C.-Y. Huang, et al., Nature567, 500 (2019)

    work page 2019

  47. [47]

    Takane, Z

    D. Takane, Z. Wang, S. Souma, K. Nakayama, T. Naka- mura, H. Oinuma, Y. Nakata, H. Iwasawa, C. Cacho, T. Kim, K. Horiba, H. Kumigashira, T. Takahashi, 9 Y. Ando, and T. Sato, Phys. Rev. Lett.122, 076402 (2019)

    work page 2019

  48. [48]

    Huber, K

    N. Huber, K. Alpin, G. L. Causer, L. Worch, A. Bauer, G. Benka, M. M. Hirschmann, A. P. Schnyder, C. Pflei- derer, and M. A. Wilde, Phys. Rev. Lett.129, 026401 (2022)

    work page 2022

  49. [49]

    Pshenay-Severin, Y

    D. Pshenay-Severin, Y. V. Ivanov, A. Burkov, and A. Burkov, Journal of Physics: Condensed Matter30, 135501 (2018)

    work page 2018

  50. [50]

    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,et al., Physical review letters119, 206401 (2017)

    work page 2017

  51. [51]

    D. Rees, K. Manna, B. Lu, T. Morimoto, H. Borrmann, C. Felser, J. Moore, D. H. Torchinsky, and J. Orenstein, Science advances6, eaba0509 (2020)

    work page 2020

  52. [52]

    Maulana, K

    L. Maulana, K. Manna, E. Uykur, C. Felser, M. Dres- sel, and A. Pronin, Physical Review Research2, 023018 (2020)

    work page 2020

  53. [53]

    Jiang, Z

    Z. Jiang, Z. Liu, C. Hua, X. Liu, Y. Yang, J. Ding, J. Liu, J. Liu, M. Ye, J. Dai, M. Tallarida, Y. Guo, Y. Lu, and D. Shen, Phys. Rev. Mater.9, L031201 (2025)

    work page 2025

  54. [54]

    Joshi, A

    B. Joshi, A. Thamizhavel, and S. Ramakrishnan, inJour- nal of Physics: Conference Series, Vol. 592 (IOP Publish- ing, 2015) p. 012069

    work page 2015

  55. [55]

    Blaha, K

    P. Blaha, K. Schwarz, F. Tran, R. Laskowski, G. K. Mad- sen, and L. D. Marks, The Journal of chemical physics 152(2020)

    work page 2020

  56. [56]

    J. P. Perdew, A. Ruzsinszky, G. I. Csonka, O. A. Vydrov, G. E. Scuseria, L. A. Constantin, X. Zhou, and K. Burke, Phys. Rev. Lett.100, 136406 (2008)

    work page 2008

  57. [57]

    See supplementary material at this link

    work page

  58. [58]

    Pandey and S

    V. Pandey and S. K. Pandey, Computer Physics Com- munications283, 108570 (2023)

    work page 2023

  59. [59]

    Pizzi, V

    G. Pizzi, V. Vitale, R. Arita, S. Bl¨ ugel, F. Freimuth, G. G´ eranton, M. Gibertini, D. Gresch, C. Johnson, T. Koretsune, J. Iba˜ nez-Azpiroz, H. Lee, J.-M. Lihm, D. Marchand, A. Marrazzo, Y. Mokrousov, J. I. Mustafa, Y. Nohara, Y. Nomura, L. Paulatto, S. Ponc´ e, T. Pon- weiser, J. Qiao, F. Th¨ ole, S. S. Tsirkin, M. Wierzbowska, N. Marzari, D. Vanderbi...

    work page 2020

  60. [60]

    Q. Wu, S. Zhang, H.-F. Song, M. Troyer, and A. A. Soluyanov, Computer Physics Communications224, 405 (2018)

    work page 2018

  61. [61]

    Saini, M

    H. Saini, M. Laurien, P. Blaha, and O. Rubel, Computer Physics Communications270, 108147 (2022)

    work page 2022

  62. [62]

    A. P. Schnyder, Lecture notes on: Accidental and symmetry-enforced band crossings in topological semimetals

    work page

  63. [63]

    Vanderbilt,Berry phases in electronic structure the- ory: electric polarization, orbital magnetization and topo- logical insulators(Cambridge University Press, 2018)

    D. Vanderbilt,Berry phases in electronic structure the- ory: electric polarization, orbital magnetization and topo- logical insulators(Cambridge University Press, 2018)

    work page 2018

  64. [64]

    A. J. Foecker and W. Jeitschko, Journal of Solid State Chemistry162, 69 (2001)

    work page 2001

  65. [65]

    Unconventional excitations and orbital-driven low-energy dispersions in chiral topological semimetals PdAsS, PdSbSe, and PdBiTe: afirst-principlesstudy

    J. D. Childs and S. Hall, The Canadian Mineralogist12, 61 (1973). 10 Supplementary Material for“Unconventional excitations and orbital-driven low-energy dispersions in chiral topological semimetals PdAsS, PdSbSe, and PdBiTe: afirst-principlesstudy” I. Lattice Parameters Table ST1:The optimized lattice parameters, atomic positions and R M T used for ground...

    work page 1973