Pith. sign in

REVIEW 4 major objections 4 minor 46 references

Pressure induced electronic structure transformation of topological semimetal

T0 review · 4 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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

Pith's one-line read The paper argues that hexagonal YH3 is a pseudo nodal surface semimetal in class BDI at zero pressure and that pressure above 31 GPa turns it into a trivial insulator.

desk verdict A plausible spinless story about pressure-driven trivialization in YH3, but the SOC neglect for a 4d element leaves the central claim unverified. read the letter →

arxiv 1908.06494 v2 pith:GARQ257F submitted 2019-08-18 cond-mat.mtrl-sci cond-mat.str-el

Feihu Liu , Lina Wu This is my paper · ORCID
classification cond-mat.mtrl-scicond-mat.str-el
keywords topologicalsemimetalnodalsurfaceringyttriumtrihydrideYH3AZ+Iclassificationpressure-inducedtransitionfirst-principlescalculation
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

The paper argues that the band crossings near the Fermi level in hexagonal YH3 are caused by the overlap of an electron-like and a hole-like band, and that their protection comes mainly from non-spatial symmetries rather than crystalline symmetries. Because time reversal, inversion, and an approximate particle-hole symmetry are present, the crossings can be viewed as a pseudo nodal surface in class BDI of the AZ+I classification of gapless topological matter. The word “pseudo” matters: away from a closed nodal line a small gap of about 0.005 eV opens, so the strictly protected object is a nodal ring in class AI. The paper then claims that hydrostatic pressure gradually breaks the particle-hole symmetry, shrinks the nodal ring, and at about 31 GPa collapses it to a point; above 31 GPa all crossings are gapped and YH3 becomes a trivial insulator. If correct, this gives a concrete material in which a pressure-driven electronic topology transition can be followed step by step in first-principles band structure.

What carries the argument

The load-bearing object is the effective two-band Hamiltonian $H(k)=f(k)\sigma_z+g(k)\sigma_x$ with symmetry operators $T=K$, $P=\sigma_z K$, and $C=\sigma_z$. When $f(k)=0$, particle-hole symmetry is exact and the nodes form the surface $g(k)=0$, which belongs to class BDI; the small term $f(k)$ breaks particle-hole symmetry and leaves only the nodal ring satisfying $f(k)=0$ and $g(k)=0$, which belongs to class AI. The paper locates this ring numerically by searching for k-points where the lowest unoccupied conduction band and the highest occupied valence band agree to within 0.005 eV, and it tracks the ring radius as a function of pressure.

What would settle it

A relativistic density-functional band calculation of $P\bar{3}c1$ YH3, including spin-orbit coupling, at ambient pressure and at 28–32 GPa, resolving energies around the nodal ring; if the ring acquires a gap at any pressure below 31 GPa, the claimed pressure-driven trivialization fails, whereas survival of the ring would support the pseudo nodal surface picture.

Watch

Extended reading notes

Core claim

The core claim is that at zero pressure YH3 hosts accidental band crossings, not symmetry-enforced crystalline degeneracies: a lowest unoccupied conduction band and a highest occupied valence band overlap and mirror each other approximately across the Fermi level. With the approximate particle-hole symmetry taken as exact, the crossings form a nodal surface belonging to class BDI; once the small symmetry-breaking term is included, the protected object is a closed nodal ring belonging to class AI with a $Z_2$ Berry phase. The paper traces this ring under hydrostatic pressure and finds that it shrinks continuously from 28 GPa to 31 GPa, becomes a point at about 31 GPa, and is fully gapped above 32 GPa. Because the gapping happens smoothly without a sudden level crossing, the paper concludes that the nodal ring carries a trivial $Z_2$ invariant, so the pressure evolution is a topological phase transformation from a semimetal to a trivial insulator.

Load-bearing premise

The classification assumes spin-orbit coupling is negligible because yttrium and hydrogen are light elements, but yttrium is a 4d transition metal; if spin-orbit coupling gaps the nodes, the BDI/AI classification and the pressure-driven trivialization would not hold as described.

Editorial extensions

If this is right

  • If the claim is correct, YH3 provides a realistic material realization of a gapless phase from the AZ+I classification, with a pressure knob that tunes it toward a trivial insulator.
  • The continuous shrinkage and disappearance of the nodal ring without a sudden level crossing establishes that the ring's $Z_2$ Berry phase is 0, meaning this nodal ring is not topologically protected.
  • The predicted electronic transition near 31 GPa is distinct from the reported structural phase transition near 21 GPa, so the two transitions can be separated and studied independently.
  • Above about 32 GPa YH3 should behave as a fully gapped trivial insulator, a statement that can be checked by pressure-dependent transport or optical measurements.

Reading between the lines

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

  • The paper leaves spin-orbit coupling untested; a relativistic calculation would reveal whether the 0.005 eV-scale crossings and the nodal ring survive, and this is the most direct check of the classification.
  • A similar electron-hole overlap mechanism might occur in other rare-earth hydrides, so the strategy of looking for bands mirrored around the Fermi level could identify additional BDI/AI nodal materials.
  • Because the particle-hole symmetry is only approximate, the robust experimental prediction is the class-AI nodal ring rather than the class-BDI surface; measurements should target the ring itself.
  • One could test the pressure evolution experimentally by measuring quantum oscillations or the Berry phase of the occupied bands around the ring as pressure crosses 31 GPa.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. The manuscript reports a first-principles study of hexagonal P-3c1 YH3 under hydrostatic pressure. Using PBE DFT with Wannier interpolation, the authors identify two bands near the Fermi level whose crossings form, within a 5 meV tolerance, a 'pseudo nodal surface' around the Γ point. They assign the zero-pressure crossings to class BDI of the AZ+I classification of Bzdusek and Sigrist, based on an approximate particle-hole symmetry; under pressure, they argue that this symmetry is gradually broken, leaving an AI nodal ring that shrinks and closes at about 31 GPa, after which YH3 becomes a trivial insulator. The paper presents no fitted parameters, uses standard computational tools, and gives a concrete pressure-evolution scenario.

Significance. If substantiated, the paper would add YH3 to the short list of concrete material realizations of the centrosymmetric AZ+I classification and would provide a pressure-driven route from a nodal-surface-like semimetal to a trivial insulator. The DFT setup is standard, the symmetry analysis with Bilbao irreps is detailed, and the WannierTools-based node search is reproducible in principle. The paper also makes a falsifiable prediction: the nodal ring annihilates near 31 GPa. However, the central classification is currently conditional on three load-bearing approximations: spin-orbit coupling is neglected without quantitative justification, the particle-hole symmetry is identified from the very band structure it is used to classify, and the claimed trivial Z2 charge is inferred rather than computed. These are testable and fixable, but they need to be addressed before the central claims can be accepted.

major comments (4)
  1. [Introduction, Eq. (5), Fig. 1d] The entire AZ+I classification is carried out in the spinless realization, with T=K and T^2=1 in Eq. (5), justified by the statement that 'both Y and H are light elements.' This justification is inaccurate for yttrium (Z=39, a 4d transition metal), and the pseudo nodal surface is defined with an energy tolerance E_error=0.005 eV in Fig. 1d, which is an order of magnitude smaller than typical 4d spin-orbit splittings (tens of meV). If spin-orbit coupling opens a gap of that size on the purported nodal surface or nodal ring, the BDI/AI assignment and the pressure-driven trivialization would not apply as described. The manuscript contains no SOC-included calculation. Please provide band structures with SOC at the relevant pressures (0, 28, 31, and 32 GPa) and report the gap on the purported nodal ring, or otherwise quantitatively demonstrate that SOC effects are below the 0.005 eV tolerance used to define the nodes.
  2. [pp. 8-9, Eqs. (3)-(6)] The existence of particle-hole symmetry P is inferred from the approximate mirror symmetry of the two bands about the Fermi level and is then used to assign the BDI class. This is partly circular, and no operator P is constructed or tested in the DFT/Wannier basis. Because P is only approximate, the exact band crossings are nodal lines rather than a true nodal surface, so the 'class BDI' label is a heuristic classification of near-degeneracies, not a symmetry-protected topological statement. Please quantify the P-breaking, for example by giving the norm of the anticommutator {P,H} or the maximal deviation of the two-band spectrum from particle-hole symmetry over the Brillouin zone, specify the action of P on the basis states used for the Wannier interpolation, and show how this measure evolves from 0 to 32 GPa. Without this, the zero-pressure 'class BDI' claim is not established at the quantitative level needed for the paper's title claim.
  3. [p. 10, paragraph beginning 'To figure out whether...'] The paper concludes that the nodal ring is topologically trivial and that the Berry phase for all occupied bands is quantized to 0, based solely on the observation that the ring shrinks continuously and gaps out without sudden changes. A continuous annihilation is not a proof of zero Berry phase; a nontrivial ring could also disappear through pair annihilation with another ring or through gap-closing events elsewhere in the Brillouin zone. Please compute the Berry phase, or the Z2 invariant of Ref. 13, on a loop enclosing the nodal ring at several pressures, or provide an independent symmetry-based argument. This is load-bearing for the claimed 'topological phase transformation' and for the statement that YH3 becomes a trivial insulator.
  4. [Abstract and Fig. 2] All pressure-dependent calculations are performed in the P-3c1 structure up to 32 GPa, although the cited Ref. 21 places a structural transition to a cubic phase at 21 GPa. The claims for 28-32 GPa therefore describe a metastable or hypothetical phase rather than the ground-state material. Please either demonstrate that P-3c1 remains (meta)stable in this pressure range, or restrict the central claims to pressures below 21 GPa, or extend the calculation to the high-pressure phase. The abstract's 'above 31 GPa' statement needs to be qualified accordingly.
minor comments (4)
  1. [Throughout] The manuscript contains numerous typos and grammatical errors, including 'A lots of progress', 'can be understand', 'classification sheme', 'oftenly', the corrupted character sequence 'BerryâAZs', and 'zhe AZ+I'. A thorough language edit is needed.
  2. [Fig. 1d] The definition of nodes by E_LUCB - E_HOVB < 0.005 eV should be accompanied by a convergence check of the Wannier interpolation at this energy scale, since 5 meV is close to typical interpolation errors. Please report the interpolation accuracy and how the node count in Fig. 1d depends on the tolerance near this value.
  3. [Introduction, Refs. 22-23] The relationship between the non-spatial-symmetry protection proposed here and the crystalline-symmetry protection proposed in Refs. 22 and 23 is asserted but not developed. Since those papers attribute the same or similar crossings to glide-plane or mirror symmetries, the manuscript should explicitly state whether the non-spatial protection is compatible with, or an alternative to, the crystalline-symmetry protection, and how the two descriptions can be distinguished in the band structure.
  4. [Eq. (6)] The two-band Hamiltonian in Eq. (6) omits a σy term. The text should state explicitly that this follows from the spinless time-reversal and inversion symmetries, which make the Hamiltonian real in the chosen basis, so that the reader can follow the symmetry constraints without additional derivation.

Circularity Check

1 steps flagged · score 2.0 of 10

No significant circularity: central DFT pressure evolution is self-contained; only the BDI label partly restates the observed approximate mirror symmetry.

  1. self definitional [Section on non-spatial symmetries, near Eq. (5)-(6), paragraph beginning 'For a system with particle-hole symmetry']
    "For a system with particle-hole symmetry, the band structure will have a recognizable feature: the spectrum must be symmetric around the Fermi level. Indeed, for every state ψ with energy E, there will be a particle-hole symmetric state Pψ with energy −E. As one can see, the two bands are approximately mirrored by the fermi level. This is not an accident, but rather a signature of approximate particle-hole symmetry."

    The approximate particle-hole symmetry used to assign class BDI is inferred from the same LUCB/HOVB mirroring that defines the 'pseudo nodal surface.' The paper then uses this inferred symmetry to label the crossings as class BDI ('if we take the imperfection of the particle-hole symmetry as a small effect, the band crossings can be considered as class BDI'). Thus the BDI classification is partly a restatement of the observed approximate mirror symmetry rather than a consequence of an independently established symmetry. The pressure-driven nodal-ring shrinkage, gapping, and trivial Berry phase are separate DFT results and are not affected.

full rationale

The paper's main results—the zero-pressure near-degeneracy of LUCB/HOVB, the shrinkage of the nodal ring under pressure, and the trivial Berry phase—are obtained directly from DFT band structures with no parameter fitted to the target conclusion. The AZ+I classification is an external framework (Ref. 1), and the Berry-phase criterion is likewise external (Ref. 13). Prior work (Refs. 22-23) is cited for comparison and for the word 'pseudo', but the present pressure-dependent claim does not rest on those citations. The only mild circularity is in the BDI labeling: the approximate particle-hole symmetry is inferred from the same band mirroring that defines the pseudo nodal surface, so calling the system 'class BDI' is partly a restatement of the observed approximate mirror symmetry rather than a prediction from an independent symmetry input. This does not compromise the independent pressure-driven transformation. The explicit neglect of spin-orbit coupling ('both Y and H are light elements', Introduction) is a correctness risk for Y (Z=39), but it is an accuracy concern, not circularity.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The central claim rests on one hand-set tolerance, an inferred approximate symmetry, and standard DFT assumptions; no new entities are postulated.

free parameters (1)
  • E_error (node search tolerance) = 0.005 eV
    Threshold for defining k-points as band crossings (|E_LUCB(k) - E_HOVB(k)| < E_error). The authors chose this value by hand; the size and shape of the pseudo nodal surface depend on it.
assumptions (5)
  • ad hoc to paper An approximate particle-hole symmetry P exists for the two bands near the Fermi level at zero pressure
    Inferred from the observation that the two bands are approximately mirrored about the Fermi level; it is not derived from a microscopic Hamiltonian, and the entire BDI classification relies on it.
  • domain assumption Spin-orbit coupling is negligible
    Justified by the claim that both Y and H are light elements; yttrium is Z=39 with 4d electrons, so SOC may be non-negligible, and the classification could change.
  • standard math The AZ+I classification of gapless topological matter (Ref 1) applies to this material
    The paper imports the classification table from Bzdusek and Sigrist without modification.
  • domain assumption PBE-GGA DFT accurately captures the band crossings and their pressure evolution
    Standard DFT approximation with no hybrid functionals or GW correction; the nodal energy differences of about 0.005 eV are near typical DFT accuracy limits.
  • domain assumption The hexagonal P-3c1 phase remains the relevant structure up to 32 GPa
    Ref 21 reports a structural transition at 21 GPa; the paper continues to use the hexagonal phase above that pressure without discussing metastability.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Pressure induced electronic structure transformation of topological semimetal." pith.science (2026). https://pith.science/paper/GARQ257F

@misc{pith2026190806494,
  author       = {Pith},
  title        = {Pith review of: Pressure induced electronic structure transformation of topological semimetal},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GARQ257F}},
  note         = {Machine review of arXiv:1908.06494}
}
abstract

We study the electronic structure change of yttrium trihydride $\mathrm{YH_3}$ by applying a hydrostatic pressure. At zero pressure, $\mathrm{YH_3}$ has the structure with energy favored symmetry group $P\bar{3}c1$ (165). From first principle calculation, we argue that the band crossings are caused by overlapping of an electron- and hole-like bands. Besides the space inversion symmetry ($\mathcal{I}$) and the time reversal symmetry, the band structure also exhibits an approximate particle-hole symmetry. Thus, $\mathrm{YH_3}$ can be viewed as a pseudo nodal surface semimetal belongs to class BDI of the ten-fold AZ+ $\mathcal{I}$ classifications of gapless topological matter. As pressure increases, the approximate particle-hole symmetry is gradually broken and the pseudo nodal surface turns into a nodal ring belonging to the class AI with fewer non-spatial symmetries. Also, the nodal ring is shrinking in the process. At about $31$ GPa, which is higher than the reported structure phase transition pressure $21$ GPa, the nodal ring shrinks to a nodal point. When above $31$ GPa, all band crossings are gapped out and $\mathrm{YH_3}$ becomes a trivial insulator eventually.

Figures

Figures reproduced from arXiv: 1908.06494 by the authors.

Figure 1
Figure 1. FIG. 1: The crystal structure and electronic structure of YH [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Pressure induced electronic structure changes. (a) The highest energy of h-band [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

46 extracted references · 17 canonical work pages

  1. [1]

    Bzdusek \ and\ author M

    author author T. Bzdusek \ and\ author M. Sigrist ,\ 10.1103/PhysRevB.96.155105 journal journal Physical Review B \ volume 96 ( year 2017 ),\ 10.1103/PhysRevB.96.155105 NoStop

    doi:10.1103/physrevb.96.155105 2017

  2. [2]

    Fu , author C

    author author L. Fu , author C. L. \ Kane , \ and\ author E. J. \ Mele ,\ 10.1103/PhysRevLett.98.106803 journal journal Phys. Rev. Lett. \ volume 98 ,\ pages 106803 ( year 2007 ) NoStop

    doi:10.1103/physrevlett.98.106803 2007

  3. [3]

    author author M. Z. \ Hasan \ and\ author C. L. \ Kane ,\ 10.1103/RevModPhys.82.3045 journal journal Reviews of Modern Physics \ volume 82 ,\ pages 3045 ( year 2010 ) NoStop

    doi:10.1103/revmodphys.82.3045 2010

  4. [4]

    Witten ,\ 10.1393/ncr/i2016-10125-3 journal journal La Rivista del Nuovo Cimento \ volume 39 ,\ pages 313 ( year 2016 ) ,\ note arXiv: 1510.07698 NoStop

    author author E. Witten ,\ 10.1393/ncr/i2016-10125-3 journal journal La Rivista del Nuovo Cimento \ volume 39 ,\ pages 313 ( year 2016 ) ,\ note arXiv: 1510.07698 NoStop

    arXiv 2016

  5. [5]

    author author A. P. \ Schnyder , author S. Ryu , author A. Furusaki , \ and\ author A. W. W. \ Ludwig ,\ 10.1103/PhysRevB.78.195125 journal journal Physical Review B \ volume 78 ,\ pages 195125 ( year 2008 ) NoStop

    doi:10.1103/physrevb.78.195125 2008

  6. [6]

    Kitaev ,\ 10.1063/1.3149495 journal journal AIP Conference Proceedings \ volume 1134 ,\ pages 22 ( year 2009 ) NoStop

    author author A. Kitaev ,\ 10.1063/1.3149495 journal journal AIP Conference Proceedings \ volume 1134 ,\ pages 22 ( year 2009 ) NoStop

    doi:10.1063/1.3149495 2009

  7. [7]

    Ryu , author A

    author author S. Ryu , author A. P. \ Schnyder , author A. Furusaki , \ and\ author A. W. W. \ Ludwig ,\ 10.1088/1367-2630/12/6/065010 journal journal New Journal of Physics \ volume 12 ,\ pages 065010 ( year 2010 ) NoStop

    doi:10.1088/1367-2630/12/6/065010 2010

  8. [8]

    author author Nature ,\ https://www.nature.com/collections/vrlsgqqjbh/ title Topological semimetals \ ( year 2016 ) NoStop

    work page 2016

Show all 46 references
  1. [9]

    author author A. A. \ Burkov ,\ https://doi.org/10.1038/nmat4788 journal journal Nature Materials \ volume 15 ,\ pages 1145 ( year 2016 ) NoStop

    2016 doi

  2. [10]

    \ Xu , author I

    author author S.-Y. \ Xu , author I. Belopolski , author N. Alidoust , author M. Neupane , author G. Bian , author C. Zhang , author R. Sankar , author G. Chang , author Z. Yuan , author C.-C. \ Lee , author S.-M. \ Huang , author H. Zheng , author J. Ma , author D. S. \ Sanch...

    doi

  3. [11]

    Lu , author Z

    author author L. Lu , author Z. Wang , author D. Ye , author L. Ran , author L. Fu , author J. D. \ Joannopoulos , \ and\ author M. Solja i ,\ 10.1126/science.aaa9273 journal journal Science \ volume 349 ,\ pages 622 ( year 2015 ) NoStop

    doi

  4. [12]

    Lv , author H

    author author B. Lv , author H. Weng , author B. Fu , author X. Wang , author H. Miao , author J. Ma , author P. Richard , author X. Huang , author L. Zhao , author G. Chen , author Z. Fang , author X. Dai , author T. Qian , \ and\ author H. Ding ,\ 10.1103/PhysRevX.5.031013 j...

    doi

  5. [13]

    Fang , author Y

    author author C. Fang , author Y. Chen , author H.-Y. \ Kee , \ and\ author L. Fu ,\ 10.1103/PhysRevB.92.081201 journal journal Physical Review B \ volume 92 ,\ pages 081201 ( year 2015 ) NoStop

    2015 doi

  6. [14]

    Wang \ and\ author M

    author author Y. Wang \ and\ author M. Y. \ Chou ,\ 10.1103/PhysRevB.51.7500 journal journal Physical Review B \ volume 51 ,\ pages 7500 ( year 1995 ) NoStop

    1995 doi

  7. [15]

    Ahuja , author B

    author author R. Ahuja , author B. Johansson , author J. M. \ Wills , \ and\ author O. Eriksson ,\ 10.1063/1.120371 journal journal Applied Physics Letters \ volume 71 ,\ pages 3498 ( year 1997 ) NoStop

    1997 doi

  8. [16]

    Palasyuk \ and\ author M

    author author T. Palasyuk \ and\ author M. Tkacz ,\ 10.1016/j.ssc.2004.01.040 journal journal Solid State Communications \ volume 130 ,\ pages 219 ( year 2004 ) NoStop

    2004 doi

  9. [17]

    Ohmura , author A

    author author A. Ohmura , author A. Machida , author T. Watanuki , author K. Aoki , author S. Nakano , \ and\ author K. Takemura ,\ 10.1103/PhysRevB.73.104105 journal journal Physical Review B \ volume 73 ,\ pages 104105 ( year 2006 ) NoStop

    doi

  10. [18]

    Machida , author A

    author author A. Machida , author A. Ohmura , author T. Watanuki , author T. Ikeda , author K. Aoki , author S. Nakano , \ and\ author K. Takemura ,\ 10.1016/j.ssc.2006.04.011 journal journal Solid State Communications \ volume 138 ,\ pages 436 ( year 2006 ) NoStop

    2006 doi

  11. [19]

    Remhof , author G

    author author A. Remhof , author G. Song , author C. Sutter , author A. Schreyer , author R. Siebrecht , author H. Zabel , author F. Guthoff , \ and\ author J. Windgasse ,\ 10.1103/PhysRevB.59.6689 journal journal Physical Review B \ volume 59 ,\ pages 6689 ( year 1999 ) NoStop

    doi

  12. [20]

    Wolf \ and\ author P

    author author W. Wolf \ and\ author P. Herzig ,\ 10.1103/PhysRevB.66.224112 journal journal Physical Review B \ volume 66 ,\ pages 224112 ( year 2002 ) NoStop

    2002 doi

  13. [21]

    author author J. S. \ de Almeida , author D. Y. \ Kim , author C. Ortiz , author M. Klintenberg , \ and\ author R. Ahuja ,\ 10.1063/1.3155505 journal journal Applied Physics Letters \ volume 94 ,\ pages 251913 ( year 2009 ) NoStop

    2009 doi

  14. [22]

    Shao , author T

    author author D. Shao , author T. Chen , author Q. Gu , author Z. Guo , author P. Lu , author J. Sun , author L. Sheng , \ and\ author D. Xing ,\ 10.1038/s41598-018-19870-5 journal journal Scientific Reports \ volume 8 ( year 2018 ),\ 10.1038/s41598-018-19870-5 NoStop

    doi

  15. [23]

    Wang , author Y

    author author J. Wang , author Y. Liu , author K.-H. \ Jin , author X. Sui , author L. Zhang , author W. Duan , author F. Liu , \ and\ author B. Huang ,\ 10.1103/PhysRevB.98.201112 journal journal Physical Review B \ volume 98 ( year 2018 ),\ 10.1103/PhysRevB.98.201112 NoStop

    doi

  16. [24]

    Persson ,\ 10.17188/1199674 title Materials Data on YH 3 ( SG :165) by Materials Project \ ( year 2016 ) NoStop

    author author K. Persson ,\ 10.17188/1199674 title Materials Data on YH 3 ( SG :165) by Materials Project \ ( year 2016 ) NoStop

    2016 doi

  17. [25]

    author author M. I. Aroyo , author J. M. Perez-Mato , author D. Orobengoa , author E. Tasci , author G. De la Flor Martin , \ and\ author A. Kirov ,\ @noop journal journal Bulgarian Chemical Communications \ volume 43 ,\ pages 183 ( year 2011 ) NoStop

    2011

  18. [26]

    author author M. I. \ Aroyo , author J. M. \ Perez-Mato , author C. Capillas , author E. Kroumova , author S. Ivantchev , author G. Madariaga , author A. Kirov , \ and\ author H. Wondratschek ,\ 10.1524/zkri.2006.221.1.15 journal journal Zeitschrift fur Kristallographie - Crys...

    2006 doi

  19. [27]

    author author M. I. \ Aroyo , author A. Kirov , author C. Capillas , author J. M. \ Perez-Mato , \ and\ author H. Wondratschek ,\ 10.1107/S0108767305040286 journal journal Acta Crystallographica Section A Foundations of Crystallography \ volume 62 ,\ pages 115 ( year 2006 b ) NoStop

    doi

  20. [28]

    Hohenberg \ and\ author W

    author author P. Hohenberg \ and\ author W. Kohn ,\ 10.1103/PhysRev.136.B864 journal journal Physical Review \ volume 136 ,\ pages B864 ( year 1964 ) NoStop

    1964 doi

  21. [29]

    Kohn \ and\ author L

    author author W. Kohn \ and\ author L. J. \ Sham ,\ 10.1103/PhysRev.140.A1133 journal journal Physical Review \ volume 140 ,\ pages A1133 ( year 1965 ) NoStop

    1965 doi

  22. [30]

    Kresse \ and\ author J

    author author G. Kresse \ and\ author J. Furthmuller ,\ 10.1103/PhysRevB.54.11169 journal journal Physical Review B \ volume 54 ,\ pages 11169 ( year 1996 a ) NoStop

    1996 doi

  23. [31]

    Kresse \ and\ author J

    author author G. Kresse \ and\ author J. Furthmuller ,\ 10.1016/0927-0256(96)00008-0 journal journal Computational Materials Science \ volume 6 ,\ pages 15 ( year 1996 b ) NoStop

    1996 doi

  24. [32]

    author author P. E. \ Blochl ,\ 10.1103/PhysRevB.50.17953 journal journal Physical Review B \ volume 50 ,\ pages 17953 ( year 1994 ) NoStop

    1994 doi

  25. [33]

    Kresse \ and\ author D

    author author G. Kresse \ and\ author D. Joubert ,\ 10.1103/PhysRevB.59.1758 journal journal Physical Review B \ volume 59 ,\ pages 1758 ( year 1999 ) NoStop

    1999 doi

  26. [34]

    author author J. P. \ Perdew , author K. Burke , \ and\ author M. Ernzerhof ,\ 10.1103/PhysRevLett.77.3865 journal journal Physical Review Letters \ volume 77 ,\ pages 3865 ( year 1996 ) NoStop

    1996 doi

  27. [35]

    author author H. J. \ Monkhorst \ and\ author J. D. \ Pack ,\ 10.1103/PhysRevB.13.5188 journal journal Physical Review B \ volume 13 ,\ pages 5188 ( year 1976 ) NoStop

    1976 doi

  28. [36]

    Kruthoff , author J

    author author J. Kruthoff , author J. de Boer , author J. van Wezel , author C. L. \ Kane , \ and\ author R.-J. \ Slager ,\ 10.1103/PhysRevX.7.041069 journal journal Physical Review X \ volume 7 ,\ pages 041069 ( year 2017 ) NoStop

    2017 doi

  29. [37]

    Bradlyn , author L

    author author B. Bradlyn , author L. Elcoro , author J. Cano , author M. G. \ Vergniory , author Z. Wang , author C. Felser , author M. I. \ Aroyo , \ and\ author B. A. \ Bernevig ,\ 10.1038/nature23268 journal journal Nature \ volume 547 ,\ pages 298 ( year 2017 ) ,\ note arX...

    arXiv

  30. [38]

    author author M. G. \ Vergniory , author L. Elcoro , author Z. Wang , author J. Cano , author C. Felser , author M. I. \ Aroyo , author B. A. \ Bernevig , \ and\ author B. Bradlyn ,\ 10.1103/PhysRevE.96.023310 journal journal Physical Review E \ volume 96 ,\ pages 023310 ( yea...

    arXiv

  31. [39]

    Bradlyn , author L

    author author B. Bradlyn , author L. Elcoro , author M. G. \ Vergniory , author J. Cano , author Z. Wang , author C. Felser , author M. I. \ Aroyo , \ and\ author B. A. \ Bernevig ,\ 10.1103/PhysRevB.97.035138 journal journal Physical Review B \ volume 97 ,\ pages 035138 ( yea...

    doi

  32. [40]

    author author A. A. \ Mostofi , author J. R. \ Yates , author G. Pizzi , author Y.-S. \ Lee , author I. Souza , author D. Vanderbilt , \ and\ author N. Marzari ,\ 10.1016/j.cpc.2014.05.003 journal journal Computer Physics Communications \ volume 185 ,\ pages 2309 ( year 2014 ) NoStop

    2014 doi

  33. [41]

    Wu , author S

    author author Q. Wu , author S. Zhang , author H.-F. \ Song , author M. Troyer , \ and\ author A. A. \ Soluyanov ,\ https://doi.org/10.1016/j.cpc.2017.09.033 journal journal Computer Physics Communications \ volume 224 ,\ pages 405 ( year 2018 ) NoStop

    2017 doi

  34. [42]

    author author N. W. \ Ashcroft ,\ 10.1103/PhysRevLett.92.187002 journal journal Physical Review Letters \ volume 92 ,\ pages 187002 ( year 2004 ) NoStop

    2004 doi

  35. [43]

    \ Liu , author H.-J

    author author L.-L. \ Liu , author H.-J. \ Sun , author C. Z. \ Wang , \ and\ author W.-C. \ Lu ,\ 10.1088/1361-648x/aa787d journal journal Journal of Physics: Condensed Matter \ volume 29 ,\ pages 325401 ( year 2017 a ) NoStop

    2017 doi

  36. [44]

    Liu , author I

    author author H. Liu , author I. I. \ Naumov , author R. Hoffmann , author N. W. \ Ashcroft , \ and\ author R. J. \ Hemley ,\ 10.1073/pnas.1704505114 journal journal Proceedings of the National Academy of Sciences \ volume 114 ,\ pages 6990 ( year 2017 b ) NoStop

    doi

  37. [45]

    Peng , author Y

    author author F. Peng , author Y. Sun , author C. J. \ Pickard , author R. J. \ Needs , author Q. Wu , \ and\ author Y. Ma ,\ 10.1103/PhysRevLett.119.107001 journal journal Physical Review Letters \ volume 119 ,\ pages 107001 ( year 2017 ) NoStop

    doi

  38. [46]

    author author R. W. \ Keyes ,\ in\ 10.1016/S0081-1947(08)60168-X booktitle Solid State Physics ,\ Vol. volume 11 ,\ editor edited by\ editor F. SEITZ \ and\ editor D. TURNBULL \ ( publisher Academic Press ,\ year 1960 )\ pp.\ pages 149--221 NoStop

    1947 doi

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.