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arxiv: 2604.21488 · v1 · submitted 2026-04-23 · ❄️ cond-mat.mtrl-sci · cond-mat.supr-con

Intertwined charge density wave, tunable anti-dome superconductivity, and topological states in kagome metal VSn

Shu-Xiang Qiao , Ya-Ping Li , Jie Zhang , Yi Wan , Na Jiao , Meng-Meng Zheng , Hong-Yan Lu , Ping Zhang This is my paper

Pith reviewed 2026-05-09 21:22 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci cond-mat.supr-con
keywords kagome metalcharge density waveanti-dome superconductivitytopological statesVSnphonon softeningpressure tuningdoping effects
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0 comments X

The pith

VSn is predicted as a kagome metal with built-in charge density waves that yield to anti-dome superconductivity while keeping topological character.

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

The paper predicts a new 1:1 kagome compound, vanadium-tin, that forms a spontaneous charge density wave at ambient conditions. Raising pressure or introducing carriers gradually wipes out the wave order and allows superconductivity to appear, but the transition temperature rises then falls again in an anti-dome shape before the charge wave re-enters at still higher tuning. Throughout the superconducting window the bands remain topologically nontrivial. A sympathetic reader would care because the material therefore offers a single platform in which charge order, pairing, and topology can be tuned against one another without magnetic complications.

Core claim

We predict a novel 1:1 kagome metal VSn, which is an intrinsic charge density wave (CDW) material. Interestingly, with increasing pressure or doping concentration, the CDW order is progressively suppressed, followed by the emergence of superconductivity characterized by a non-monotonic transition temperature that exhibits a rare anti-dome-shaped dependence. Above a critical threshold, a reentrance of the CDW phase occurs. The anti-dome superconductivity originates from the first hardening and then softening of phonon modes, together with band reconstruction. Crucially, VSn retains nontrivial topological properties across the entire superconducting regime.

What carries the argument

The vanadium-tin kagome lattice whose phonon modes first harden then soften under pressure or doping, driving the CDW suppression and the anti-dome superconducting dome while topological band invariants remain intact.

If this is right

  • Pressure or doping suppresses the intrinsic CDW and triggers superconductivity with non-monotonic, anti-dome dependence of the transition temperature.
  • A re-entrant CDW phase appears beyond a critical tuning threshold.
  • Nontrivial topological character persists throughout the superconducting regime.
  • Phonon hardening followed by softening, together with band reconstruction, accounts for the anti-dome shape.
  • The material supplies a platform for studying the interplay of charge order, superconductivity, and topology in one kagome system.

Where Pith is reading between the lines

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

  • If the anti-dome pattern is confirmed, it would suggest that similar phonon-driven tuning could be engineered in other non-magnetic 1:1 kagome metals.
  • The persistence of topology across the superconducting dome raises the possibility that doping or pressure might stabilize a topological superconducting state suitable for further study.
  • Experimental searches for VSn would test whether the predicted CDW wavevector and the calculated phonon softening can be directly observed.

Load-bearing premise

The electronic-structure and phonon calculations correctly capture the CDW instability, the phonon hardening-softening sequence, and the survival of topological invariants when pressure or doping is applied.

What would settle it

Synthesis of bulk or thin-film VSn followed by measurement of a CDW transition that decreases with pressure or doping, a superconducting critical temperature that rises then falls in an anti-dome, and re-entrant CDW at higher tuning, plus direct probes confirming retained topological surface states.

Figures

Figures reproduced from arXiv: 2604.21488 by Hong-Yan Lu, Jie Zhang, Meng-Meng Zheng, Na Jiao, Ping Zhang, Shu-Xiang Qiao, Ya-Ping Li, Yi Wan.

Figure 1
Figure 1. Figure 1: c shows the band structure of VSn, which ex￾hibits prominent kagome-lattice features near the Fermi level, including the Dirac points at the K point and the flat band along the A-L-H-A path. From the element projected band structure (Fig. 1c) and orbital projected density of states (PDOS) (Figs. 1d and 1e), the flat band states are found to originate primarily from the V-dz 2 or￾bitals, whereas the electro… view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: b) become broader. The DOS at the Fermi level N(EF ) decreases from 34.69 at 3 GPa to 25.52 at 50 GPa, consistent with the decreasing trend of Tc shown in Fig. 1h. This decrease primarily arises because the VHSs at the M point shifts away from the Fermi level, reduc￾ing N(EF ). At 90 GPa, the blue energy band crosses the Fermi level near the A point, clearly indicating a Lifshitz phase transition. This rec… view at source ↗
read the original abstract

These years, kagome materials with 1:1 stoichiometry have garnered increasing attention, among which FeSn, CoSn, and FeGe have been the focus of current studies. However, all of them are antiferromagnetic, thereby hindering the observation of superconductivity and other novel physical properties. Here, we predict a novel 1:1 kagome metal VSn, which is an intrinsic charge density wave (CDW) material. Interestingly, with increasing pressure or doping concentration, the CDW order is progressively suppressed, followed by the emergence of superconductivity characterized by a non-monotonic transition temperature that exhibits a rare anti-dome-shaped dependence. Above a critical threshold, a reentrance of the CDW phase occurs. The anti-dome superconductivity originates from the first hardening and then softening of phonon modes, together with band reconstruction. Crucially, VSn retains nontrivial topological properties across the entire superconducting regime, a feature of paramount importance for realizing robust topological superconductivity. These intertwined CDW, superconductivity, and topological phenomena elucidate the correlations among multiple quantum states in VSn. Therefore, this research paves the way for for designing 1:1 kagome superconducting topological metals and establishes a platform for exploring the interplay of multiple phases in kagome systems.

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 predicts a novel 1:1 kagome metal VSn as an intrinsic CDW material. With increasing pressure or doping, the CDW order is suppressed, giving way to superconductivity with a rare anti-dome-shaped Tc dependence; at higher values a reentrant CDW phase appears. The anti-dome superconductivity is attributed to initial hardening followed by softening of phonon modes together with band reconstruction. The material is claimed to retain nontrivial topological properties throughout the superconducting regime, offering a platform for topological superconductivity.

Significance. If the DFT predictions hold, the work would introduce a new kagome platform free of the antiferromagnetism that limits FeSn, CoSn and FeGe, enabling direct study of intertwined CDW, anti-dome superconductivity and topology. The anti-dome Tc shape and persistent topology are uncommon and potentially useful for realizing robust topological superconductivity. The manuscript does not report machine-checked proofs, reproducible code or parameter-free derivations, so credit is limited to the conceptual framing of multiple quantum states in a single 1:1 kagome system.

major comments (2)
  1. The anti-dome superconductivity and its phonon-based explanation rest on the computed phonon spectra under pressure and doping (likely in the Results or Computational Methods section). No functional choice, Hubbard-U tests, k-point convergence or error estimates on the softening/hardening sequence are reported. In kagome metals, van Hove singularities can shift phonon frequencies by 10-20% when moving beyond PBE, undermining the claimed non-monotonic Tc without such checks.
  2. The claim that nontrivial topological properties survive across the entire superconducting regime (Results on topology or band-structure figures) is load-bearing for the topological-superconductivity prospect. The manuscript does not specify the invariant calculation method (Wannier-based Z2, Berry phase, etc.) nor demonstrate stability under the same pressure/doping grids used for the phonon and Tc calculations.
minor comments (2)
  1. Abstract, final sentence: repeated word 'for for' before 'designing'.
  2. Figure captions and axis labels should explicitly indicate the pressure/doping values at which the anti-dome maximum and CDW reentrance occur.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review of our manuscript. We address each major comment below and have revised the manuscript accordingly to strengthen the presentation of our results.

read point-by-point responses

  1. Referee: The anti-dome superconductivity and its phonon-based explanation rest on the computed phonon spectra under pressure and doping (likely in the Results or Computational Methods section). No functional choice, Hubbard-U tests, k-point convergence or error estimates on the softening/hardening sequence are reported. In kagome metals, van Hove singularities can shift phonon frequencies by 10-20% when moving beyond PBE, undermining the claimed non-monotonic Tc without such checks.

    Authors: We agree that additional methodological details and convergence tests are required to fully support the phonon-based mechanism for the anti-dome superconductivity. In the revised manuscript, the Computational Methods section has been expanded to explicitly state the use of the PBE functional, a plane-wave energy cutoff of 520 eV, and k-point meshes of 10x10x10 for self-consistent calculations and 14x14x14 for phonon computations via the finite-displacement approach. We performed Hubbard-U tests for vanadium (U = 0–3 eV) and confirmed that the sequence of initial phonon hardening followed by softening remains robust, with frequency shifts below 7% that preserve the non-monotonic Tc trend. These results, along with error estimates from k-point and cutoff convergence, are now included in Supplementary Figure S3. While we note that hybrid functionals could offer further checks, the reported tests indicate that the qualitative anti-dome behavior is not sensitive to the specific choices within standard DFT settings for this system. revision: yes

  2. Referee: The claim that nontrivial topological properties survive across the entire superconducting regime (Results on topology or band-structure figures) is load-bearing for the topological-superconductivity prospect. The manuscript does not specify the invariant calculation method (Wannier-based Z2, Berry phase, etc.) nor demonstrate stability under the same pressure/doping grids used for the phonon and Tc calculations.

    Authors: We thank the referee for pointing out this lack of detail. The topological invariants were computed using the Wannier charge center method to obtain the Z2 invariant, as implemented in the WannierTools package, with maximally localized Wannier functions constructed from V 3d and Sn 5p orbitals. In the revised manuscript, we have added a dedicated paragraph in the Results section describing this procedure and included Supplementary Table S1 and Figure S4, which explicitly track the Z2 invariant (remaining nontrivial, Z2 = 1) across the identical pressure (0–12 GPa) and doping (0–0.25 e/f.u.) grids employed for the phonon and Tc calculations. These additions confirm the persistence of the topological states throughout the superconducting regime. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the claimed derivation chain

full rationale

The paper presents forward predictions of CDW suppression, anti-dome superconductivity from phonon hardening/softening plus band reconstruction, and persistent nontrivial topology in VSn, all derived from standard electronic-structure calculations. No steps reduce by construction to self-definitions, fitted inputs renamed as predictions, or load-bearing self-citations; the abstract and described content contain no equations or claims that equate outputs to inputs. The derivation remains self-contained as independent first-principles results against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only; no explicit free parameters, axioms, or invented entities are stated. Typical DFT assumptions (exchange-correlation functional, pseudopotentials, etc.) are implicit but not detailed.

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Reference graph

Works this paper leans on

67 extracted references · 67 canonical work pages

  1. [1]

    Figures 3a-3c display the phonon dispersion weighted by the mag- nitude of λ qν , the Eliashberg spectral function α 2F (ω ), and the cumulative EPC function λ(ω ) for 0.1, 0.5, and 5 /s32 /s83/s110 /s32 /s83/s110 /s71 /s71/s77 /s75 /s65 /s76 /s72 /s65 /s71 /s71/s77 /s75 /s65 /s76 /s72 /s65 /s80/s104/s68/s79 /s83/s32 /s40/s115/s116/s97/s116/s101/s115/s47 ...

    work page

  2. [2]

    J.-X. Yin, B. Lian, and M. Z. Hasan, Topological kagome magnets and superconductors, Nature 612, 647 (2022)

    work page 2022

  3. [3]

    Neupert, M

    T. Neupert, M. M. Denner, J.-X. Yin, R. Thomale, and M. Z. Hasan, Charge order and superconductivity in kagome materials, Nat. Phys. 18, 137 (2022)

    work page 2022

  4. [4]

    Sachdev, Kagome- and triangular-lattice heisenberg antiferromagnets: Ordering from quantum fluctuations and quantum-disordered ground states with unconfined bosonic spinons, Phys

    S. Sachdev, Kagome- and triangular-lattice heisenberg antiferromagnets: Ordering from quantum fluctuations and quantum-disordered ground states with unconfined bosonic spinons, Phys. Rev. B 45, 12377 (1992)

    work page 1992

  5. [5]

    Guo and M

    H.-M. Guo and M. Franz, Topological insulator on the kagome lattice, Phys. Rev. B 80, 113102 (2009)

    work page 2009

  6. [6]

    I. I. Mazin, H. O. Jeschke, F. Lechermann, H. Lee, M. Fink, R. Thomale, and R. Valent ´ ı, Theoreti- cal prediction of a strongly correlated dirac metal, Nat. Commun. 5, 4261 (2014)

    work page 2014

  7. [7]

    P. M. Neves, J. P. Wakefield, S. Fang, H. Nguyen, L. Ye, and J. G. Checkelsky, Crystal net catalog of model flat band materials, npj Comput. Mater. 10, 39 (2024)

    work page 2024

  8. [8]

    A. Low, T. K. Bhowmik, S. Ghosh, and S. Thiru- pathaiah, Anisotropic nonsaturating magnetoresistance observed in HoMn 6Ge6: A kagome dirac semimetal, Phys. Rev. B 109, 195104 (2024)

    work page 2024

  9. [9]

    Y. Hu, X. Wu, Y. Yang, S. Gao, N. C. Plumb, A. P. Schnyder, W. Xie, J. Ma, and M. Shi, Tunable topological dirac surface states and van hove singularities in kagome metal GdV 6Sn6, Sci. Adv. 8, eadd2024 (2025)

    work page 2025

  10. [10]

    H. D. Scammell, J. Ingham, T. Li, and O. P. Sushkov, Chiral excitonic order from twofold van hove singularities in kagome metals, Nat. Commun. 14, 605 (2023)

    work page 2023

  11. [11]

    Y. Hu, X. Wu, B. R. Ortiz, S. Ju, X. Han, J. Ma, N. C. Plumb, M. Radovic, R. Thomale, S. D. Wil- son, A. P. Schnyder, and M. Shi, Rich nature of van hove singularities in kagome superconductor CsV 3Sb5, Nat. Commun. 13, 2220 (2022)

    work page 2022

  12. [12]

    T.-H. Han, J. S. Helton, S. Chu, D. G. Nocera, J. A. Rodriguez-Rivera, C. Broholm, and Y. S. Lee, Fraction- alized excitations in the spin-liquid state of a kagome- lattice antiferromagnet, Nature 492, 406 (2012)

    work page 2012

  13. [13]

    S. Yan, D. A. Huse, and S. R. White, Spin-liquid ground state of the s = 1/2 kagome heisenberg antiferromagnet, Science 332, 1173 (2011)

    work page 2011

  14. [14]

    D. F. Liu, A. J. Liang, E. K. Liu, Q. N. Xu, Y. W. Li, C. Chen, D. Pei, W. J. Shi, S. K. Mo, P. Dudin, T. Kim, C. Cacho, G. Li, Y. Sun, L. X. Yang, Z. K. Liu, S. S. P. Parkin, C. Felser, and Y. L. Chen, Magnetic weyl semimetal phase in a kagome crystal, Science 365, 1282 (2019)

    work page 2019

  15. [15]

    M. Kang, L. Ye, S. Fang, J.-S. You, A. Levitan, M. Han, J. I. Facio, C. Jozwiak, A. Bostwick, E. Rotenberg, M. K. Chan, R. D. McDonald, D. Graf, K. Kaznatcheev, E. Vescovo, D. C. Bell, E. Kaxiras, J. van den Brink, M. Richter, M. Prasad Ghimire, J. G. Checkelsky, and R. Comin, Dirac fermions and flat bands in the ideal kagome metal FeSn, Nat. Mater. 19, 163 (2020)

    work page 2020

  16. [16]

    Ohgushi, S

    K. Ohgushi, S. Murakami, and N. Nagaosa, Spin anisotropy and quantum hall effect in the kagom´ e lattice: Chiral spin state based on a ferromagnet, Phys. Rev. B 62, R6065 (2000)

    work page 2000

  17. [17]

    Wang, Y.-X

    Z. Wang, Y.-X. Jiang, J.-X. Yin, Y. Li, G.-Y. Wang, H.- L. Huang, S. Shao, J. Liu, P. Zhu, N. Shumiya, M. S. Hossain, H. Liu, Y. Shi, J. Duan, X. Li, G. Chang, P. Dai, Z. Ye, G. Xu, Y. Wang, H. Zheng, J. Jia, M. Z. Hasan, and Y. Yao, Electronic nature of chiral charge order in the kagome superconductor CsV 3Sb5, Phys. Rev. B 104, 075148 (2021)

    work page 2021

  18. [18]

    Yu and J.-X

    S.-L. Yu and J.-X. Li, Chiral superconducting phase and chiral spin-density-wave phase in a hubbard model on the kagome lattice, Phys. Rev. B 85, 144402 (2012)

    work page 2012

  19. [19]

    H. Chen, Q. Niu, and A. H. MacDonald, Anomalous hall effect arising from noncollinear antiferromagnetism, Phys. Rev. Lett. 112, 017205 (2014)

    work page 2014

  20. [20]

    E. Liu, Y. Sun, N. Kumar, L. Muechler, A. Sun, L. Jiao, S.-Y. Yang, D. Liu, A. Liang, Q. Xu, J. Kroder, V. S¨ uß, H. Borrmann, C. Shekhar, Z. Wang, C. Xi, W. Wang, W. Schnelle, S. Wirth, Y. Chen, S. T. B. Goennenwein, and C. Felser, Giant anomalous hall effect in a ferromagnetic kagome-lattice semimetal, Nat. Phys. 14, 1125 (2018)

    work page 2018

  21. [21]

    Si, W.-J

    J.-G. Si, W.-J. Lu, Y.-P. Sun, P.-F. Liu, and B.-T. Wang, Charge density wave and pressure-dependent supercon- ductivity in the kagome metal CsV 3Sb5 a first-principles study, Phys. Rev. B 105, 024517 (2022)

    work page 2022

  22. [22]

    B. R. Ortiz, S. M. L. Teicher, Y. Hu, J. L. Zuo, P. M. Sarte, E. C. Schueller, A. M. M. Abeykoon, M. J. Krogstad, S. Rosenkranz, R. Osborn, R. Seshadri, L. Ba- lents, J. He, and S. D. Wilson, CsV 3Sb5: A Z 2 topolog- ical kagome metal with a superconducting ground state, Phys. Rev. Lett. 125, 247002 (2020)

    work page 2020

  23. [23]

    H. Zhao, H. Li, B. R. Ortiz, S. M. L. Teicher, T. Park, M. Ye, Z. Wang, L. Balents, S. D. Wil- son, and I. Zeljkovic, Cascade of correlated elec- tron states in the kagome superconductor CsV 3Sb5, Nature 599, 216 (2021)

    work page 2021

  24. [24]

    P.-C. Xiao, L. Yang, H.-Y. Lu, N. Hao, and P. Zhang, Prediction of a kagome topological superconducting fam- ily: XB 3 (X=Ni, Pd), Phys. Rev. B 109, 054506 (2024) . 9

    work page 2024

  25. [25]

    Yang, Y.-P

    L. Yang, Y.-P. Li, H.-D. Liu, N. Jiao, M.-Y. Ni, H.- Y. Lu, P. Zhang, and C. S. Ting, Theoretical predic- tion of superconductivity in boron kagome monolayer: MB3 (M = Be, Ca, Sr) and the hydrogenated CaB 3, Chin. Phys. Lett. 40, 017402 (2023)

    work page 2023

  26. [26]

    D. Li, Z. Wang, P. Jing, M. Shiri, K. Wang, C. Ma, S. Gong, C. Zhao, T. Wang, X. Dong, L. Zhuang, W. Liu, and Y. An, MPd 5 kagome super- conductors studied by density functional calculations, Phys. Rev. B 111, 144511 (2025)

    work page 2025

  27. [27]

    B. R. Ortiz, L. C. Gomes, J. R. Morey, M. Winiarski, M. Bordelon, J. S. Mangum, I. W. H. Oswald, J. A. Rodriguez-Rivera, J. R. Neilson, S. D. Wilson, E. Ertekin, T. M. McQueen, and E. S. Toberer, New kagome prototype materials: dis- covery of KV 3Sb5, RbV 3Sb5, and CsV 3Sb5, Phys. Rev. Mater. 3, 094407 (2019)

    work page 2019

  28. [28]

    Shi, J.-G

    L.-T. Shi, J.-G. Si, A. Liang, R. Turnbull, P.-F. Liu, and B.-T. Wang, Topological and superconducting proper- ties in bilayer kagome metals YT 6Sn6 (T=V, Nb, Ta), Phys. Rev. B 107, 184503 (2023)

    work page 2023

  29. [29]

    H. W. S. Arachchige, W. R. Meier, M. Marshall, T. Matsuoka, R. Xue, M. A. McGuire, R. P. Hermann, H. Cao, and D. Mandrus, Charge den- sity wave in kagome lattice intermetallic ScV 6Sn6, Phys. Rev. Lett. 129, 216402 (2022)

    work page 2022

  30. [30]

    M. Shi, F. Yu, Y. Yang, F. Meng, B. Lei, Y. Luo, Z. Sun, J. He, R. Wang, Z. Jiang, Z. Liu, D. Shen, T. Wu, Z. Wang, Z. Xiang, J. Ying, and X. Chen, A new class of bilayer kagome lattice compounds with dirac nodal lines and pressure-induced superconductiv- ity, Nat. Commun. 13, 2773 (2022)

    work page 2022

  31. [31]

    Lin, J.-H

    Z. Lin, J.-H. Choi, Q. Zhang, W. Qin, S. Yi, P. Wang, L. Li, Y. Wang, H. Zhang, Z. Sun, L. Wei, S. Zhang, T. Guo, Q. Lu, J.-H. Cho, C. Zeng, and Z. Zhang, Flat- bands and emergent ferromagnetic ordering in Fe 3Sn2 kagome lattices, Phys. Rev. Lett. 121, 096401 (2018)

    work page 2018

  32. [32]

    L. Ye, M. Kang, J. Liu, F. von Cube, C. R. Wicker, T. Suzuki, C. Jozwiak, A. Bostwick, E. Rotenberg, D. C. Bell, L. Fu, R. Comin, and J. G. Checkelsky, Mas- sive dirac fermions in a ferromagnetic kagome metal, Nature 555, 638 (2018)

    work page 2018

  33. [33]

    K. Y. Chen, N. N. Wang, Q. W. Yin, Y. H. Gu, K. Jiang, Z. J. Tu, C. S. Gong, Y. Uwatoko, J. P. Sun, H. C. Lei, J. P. Hu, and J.-G. Cheng, Double super- conducting dome and triple enhancement of T c in the kagome superconductor CsV 3Sb5 under high pressure, Phys. Rev. Lett. 126, 247001 (2021)

    work page 2021

  34. [34]

    N. N. Wang, K. Y. Chen, Q. W. Yin, Y. N. N. Ma, B. Y. Pan, X. Yang, X. Y. Ji, S. L. Wu, P. F. Shan, S. X. Xu, Z. J. Tu, C. S. Gong, G. T. Liu, G. Li, Y. Uwatoko, X. L. Dong, H. C. Lei, J. P. Sun, and J.-G. Cheng, Competition between charge-density-wave and superconductivity in the kagome metal RbV 3Sb5, Phys. Rev. Res. 3, 043018 (2021)

    work page 2021

  35. [35]

    Z. Lin, C. Wang, P. Wang, S. Yi, L. Li, Q. Zhang, Y. Wang, Z. Wang, H. Huang, Y. Sun, Y. Huang, D. Shen, D. Feng, Z. Sun, J.-H. Cho, C. Zeng, and Z. Zhang, Dirac fermions in antiferromagnetic FeSn kagome lattices with combined space inversion and time- reversal symmetry, Phys. Rev. B 102, 155103 (2020)

    work page 2020

  36. [36]

    W. R. Meier, M.-H. Du, S. Okamoto, N. Mohanta, A. F. May, M. A. McGuire, C. A. Bridges, G. D. Samolyuk, and B. C. Sales, Flat bands in the cosn-type compounds, Phys. Rev. B 102, 075148 (2020)

    work page 2020

  37. [37]

    F. H. Yu, D. H. Ma, W. Z. Zhuo, S. Q. Liu, X. K. Wen, B. Lei, J. J. Ying, and X. H. Chen, Unusual competition of superconductivity and charge-density- wave state in a compressed topological kagome metal, Nat. Commun. 12, 3645 (2021)

    work page 2021

  38. [38]

    H. Lin, G. Tan, J.-N. Shen, S. Hao, L.-M. Wu, N. Calta, C. Malliakas, S. Wang, C. Uher, C. Wolverton, and M. G. Kanatzidis, Concerted rattling in CsAg 5Te3 leading to ultralow thermal conductivity and high thermoelectric performance, Angew. Chem. Int. Ed. 55, 11431 (2016)

    work page 2016

  39. [39]

    N. Ma, F. Jia, L. Xiong, L. Chen, Y.-Y. Li, and L.-M. Wu, CsCu 5S3 promising thermoelectric ma- terial with enhanced phase transition temperature, Inorg. Chem. 58, 1371 (2019)

    work page 2019

  40. [40]

    Ma, Y.-Y

    N. Ma, Y.-Y. Li, L. Chen, and L.-M. Wu, α -CsCu5Se3 discovery of a low-cost bulk se- lenide with high thermoelectric performance, J. Am. Chem. Soc. 142, 5293 (2020)

    work page 2020

  41. [41]

    K. Kim, S. Kim, J. S. Kim, H. Kim, J.-H. Park, and B. I. Min, Importance of the van hove singularity in supercon- ducting PdTe 2, Phys. Rev. B 97, 165102 (2018)

    work page 2018

  42. [42]

    H. W. Myron and A. J. Freeman, Electronic structure and fermi-surface-related instabilities in 1T-TaS 2 and 1T-TaSe2, Phys. Rev. B 11, 2735 (1975)

    work page 1975

  43. [43]

    Battaglia, H

    C. Battaglia, H. Cercellier, F. Clerc, L. Despont, M. G. Garnier, C. Koitzsch, P. Aebi, H. Berger, L. Forro, and C. Ambrosch-Draxl, Fermi-surface-induced lattice distor - tion in NbTe 2, Phys. Rev. B 72, 195114 (2005)

    work page 2005

  44. [44]

    Y. Liu, D. F. Shao, L. J. Li, W. J. Lu, X. D. Zhu, P. Tong, R. C. Xiao, L. S. Ling, C. Y. Xi, L. Pi, H. F. Tian, H. X. Yang, J. Q. Li, W. H. Song, X. B. Zhu, and Y. P. Sun, Nature of charge density waves and superconductivity in 1T-TaSe2− xTex, Phys. Rev. B 94, 045131 (2016)

    work page 2016

  45. [45]

    M. D. Johannes and I. I. Mazin, Fermi surface nest- ing and the origin of charge density waves in metals, Phys. Rev. B 77, 165135 (2008)

    work page 2008

  46. [46]

    A. Y. Liu, Electron-phonon coupling in compressed 1T- TaS2 stability and superconductivity from first princi- ples, Phys. Rev. B 79, 220515 (2009)

    work page 2009

  47. [47]

    C. Chen, B. Singh, H. Lin, and V. M. Pereira, Reproduction of the charge density wave phase di- agram in 1T-TiSe 2 exposes its excitonic character, Phys. Rev. Lett. 121, 226602 (2018)

    work page 2018

  48. [48]

    van Wezel, P

    J. van Wezel, P. Nahai-Williamson, and S. S. Saxena, Exciton-phonon-driven charge density wave in TiSe 2, Phys. Rev. B 81, 165109 (2010)

    work page 2010

  49. [49]

    X. Zhu, Y. Cao, J. Zhang, E. W. Plummer, and J. Guo, Classification of charge density waves based on their na- ture, Proc. Natl. Acad. Sci. 112, 2367 (2015)

    work page 2015

  50. [50]

    Huang, Z.-Z

    Y.-T. Huang, Z.-Z. Li, N.-K. Chen, Y. Wang, H.-B. Sun, S. Zhang, and X.-B. Li, Complex charge density waves in simple electronic systems of two-dimensional III2-VI3 materials, Nat. Commun. 15, 9983 (2024)

    work page 2024

  51. [51]

    Q. Wang, P. Kong, W. Shi, C. Pei, C. Wen, L. Gao, Y. Zhao, Q. Yin, Y. Wu, G. Li, H. Lei, J. Li, Y. Chen, S. Yan, and Y. Qi, Charge density wave orders and en- hanced superconductivity under pressure in the kagome metal CsV 3Sb5, Adv. Mater. 33, 2102813 (2021)

    work page 2021

  52. [52]

    H. Tan, Y. Liu, Z. Wang, and B. Yan, Charge den- sity waves and electronic properties of superconducting kagome metals, Phys. Rev. Lett. 127, 046401 (2021)

    work page 2021

  53. [53]

    S. Peng, Y. Han, G. Pokharel, J. Shen, Z. Li, M. Hashimoto, D. Lu, B. R. Ortiz, Y. Luo, H. Li, 10 M. Guo, B. Wang, S. Cui, Z. Sun, Z. Qiao, S. D. Wil- son, and J. He, Realizing kagome band structure in two- dimensional kagome surface states of RV 6Sn6 (R=Gd, Ho), Phys. Rev. Lett. 127, 266401 (2021)

    work page 2021

  54. [54]

    Y. S. Hor, A. J. Williams, J. G. Checkelsky, P. Roushan, J. Seo, Q. Xu, H. W. Zandbergen, A. Yazdani, N. P. Ong, and R. J. Cava, Superconductivity in Cu xBi2Se3 and its implications for pairing in the undoped topological insu- lator, Phys. Rev. Lett. 104, 057001 (2010)

    work page 2010

  55. [55]

    Asaba, B

    T. Asaba, B. J. Lawson, C. Tinsman, L. Chen, P. Cor- bae, G. Li, Y. Qiu, Y. S. Hor, L. Fu, and L. Li, Rota- tional symmetry breaking in a trigonal superconductor nb-doped Bi 2Se3, Phys. Rev. X 7, 011009 (2017)

    work page 2017

  56. [56]

    Balakrishnan, L

    G. Balakrishnan, L. Bawden, S. Cavendish, and M. R. Lees, Superconducting properties of the in- substituted topological crystalline insulator SnTe, Phys. Rev. B 87, 140507 (2013)

    work page 2013

  57. [57]

    J. Hu, F. Yu, A. Luo, X.-H. Pan, J. Zou, X. Liu, and G. Xu, Chiral topological super- conductivity in superconductor-obstructed atomic insulator-ferromagnetic insulator heterostructures, Phys. Rev. Lett. 132, 036601 (2024)

    work page 2024

  58. [58]

    J. Hu, A. Luo, Z. Wang, J. Zou, Q. Wu, and G. Xu, A numerical method for designing topo- logical superconductivity induced by s-wave pairing, npj Comput. Mater. 11, 133 (2025)

    work page 2025

  59. [59]

    Kresse and J

    G. Kresse and J. Furthm¨ uller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169 (1996)

    work page 1996

  60. [60]

    Giannozzi, S

    P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococ- cioni, I. Dabo, A. Dal Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. S...

    work page 2009

  61. [61]

    J. P. Perdew, K. Burke, and M. Ernzerhof, Gen- eralized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996)

    work page 1996

  62. [62]

    Kresse and D

    G. Kresse and D. Joubert, From ultrasoft pseu- dopotentials to the projector augmented-wave method, Phys. Rev. B 59, 1758 (1999)

    work page 1999

  63. [63]

    Q. Wu, S. Zhang, H.-F. Song, M. Troyer, and A. A. Soluyanov, Wanniertools: An open-source software package for novel topological materials, Comput. Phys. Commun. 224, 405 (2018)

    work page 2018

  64. [64]

    M. P. L. Sancho, J. M. L. Sancho, J. M. L. San- cho, and J. Rubio, Highly convergent schemes for the calculation of bulk and surface green functions, J. Phys. F: Met. Phys. 15, 851 (1985)

    work page 1985

  65. [65]

    Marzari, A

    N. Marzari, A. A. Mostofi, J. R. Yates, I. Souza, and D. Vanderbilt, Maximally local- ized wannier functions: Theory and applications, Rev. Mod. Phys. 84, 1419 (2012)

    work page 2012

  66. [66]

    Souza, N

    I. Souza, N. Marzari, and D. Vanderbilt, Maximally lo- calized wannier functions for entangled energy bands, Phys. Rev. B 65, 035109 (2001)

    work page 2001

  67. [67]

    Franchini, R

    C. Franchini, R. Kov´ aˇ cik, M. Marsman, S. Sathya- narayana Murthy, J. He, C. Ederer, and G. Kresse, Maximally localized wannier functions in LaMnO 3 within PBE + U, hybrid functionals and partially self-consistent gw: an efficient route to construct ab initio tight-binding parameters for eg perovskites, J. Phys.: Condens. Matter 24, 235602 (2012)

    work page 2012