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REVIEW 3 major objections 4 minor 43 references

Topological Lifshitz Transitions and Fermi Arc Manipulation in Weyl Semimetal NbAs

T0 review · 3 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Potassium decoration of a cleaved NbAs surface switches the surface Fermi arcs from connecting adjacent Weyl points to connecting Weyl points in different Brillouin zones, with no change in bulk carrier concentration.

desk verdict A careful ARPES study showing that potassium decoration reshapes the surface Fermi surface of NbAs into a clean figure-8, but the headline claim that the Fermi arcs switch their Weyl-point pairing rests on an unmeasured DFT adlayer model, so the paper is a solid experiment with an over-interpreted abstract. read the letter →

arxiv 1908.01155 v1 pith:2HQXVX4F submitted 2019-08-03 cond-mat.mtrl-sci

H. F. Yang , L. X. Yang , Z. K. Liu , Y. Sun , C. Chen , H. Peng , M. Schmidt , D. Prabhakaran
show 4 more authors
B. A. Bernevig C. Felser B. H. Yan Y. L. Chen
This is my paper · ORCID
classification cond-mat.mtrl-sci
keywords WeylsemimetalsurfaceFermiarcstopologicalLifshitztransitionpotassiumdecorationNbAsangle-resolvedphotoemissiontopologystates
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

Surface Fermi arcs are open curves on the surface of a Weyl semimetal that must start and end at projections of Weyl points of opposite chirality. This paper reports that depositing potassium onto a freshly cleaved NbAs (001) surface reshapes and ultimately rewires those arcs: the arcs switch from connecting neighbouring Weyl-point projections inside one Brillouin zone to connecting Weyl-point projections from different Brillouin zones. The change happens without a rigid shift of the bulk Fermi energy, so the authors identify it as a topological Lifshitz transition driven by surface modification. A sympathetic reader would care because it shows that the connectivity of Fermi arcs is a controllable surface property while the arcs themselves remain topologically protected.

What carries the argument

The central object is the surface Fermi arc: an open Fermi-surface contour on the boundary of a Weyl semimetal that must terminate at the surface projections of two Weyl points with opposite chirality. The mechanism carrying the argument is in-situ potassium decoration, which in the authors' slab calculations changes the surface potential enough to eliminate the trivial bowtie surface states and reconnect the arcs into a figure-eight pattern whose endpoints lie in different Brillouin zones. The organizing identity is the bulk-boundary correspondence: no matter how the arcs are rearranged, each arc must still connect one Weyl point of each chirality, and the paper uses this rule to distinguish the two topologically distinct connection patterns.

What would settle it

Measure the potassium adatom registry on the K-decorated NbAs(001) surface with scanning tunnelling microscopy or low-energy electron diffraction, feed that measured registry into the slab calculation, and compare the resulting Fermi surface with the photoemission data; the claimed connection switch is falsified if the real registry does not produce the figure-eight pattern seen in the data.

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Extended reading notes

Core claim

On a pristine As-terminated NbAs(001) surface, angle-resolved photoemission shows a cross-shaped Fermi surface with spoon-like Fermi arcs connecting projections of adjacent Weyl points within the same surface Brillouin zone, alongside trivial bowtie-like surface states. After in-situ potassium deposition, the Fermi surface changes to a figure-eight pattern made of two long arcs that connect Weyl points from different Brillouin zones, and the trivial states vanish. The paper interprets the sharp change between two stages of potassium dosing as a surface topological Lifshitz transition: the Fermi-surface connectivity changes discontinuously and the arcs are 'teleported' across the surface Brillouin zone, yet each arc remains pinned at both ends to Weyl points of opposite chirality. Ab initio slab calculations for a potassium-covered As-terminated surface reproduce the figure-eight Fermi surface and the new connection pattern, and the authors argue the transition cannot be explained by a rigid band shift from doping alone.

Load-bearing premise

The load-bearing premise is that the potassium atoms sit in one particular ordered arrangement on the arsenic-terminated surface: the rewired Fermi-arc connectivity is taken from a calculation built on that assumed arrangement, and the experiments do not directly measure where the potassium atoms actually sit.

Editorial extensions

If this is right

  • Potassium dosing gives a practical control knob: the same NbAs crystal can be switched between two distinct Fermi-arc topologies, and the switch happens without a change in bulk carrier concentration.
  • On the decorated surface the Fermi surface consists only of two long Fermi arcs, with the bowtie-like trivial surface states gone, so Fermi-arc-mediated phenomena can be studied without a trivial-state background.
  • Because each arc still terminates on Weyl points of opposite chirality after the transition, the observation confirms that Fermi arcs are topologically protected by the bulk and cannot be removed by surface modification.
  • The transition is a Lifshitz transition of an open Fermi surface, meaning the topology of the arc connectivity changes at a critical surface condition while the Fermi energy itself does not shift rigidly.
  • Potassium-dose-dependent measurements show the rewiring happens sharply between two stages, so experiments probing surface-dominated transport near the transition should see an abrupt change in surface-mediated responses.

Reading between the lines

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

  • Our inference: the same decoration approach should extend to other transition-metal monopnictide Weyl semimetals, and the clean arc-only Fermi surface could make those materials better platforms for transport experiments.
  • Our inference: if the adatom registry is the true control parameter, varying potassium coverage or ordering could open a small phase diagram of Fermi-arc connectivities, potentially accessible by combining scanning tunnelling microscopy with photoemission.
  • Our inference: rewired arcs should change the Weyl-orbit geometry linking top and bottom surfaces, so magnetic-field transport signatures such as arc-mediated quantum oscillations may change discontinuously when the transition is crossed.
  • Our inference: a direct transport test would compare nonlocal voltage or electromagnetic-wave transmission before and after the transition, sharpening the connection between arc topology and the predicted exotic responses.
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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 / 4 minor

Summary. The paper reports an ARPES and DFT study of pristine and K-decorated NbAs(001). On the pristine surface, the measured Fermi surface consists of spoon-like surface Fermi arcs (SFAs) coexisting with bowtie-like trivial surface states, consistent with previous work and with the authors' slab calculations. After in-situ potassium deposition, the Fermi surface transforms into a figure-8-like structure that the authors interpret as two long SFAs with no accompanying trivial surface states. The central claim is that this surface decoration drives a topological Lifshitz transition: the SFAs switch their connectivity from adjacent Weyl-point projections within the same Brillouin zone (pristine) to Weyl-point projections belonging to different Brillouin zones (K-decorated), while each SFA continues to connect Weyl points of opposite chirality. The authors further claim that this transition is not caused by a rigid shift of the Fermi energy or by carrier-concentration changes, but by the surface modification itself. The evidence includes photon-energy dependent ARPES showing the surface origin of the features, a systematic K-dose evolution (Fig. 5), and DFT slab calculations that reproduce the figure-8 Fermi surface and its connectivity (Supplementary Note 2 and Supplementary Fig. 9).

Significance. If the central claim is correct, the work demonstrates that surface decoration can change the topological connectivity of Fermi arcs, a new form of control over topological surface states, and it provides a Fermi-arc-only surface that would be a clean platform for transport and interference experiments. The paper's strengths include the systematic K-dose-dependent ARPES data, the use of photon-energy dependence to establish surface origins, the curvature analysis supporting the two-branch structure of the figure-8 pocket, and the agreement between measured and calculated band structures. The significance, however, is tempered by the fact that the claimed connectivity switch is not read directly from the data but is inferred from a DFT calculation that assumes a specific, unmeasured arrangement of K adatoms on the As-terminated surface. Because Fermi-arc connectivity is not uniquely fixed by bulk topology, the headline result is only as strong as that structural assumption.

major comments (3)
  1. [Results: Figure-8-like SFAs emerging on potassium decorated surface (Fig.] The central claim that the K-decorated SFAs switch from connecting adjacent Weyl-point projections within the same BZ to connecting projections from different BZs is inferred from a DFT slab calculation that assumes a particular ordered arrangement and nominal coverage of K adatoms on the As-terminated (001) surface. No LEED, STM, or quantitative coverage measurement is reported, and the '1.8 ML' in Fig. 4 is only an evaporator dose. Because Fermi-arc connectivity is not uniquely fixed by bulk topology, a different adlayer registry or coverage could plausibly yield a similar-looking figure-8 Fermi surface with the pristine pairing or a different pairing. The authors should either measure the adlayer structure or demonstrate by DFT that the connectivity change is robust to the K coverage and adsorption site (e.g., by repeating the slab calculation for several coverages and registries).
  2. [Results: Topological quantum Lifshitz transition (Fig. 5; Discussion)] The claim that the observed transition is 'not caused by the change of the carrier concentration' is not independently established by the experiments. K deposition simultaneously dopes the surface and alters the surface potential and the adlayer geometry; there is no separate control of surface carrier density (e.g., via gating or a different alkali species) that would allow the carrier-concentration effect to be isolated from the structural effect. The DFT calculation may support a structural origin, but the experimental wording overstates the level of control.
  3. [Results: Figure-8-like SFAs emerging on potassium decorated surface (Fig. 4; Methods: ab initio calculations)] The paper repeatedly states that the measured and calculated Fermi surfaces show 'excellent agreement' and that the figure-8 FS is 'composed of two long SFAs', but no quantitative comparison (e.g., fitting residuals, momentum-space widths, or error bars on the extracted Fermi-surface lines) is provided. Given that the connectivity argument rests on the fine structure of the figure-8 pocket near kx=0 and ky=0, a quantitative statement of the level of agreement would materially strengthen the case that the measured features correspond to the calculated SFA branches.
minor comments (4)
  1. [Figure 2 and text (page 5)] The panel labeling in Fig. 2 is inconsistent: the caption lists 'i' twice (once for the calculated/measured Fermi surface around the gamma point and once for the photon-energy dependence), while the text refers to 'Fig. 2l' for the photon-energy data. The panel letters should be corrected and cited consistently.
  2. [Results: Topological quantum Lifshitz transition (Fig. 5)] The transition is called 'TQLT' in the text and 'TPLT' in the caption of Fig. 5; please use one acronym consistently throughout.
  3. [Methods: ab initio calculations] The description of the slab calculation does not specify how the K adatoms were placed on the As-terminated surface, what coverage was simulated, or whether the K positions were relaxed. This information is essential for the reader to assess the uniqueness of the calculated connectivity.
  4. [Results: Figure-8-like SFAs emerging on potassium decorated surface (page 5)] The phrase 'the cleanest system of Fermi-arcs observed to date' is a strong comparative claim that is not supported by a systematic survey; suggest softening or providing a concrete comparison with prior systems.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central claim rests on independent ARPES data and DFT calculations, with no fitted parameter renamed as a prediction.

full rationale

No circular step is identifiable. The paper's central claim—that K decoration changes the SFA connection pattern in NbAs—is supported by ARPES measurements and by independent DFT slab calculations for a K-covered surface. The DFT calculation is not fitted to the ARPES data; it uses only experimental lattice parameters and an assumed K adlayer geometry, and the comparison with measured Fermi surfaces is an independent check. Self-citations (e.g., refs. 4 and 34) provide prior predictions of bulk Weyl points and pristine Fermi arcs, but these are not load-bearing for the new K-decorated result; the decoration calculation is presented as a new simulation. The concern that the K adlayer structure is not measured is an empirical testability limitation, not a circularity: the calculation's output (figure-8 Fermi surface and SFA connectivity) is not equivalent to its input by construction. No fitting of the SFA connection pattern to data, no renaming of a fitted parameter as a prediction, and no self-citation chain forcing the conclusion are present. The paper is therefore self-contained with respect to the circularity concerns checked here.

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

The central claim rests on the established Weyl-semimetal band topology, on DFT as a reliable model for the decorated surface, on the ARPES surface-state identification criterion, and on the assumption that K deposition changes only the surface. No new particles, forces, or material entities are introduced.

free parameters (1)
  • K adatom coverage and ordering in the DFT slab model = Not stated; nominal 1.8 ML in experiment
    The DFT simulation of the decorated surface must choose a K coverage and adatom positions to reproduce the figure-eight Fermi surface; this choice is not derived from first principles and directly affects the calculated SFA connection pattern.
assumptions (4)
  • domain assumption NbAs is a Weyl semimetal whose bulk Weyl points enforce surface Fermi arcs connecting opposite-chirality projections.
    Used throughout to interpret ARPES contours as Fermi arcs and to argue arcs must terminate at opposite-chirality Weyl points (Introduction, Fig. 1, Fig. 2).
  • domain assumption DFT with GGA and spin-orbit coupling accurately captures the measured surface electronic structure of pristine and K-decorated NbAs.
    The paper identifies measured bands and the figure-eight Fermi surface using DFT slab calculations; no alternative method or benchmark is given (Methods; Fig. 2h,i; Fig. 3).
  • domain assumption Photon-energy independence of a feature is sufficient to classify it as surface-derived.
    Used to separate surface states from bulk states in Fig. 2f and 2i and Supplementary Figures; standard ARPES practice but still an assumption about matrix elements and bulk-surface overlap.
  • domain assumption K deposition modifies only the surface electronic structure and does not change the bulk Weyl point positions or chiralities.
    The topological transition is attributed to surface modification alone; no bulk-sensitive measurement of K-decorated NbAs is presented to confirm unchanged bulk topology (Discussion, Fig. 5).

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Pith. "Pith review of Topological Lifshitz Transitions and Fermi Arc Manipulation in Weyl Semimetal NbAs." pith.science (2026). https://pith.science/paper/2HQXVX4F

@misc{pith2026190801155,
  author       = {Pith},
  title        = {Pith review of: Topological Lifshitz Transitions and Fermi Arc Manipulation in Weyl Semimetal NbAs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2HQXVX4F}},
  note         = {Machine review of arXiv:1908.01155}
}
read the original abstract

Surface Fermi arcs (SFAs), the unique open Fermi-surfaces (FSs) discovered recently in topological Weyl semimetals (TWSs), are unlike closed FSs in conventional materials and can give rise to many exotic phenomena, such as anomalous SFA-mediated quantum oscillations, chiral magnetic effects, three-dimensional quantum Hall effect, non-local voltage generation and anomalous electromagnetic wave transmission. Here, by using in-situ surface decoration, we demonstrate successful manipulation of the shape, size and even the connections of SFAs in a model TWS, NbAs, and observe their evolution that leads to an unusual topological Lifshitz transition not caused by the change of the carrier concentration. The phase transition teleports the SFAs between different parts of the surface Brillouin zone. Despite the dramatic surface evolution, the existence of SFAs is robust and each SFA remains tied to a pair of Weyl points of opposite chirality, as dictated by the bulk topology.

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Works this paper leans on

43 extracted references · 41 canonical work pages

  1. [1]

    M., Vishwanath, A

    Wan, X., Turner, A. M., Vishwanath, A. & Savrasov, S. Y. Topological semimetal and Fermi - arc surface states in the electronic structure of pyrochlore iridates . Phys. Rev. B 83, 205101 (2011)

    work page 2011

  2. [2]

    A., Hook, M

    Burkov, A. A., Hook, M. D. & Balents, L. Topological nodal semimetals. Phys. Rev. B 84, 235126 (2011)

    work page 2011

  3. [3]

    Weyl electrons kiss

    Balents, L. Weyl electrons kiss. Physics 4, 36 (2011)

    work page 2011

  4. [4]

    M., Fang, C., Fang, Z., Bernevig, B

    Weng, H. M., Fang, C., Fang, Z., Bernevig, B. A. & Dai, X. Weyl semimetal phase in noncentrosymmetric transition-metal monophosphides. Phys. Rev. X 5, 011029 (2015)

    work page 2015

  5. [5]

    Huang S. -M. et al. A Weyl Fermion semimetal with surface Fermi arcs in the transition metal monopnictide TaAs class. Nat. Commun. 6, 7373 (2015)

    work page 2015

  6. [6]

    C., Kimchi, I

    Potter, A. C., Kimchi, I. & Vishwanath, A. Quantum oscillations from surface Fermi arcs in Weyl and Dirac semimetals. Nat. Commun. 5, 5161 (2014)

    work page 2014

  7. [7]

    Bulmash, D. & Qi, X. -L. Quantum oscillations in Weyl and Dirac semimetal ultrathin films. Phys. Rev. B 93, 081103(R) (2016)

    work page 2016

  8. [8]

    Zhang, Y., Bulmash, D., Hosur, P., Potter, A. C. & Vishwannath, A. Quantum oscillations from generic surface Fermi arcs and bulk chiral modes in Weyl semimetals. Sci. Rep. 6, 23741 (2016)

    work page 2016

Show all 43 references
  1. [9]

    Moll, P. J. W. et al. Transport evidence for Fermi-arc-mediated chirality transfer in the Dirac semimetal Cd3As2. Nature 535, 266-270 (2016)

    2016

  2. [10]

    Zyuzin, A. A. & A. A. Burkov. Topological response in Weyl semimetals and the chiral anomaly. Phys. Rev. B 86, 115133 (2012)

    2012

  3. [11]

    -X., Ye, P

    Liu, C. -X., Ye, P. & Qi, X. -L. Chiral gauge field and axial anomaly in a Weyl semimetal. Phys. Rev. B 87, 235306 (2013)

    2013

  4. [12]

    Huang X. et al. Observation of the chiral-anomaly-induced negative magnetoresistance in 3D Weyl semimetal TaAs. Phys. Rev. X 5, 031023 (2015). Page | 9

    2015

  5. [13]

    Zhang, C. -L. et al. Signatures of the Adler–Bell–Jackiw chiral anomaly in a Weyl fermion semimetal. Nat. Commun. 7, 10735 (2016)

    2016

  6. [14]

    A., Tworzydlo, J

    Baireuther, P., Hutasoit, J. A., Tworzydlo, J. & Beenakker, C. W. J. Scattering theory of the chiral magnetic effect in a Weyl semimetal: interplay of bulk Weyl cones and surface Fermi arcs. New J. Phys. 18, 045009 (2016)

    2016

  7. [15]

    M., Sun, H

    Wang, C. M., Sun, H. -P., Lu, H. -Z. & Xie, X. C. 3D quantum Hall effect of Fermi arcs in topological semimetals. Phys. Rev. Lett. 119, 136806 (2017)

    2017

  8. [16]

    & Bernevig, B

    Kourtis, S., Li, J., Wang, Z., Yazdani, A. & Bernevig, B. A. Universal signatures of Fermi arcs in quasiparticle interference on the surface of Weyl semimetals. Phys. Rev. B 93, 041109(R) (2016)

    2016

  9. [17]

    Inoue, H. et al. Quasiparticle interference of the Fermi arcs and surface-bulk connectivity of a Weyl semimetal. Science 351, 1184-1187 (2016)

    2016

  10. [18]

    Batabyal, R. et al. Visualizing weakly bound surface Fermi arcs and their correspondence to bulk Weyl fermions. Sci. Adv. 2, e1600709 (2016)

    2016

  11. [19]

    Friedel oscillations due to Fermi arcs in Weyl semimetals

    Hosur, P. Friedel oscillations due to Fermi arcs in Weyl semimetals. Phys. Rev. B 86, 195102 (2012)

    2012

  12. [20]

    A., Grover, T., Abanin, D

    Parameswaran, S. A., Grover, T., Abanin, D. A., Pesin, D. A. & Vishwanath, A. Probing the chiral anomaly with nonlocal transport in three-dimensional topological semimetals. Phys. Rev. X 4, 031035 (2014)

    2014

  13. [21]

    Baum, Y., Berg, E., Parameswaran, S. A. & Ste rn, A. Current at a distance and resonant transparency in Weyl semimetals. Phys. Rev. X 5, 041046 (2015)

    2015

  14. [22]

    & Nagaosa, N

    Ishizuka, H., Hayata, T., Ueda, M. & Nagaosa, N. Emergent electromagnetic induction and adiabatic charge pumping in noncentrosymmetric Weyl semime tals. Phys. Rev. Lett . 117, 216601 (2016)

    2016

  15. [23]

    Rosenstein, B., Kao, H. C. & Lewkowicz, M. Nonlocal electrodynamics in Weyl semimetals. Phys. Rev. B 95, 085148 (2017)

    2017

  16. [24]

    & Beenakker, C

    Baireuther, P., Tworzydlo, J., Breitkreiz, M., Adagideli, I. & Beenakker, C. W. J. Weyl- Majorana solenoid. New J. Phys. 19, 025006 (2017)

    2017

  17. [25]

    Lv, B. Q. et al. Observation of Weyl nodes in TaAs. Nat. Phys. 11, 724-727 (2015)

    2015

  18. [26]

    Xu, S. -Y. et al. Discovery of a Weyl fermion semimetal and topological Fermi arcs. Science 349, 613-617 (2015)

    2015

  19. [27]

    Yang, L. X. et al. Weyl semimetal phase in the non -centrosymmetric compound TaAs. Nat. Phys. 11, 728-732 (2015)

    2015

  20. [28]

    Lv, B. Q. et al. Experimental discovery of Weyl semimetal TaAs. Phys. Rev. X 5, 031013 (2015)

    2015

  21. [29]

    Liu, Z. K. et al. Evolution of the Fermi surface of Weyl semimetals in the transition metal pnictide family. Nat. Mater. 15, 27-31 (2015)

    2015

  22. [30]

    Xu, S. -Y. et al. Discovery of a Weyl fermion state with Fermi arcs in niobium arsenide. Nat. Phys. 11, 748-754 (2015)

    2015

  23. [31]

    Xu, D. -F. et al. Observation of Fermi arcs in non -centrosymmetric Weyl semi -metal candidate NbP. Chin. Phys. Lett. 32, 107101 (2015)

    2015

  24. [32]

    Souma, S. et al. Direct observation of nonequivalent Fermi -arc states of opposite surfaces in the noncentrosymmetric Weyl semimetal NbP. Phys. Rev. B 93, 161112(R) (2016)

    2016

  25. [33]

    Xu, N. et al. Observation of Weyl nodes and Fermi arcs in tantalum phosphide. Nat. Commun. 7, 11006 (2016)

    2016

  26. [34]

    Sun, Y., Wu, S. -C. & Yan, B. Topological surface states and Fermi arcs of the noncentrosymmetric Weyl semimetals TaAs, TaP, NbAs, and NbP. Phys. Rev. B 92, 115428 (2015)

    2015

  27. [35]

    & Parthe , E

    Boller, H. & Parthe , E. The transposition structure of NbAs and of similar monophosphides and arsenides of niobium and tantalum. Acta Crystallogr. 16, 1095-1101 (1963). Page | 10

    1963

  28. [36]

    & Shen, Z

    Damascelli, A., Hussain, Z. & Shen, Z. X. Angle-resolved photoemission studies of the cuprate superconductors. Rev. Mod. Phys. 75, 473-541 (2003)

    2003

  29. [37]

    Hossain, M. A . et al. In situ doping control of the surface of high -temperature superconductors. Nat. Phys. 4, 527-531 (2008)

    2008

  30. [38]

    Liu, Z. K. et al. Discovery of a three -dimensional topological Dirac semimetal, Na 3Bi. Science 343, 864-867 (2014)

    2014

  31. [39]

    Liu, Z. K. et al. A stable three-dimensional topological Dirac semimetal Cd 3As2. Nat. Mater. 13, 677-681 (2014)

    2014

  32. [40]

    Zhang, P. et al. A precise method for visualizing dispersive features in image plots. Rev. Sci. Instrum. 82, 043712 (2011)

    2011

  33. [41]

    & Furthmü ller, J

    Kresse, G. & Furthmü ller, J. Effcient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169-11186 (1996)

    1996

  34. [42]

    Blö chl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953-17979 (1994)

    1994

  35. [43]

    P., Burke, K

    Perdew, J. P., Burke, K. & Ernzerhof, M. Gen eralized gradient approximation made simple. Phys. Rev. Lett. 77, 3865-3868 (1996). Acknowledgements We thank John A. McGuire for polishing the writing of this paper. This work was supported by the National Key R&D program of China ...

    1996

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