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  • Letter
  • Open Access

Competing phases in the kagome magnet FeGe from functional renormalization

Pietro M. Bonetti1,2, Yi Jiang3, Haoyu Hu4, Dumitru Călugăru4, Michael M. Scherer5, B. Andrei Bernevig3,4,6, and Laura Classen2,7

Phys. Rev. B 112, L220405 – Published 2 December, 2025

DOI: https://doi.org/10.1103/2j4h-gptn

Abstract

The discovery of a charge density wave in FeGe extends the discussion of the nature of charge order in kagome metals to a magnetic compound. Motivated by this observation, we combine density functional theory (DFT) and functional-renormalization-group calculations to study interaction-induced Fermi-surface instabilities of the magnetic state of FeGe. We argue that the leading intra-band contribution to electronic correlations are approximately two-dimensional (2D) and come from Van Hove points at the projected M points. By varying parameters around DFT values, we determine a phase diagram for the quasi-2D scenario as function of on-site and nearest-neighbor interactions. We discuss universal aspects in the electronic mechanisms for the resulting phases, as well as the role of SU(2) symmetry breaking. We find FeGe to be in a regime of strong competition between p-wave charge density wave, f-wave pairing, and d-wave spin Pomeranchuk instabilities. This interplay can be influenced in favor of superconducting pairing for slightly increased nearest-neighbor interaction, suggesting a potential to induce superconductivity in FeGe.

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References (84)

  1. 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).
  2. K. Jiang, T. Wu, J.-X. Yin, Z. Wang, M. Z. Hasan, S. D. Wilson, X. Chen, and J. Hu, Kagome superconductors AV3Sb5 (A = K, Rb, Cs), Natl. Sci. Rev. 10, nwac199 (2023).
  3. Y. Hu, X. Wu, A. P. Schnyder, and M. Shi, Electronic landscape of kagome superconductors AV3Sb5 (A = K, Rb, Cs) from angle-resolved photoemission spectroscopy, npj Quantum Mater. 8, 67 (2023).
  4. Q. Wang, H. Lei, Y. Qi, and C. Felser, Topological quantum materials with kagome lattice, Accounts Mater. Res. 5, 786 (2024).
  5. 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: Discovery of KV3Sb5,RbV3Sb5, and CsV3Sb5, Phys. Rev. Mater. 3, 094407 (2019).
  6. Y.-X. Jiang, J.-X. Yin, M. M. Denner, N. Shumiya, B. R. Ortiz, G. Xu, Z. Guguchia, J. He, M. S. Hossain, X. Liu, J. Ruff, L. Kautzsch, S. S. Zhang, G. Chang, I. Belopolski, Q. Zhang, T. A. Cochran, D. Multer, M. Litskevich, Z.-J. Cheng et al., Unconventional chiral charge order in kagome superconductor KV3Sb5, Nat. Mater. 20, 1353 (2021).
  7. Z. Liang, X. Hou, F. Zhang, W. Ma, P. Wu, Z. Zhang, F. Yu, J.-J. Ying, K. Jiang, L. Shan, Z. Wang, and X.-H. Chen, Three-dimensional charge density wave and surface-dependent vortex-core states in a kagome superconductor CsV3Sb5, Phys. Rev. X 11, 031026 (2021).
  8. R. Khasanov, D. Das, R. Gupta, C. Mielke, M. Elender, Q. Yin, Z. Tu, C. Gong, H. Lei, E. T. Ritz, R. M. Fernandes, T. Birol, Z. Guguchia, and H. Luetkens, Time-reversal symmetry broken by charge order in CsV3Sb5, Phys. Rev. Res. 4, 023244 (2022).
  9. R. Gupta, D. Das, I. Mielke, Charles, E. Ritz, F. Hotz, Q. Yin, Z. Tu, C. Gong, H. Lei, T. Birol, R. M. Fernandes, Z. Guguchia, H. Luetkens, and R. Khasanov, Two types of charge order in the superconducting kagome material CsV3Sb5, arXiv:2203.05055.
  10. H. Zhao, H. Li, B. R. Ortiz, S. M. L. Teicher, T. Park, M. Ye, Z. Wang, L. Balents, S. D. Wilson, and I. Zeljkovic, Cascade of correlated electron states in the kagome superconductor CsV3Sb5, Nature (London) 599, 216 (2021).
  11. M. Kang, S. Fang, J.-K. Kim, B. R. Ortiz, S. H. Ryu, J. Kim, J. Yoo, G. Sangiovanni, D. Di Sante, B.-G. Park, C. Jozwiak, A. Bostwick, E. Rotenberg, E. Kaxiras, S. D. Wilson, J.-H. Park, and R. Comin, Twofold van hove singularity and origin of charge order in topological kagome superconductor CsV3Sb5, Nat. Phys. 18, 301 (2022).
  12. Y. Xu, Z. Ni, Y. Liu, B. R. Ortiz, Q. Deng, S. D. Wilson, B. Yan, L. Balents, and L. Wu, Three-state nematicity and magneto-optical Kerr effect in the charge density waves in kagome superconductors, Nat. Phys. 18, 1470 (2022).
  13. M. Kang, S. Fang, J. Yoo, B. R. Ortiz, Y. M. Oey, J. Choi, S. H. Ryu, J. Kim, C. Jozwiak, A. Bostwick, E. Rotenberg, E. Kaxiras, J. G. Checkelsky, S. D. Wilson, J.-H. Park, and R. Comin, Charge order landscape and competition with superconductivity in kagome metals, Nat. Mater. 22, 186 (2023).
  14. Y. Hu, X. Wu, B. R. Ortiz, S. Ju, X. Han, J. Ma, N. C. Plumb, M. Radovic, R. Thomale, S. D. Wilson, A. P. Schnyder, and M. Shi, Rich nature of Van Hove singularities in kagome superconductor CsV3Sb5, Nat. Commun. 13, 2220 (2022).
  15. Y. Hu, X. Wu, B. R. Ortiz, X. Han, N. C. Plumb, S. D. Wilson, A. P. Schnyder, and M. Shi, Coexistence of trihexagonal and star-of-David pattern in the charge density wave of the kagome superconductor AV3Sb5, Phys. Rev. B 106, L241106 (2022).
  16. C. Li, X. Wu, H. Liu, C. Polley, Q. Guo, Y. Wang, X. Han, M. Dendzik, M. H. Berntsen, B. Thiagarajan, Y. Shi, A. P. Schnyder, and O. Tjernberg, Coexistence of two intertwined charge density waves in a kagome system, Phys. Rev. Res. 4, 033072 (2022).
  17. Y. Xing, S. Bae, E. Ritz, F. Yang, T. Birol, A. N. Capa Salinas, B. R. Ortiz, S. D. Wilson, Z. Wang, R. M. Fernandes, and V. Madhavan, Optical manipulation of the charge-density-wave state in RbV3Sb5, Nature (London) 631, 60 (2024).
  18. B. R. Ortiz, P. M. Sarte, E. M. Kenney, M. J. Graf, S. M. L. Teicher, R. Seshadri, and S. D. Wilson, Superconductivity in the Z2 kagome metal KV3Sb5, Phys. Rev. Mater. 5, 034801 (2021).
  19. 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. Balents, J. He, and S. D. Wilson, CsV3Sb5: A Z2 topological kagome metal with a superconducting ground state, Phys. Rev. Lett. 125, 247002 (2020).
  20. H. Chen, H. Yang, B. Hu, Z. Zhao, J. Yuan, Y. Xing, G. Qian, Z. Huang, G. Li, Y. Ye, S. Ma, S. Ni, H. Zhang, Q. Yin, C. Gong, Z. Tu, H. Lei, H. Tan, S. Zhou, C. Shen et al., Roton pair density wave in a strong-coupling kagome superconductor, Nature (London) 599, 222 (2021).
  21. R. Gupta, D. Das, C. H. Mielke III, Z. Guguchia, T. Shiroka, C. Baines, M. Bartkowiak, H. Luetkens, R. Khasanov, Q. Yin, Z. Tu, C. Gong, and H. Lei, Microscopic evidence for anisotropic multigap superconductivity in the CsV3Sb5 kagome superconductor, npj Quantum Mater. 7, 49 (2022).
  22. 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 superconducting dome and triple enhancement of Tc in the kagome superconductor CsV3Sb5 under high pressure, Phys. Rev. Lett. 126, 247001 (2021).
  23. Y. Zhong, S. Li, H. Liu, Y. Dong, K. Aido, Y. Arai, H. Li, W. Zhang, Y. Shi, Z. Wang, S. Shin, H. N. Lee, H. Miao, T. Kondo, and K. Okazaki, Testing electron–phonon coupling for the superconductivity in kagome metal CsV3Sb5, Nat. Commun. 14, 1945 (2023).
  24. Y. Zhong, J. Liu, X. Wu, Z. Guguchia, J. X. Yin, A. Mine, Y. Li, S. Najafzadeh, D. Das, C. Mielke, R. Khasanov, H. Luetkens, T. Suzuki, K. Liu, X. Han, T. Kondo, J. Hu, S. Shin, Z. Wang, X. Shi et al., Nodeless electron pairing in CsV3Sb5-derived kagome superconductors, Nature (London) 617, 488 (2023).
  25. X. Teng, L. Chen, F. Ye, E. Rosenberg, Z. Liu, J.-X. Yin, Y.-X. Jiang, J. S. Oh, M. Z. Hasan, K. J. Neubauer, B. Gao, Y. Xie, M. Hashimoto, D. Lu, C. Jozwiak, A. Bostwick, E. Rotenberg, R. J. Birgeneau, J.-H. Chu, M. Yi et al., Discovery of charge density wave in a kagome lattice antiferromagnet, Nature (London) 609, 490 (2022).
  26. X. Teng, J. S. Oh, H. Tan, L. Chen, J. Huang, B. Gao, J.-X. Yin, J.-H. Chu, M. Hashimoto, D. Lu, C. Jozwiak, A. Bostwick, E. Rotenberg, G. E. Granroth, B. Yan, R. J. Birgeneau, P. Dai, and M. Yi, Magnetism and charge density wave order in kagome FeGe, Nat. Phys. 19, 814 (2023).
  27. K. Tang, H. Zhou, H. Li, S. Pan, X. Wu, H. Li, N. Zhang, C. Xi, J. Zhang, A. Wang, X. Wan, Z. Xiang, and X. Chen, Evidence for unfolded fermi surfaces in the charge-density-wave state of kagome metal FeGe revealed by De Haas–Van Alphen effect, Phys. Rev. Res. 6, 013276 (2024).
  28. M. Wenzel, E. Uykur, A. A. Tsirlin, S. Pal, R. M. Roy, C. Yi, C. Shekhar, C. Felser, A. V. Pronin, and M. Dressel, Intriguing low-temperature phase in the antiferromagnetic kagome metal FeGe, Phys. Rev. Lett. 132, 266505 (2024).
  29. S. Yi, Z. Liao, Q. Wang, H. Ma, J. Liu, X. Teng, P. Dai, Y. Dai, J. Zhao, Y. Qi, B. Xu, and X. Qiu, Polarized charge dynamics of a novel charge density wave in kagome FeGe, Phys. Rev. Lett. 134, 086902 (2025).
  30. C. Shi, H. Deng, S. Rohith Kotla, Y. Liu, S. Ramakrishnan, C. Eisele, H. Agarwal, L. Noohinejad, J.-Y. Liu, T. Yang, G. Liu, B. B. Maity, Q. Wang, Z. Lin, B. Kang, W. Yang, Y. Li, Z. Yang, Y. Li, Y. Qi et al., Charge density wave without long-range structural modulation in canted antiferromagnetic kagome FeGe, arXiv:2404.00996.
  31. J. S. Oh, A. Biswas, M. Klemm, H. Tan, M. Hashimoto, D. Lu, B. Yan, P. Dai, R. J. Birgeneau, and M. Yi, Tunability of charge density wave in a magnetic kagome metal, Sci. Adv. 11, eadt2195 (2025).
  32. X. Teng, D. W. Tam, L. Chen, H. Tan, Y. Xie, B. Gao, G. E. Granroth, A. Ivanov, P. Bourges, B. Yan, M. Yi, and P. Dai, Spin-Charge-Lattice coupling across the charge density wave transition in a kagome lattice antiferromagnet, Phys. Rev. Lett. 133, 046502 (2024).
  33. S. Han, L. Li, C. Sin Tang, Q. Wang, L. Zhang, C. Diao, M. Zhao, S. Sun, L. Tian, M. B. H. Breese, C. Cai, M. V. Milosevic, Y. Qi, A. T. S. Wee, and X. Yin, Orbital origin of magnetic moment enhancement induced by charge density wave in kagome FeGe, arXiv:2407.01076.
  34. D. Subires, A. Kar, A. Korshunov, C. A. Fuller, Y. Jiang, H. Hu, D. Călugăru, C. McMonagle, C. Yi, S. Roychowdhury, C. Shekhar, J. Strempfer, A. Jana, I. Vobornik, J. Dai, M. Tallarida, D. Chernyshov, A. Bosak, C. Felser, B. A. Bernevig et al., Frustrated charge density wave and quasilong-range bond-orientational order in the magnetic kagome FeGe, Nat. Commun. 16, 4091 (2025).
  35. T. Ohoyama, K. Kanematsu, and K. Yasukōchi, A new intermetallic compound FeGe, J. Phys. Soc. Jpn. 18, 589 (1963).
  36. O. Beckman, K. Carrander, L. Lundgren, and M. Richardson, Susceptibility measurements and magnetic ordering of hexagonal FeGe, Phys. Scr. 6, 151 (1972).
  37. J. Bernhard, B. Lebech, and O. Beckman, Neutron diffraction studies of the low-temperature magnetic structure of hexagonal FeGe, J. Phys. F 14, 2379 (1984).
  38. J. Bernhard, B. Lebech, and O. Beckman, Magnetic phase diagram of hexagonal FeGe determined by neutron diffraction, J. Phys. F 18, 539 (1988).
  39. A. Ptok, S. Basak, A. Kobiałka, M. Sternik, J. Łażewski, P. T. Jochym, A. M. Oleś, and P. Piekarz, Lattice dynamics study of electron-correlation-induced charge density wave in antiferromagnetic kagome metal FeGe, Phys. Rev. Mater. 8, L080601 (2024).
  40. H. Miao, T. T. Zhang, H. X. Li, G. Fabbris, A. H. Said, R. Tartaglia, T. Yilmaz, E. Vescovo, J. X. Yin, S. Murakami, X. L. Feng, K. Jiang, X. L. Wu, A. F. Wang, S. Okamoto, Y. L. Wang, and H. N. Lee, Signature of spin-phonon coupling driven charge density wave in a kagome magnet, Nat. Commun. 14, 6183 (2023).
  41. X. Wen, Y. Zhang, C. Li, Z. Gui, Y. Li, Y. Li, X. Wu, A. Wang, P. Yang, B. Wang, J. Cheng, Y. Wang, J. Ying, and X. Chen, Unconventional charge density wave in a kagome lattice antiferromagnet FeGe, Phys. Rev. Res. 6, 033222 (2024).
  42. X. Wu, X. Mi, L. Zhang, C.-W. Wang, N. Maraytta, X. Zhou, M. He, M. Merz, Y. Chai, and A. Wang, Annealing-Tunable charge density wave in the magnetic kagome material FeGe, Phys. Rev. Lett. 132, 256501 (2024).
  43. A. Korshunov, A. Kar, C. Y. Lim, D. Subires, J. Deng, Y. Jiang, H. Hu, D. Călugăru, C. Yi, S. Roychowdhury, C. Shekhar, G. Garbarino, P. Törmä, C. Felser, B. A. Bernevig, and S. Blanco-Canosa, Pressure induced quasi-long-range 3×3 charge density wave and competing orders in the kagome metal FeGe, arXiv:2409.04325.
  44. M. L. Kiesel and R. Thomale, Sublattice interference in the kagome hubbard model, Phys. Rev. B 86, 121105(R) (2012).
  45. M. L. Kiesel, C. Platt, and R. Thomale, Unconventional Fermi surface instabilities in the kagome Hubbard model, Phys. Rev. Lett. 110, 126405 (2013).
  46. W.-S. Wang, Z.-Z. Li, Y.-Y. Xiang, and Q.-H. Wang, Competing electronic orders on kagome lattices at van Hove filling, Phys. Rev. B 87, 115135 (2013).
  47. J. B. Profe, L. Klebl, F. Grandi, H. Hohmann, M. Dürrnagel, T. Schwemmer, R. Thomale, and D. M. Kennes, Kagome hubbard model from a functional renormalization group perspective, Phys. Rev. Res. 6, 043078 (2024).
  48. T. Schwemmer, H. Hohmann, M. Dürrnagel, J. Potten, J. Beyer, S. Rachel, Y.-M. Wu, S. Raghu, T. Müller, W. Hanke, and R. Thomale, Sublattice modulated superconductivity in the kagome Hubbard model, Phys. Rev. B 110, 024501 (2024).
  49. Y.-P. Lin, C. Liu, and J. E. Moore, Complex magnetic and spatial symmetry breaking from correlations in kagome flat bands, Phys. Rev. B 110, L041121 (2024).
  50. M. H. Christensen, T. Birol, B. M. Andersen, and R. M. Fernandes, Loop currents in AV3Sb5 kagome metals: Multipolar and toroidal magnetic orders, Phys. Rev. B 106, 144504 (2022).
  51. M. H. Christensen, T. Birol, B. M. Andersen, and R. M. Fernandes, Theory of the charge density wave in AV3Sb5 kagome metals, Phys. Rev. B 104, 214513 (2021).
  52. E. T. Ritz, R. M. Fernandes, and T. Birol, Impact of sb degrees of freedom on the charge density wave phase diagram of the kagome metal CsV3Sb5, Phys. Rev. B 107, 205131 (2023).
  53. M. M. Denner, R. Thomale, and T. Neupert, Analysis of charge order in the kagome metal AV3Sb5 (A=K,Rb,Cs), Phys. Rev. Lett. 127, 217601 (2021).
  54. Y.-P. Lin and R. M. Nandkishore, Complex charge density waves at van Hove singularity on hexagonal lattices: Haldane-model phase diagram and potential realization in the kagome metals AV3Sb5 (A=K, Rb, Cs), Phys. Rev. B 104, 045122 (2021).
  55. Y. Jiang, H. Hu, D. Călugăru, C. Felser, S. Blanco-Canosa, H. Weng, Y. Xu, and B. A. Bernevig, Kagome materials II: SG 191: FeGe as a LEGO building block for the entire 1:6:6 series: Hidden d-orbital decoupling of flat band sectors, effective models and interaction hamiltonians, Phys. Rev. B 111, 125163 (2025).
  56. L. Chen, X. Teng, H. Tan, B. L. Winn, G. E. Granroth, F. Ye, D. H. Yu, R. A. Mole, B. Gao, B. Yan, M. Yi, and P. Dai, Competing itinerant and local spin interactions in kagome metal FeGe, Nat. Commun. 15, 1918 (2024).
  57. See Supplemental Material at http://link.aps.org/supplemental/10.1103/2j4h-gptn for more details, which also contains Refs. [74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84].
  58. Note that other FRG schemes realying a form factor decomposition may require the treatment of a large number of form factors, which makes them less suited to tackle the present problem.
  59. W. Metzner, M. Salmhofer, C. Honerkamp, V. Meden, and K. Schönhammer, Functional renormalization group approach to correlated fermion systems, Rev. Mod. Phys. 84, 299 (2012).
  60. C. Platt, W. Hanke, and R. Thomale, Functional renormalization group for multiorbital Fermi surface instabilities, Adv. Phys. 62, 453 (2013).
  61. C. Wu, K. Sun, E. Fradkin, and S.-C. Zhang, Fermi liquid instabilities in the spin channel, Phys. Rev. B 75, 115103 (2007).
  62. V. Gali, M. Hecker, and R. M. Fernandes, A critical nematic phase with pseudogap-like behavior in twisted bilayers, Phys. Rev. Lett. 133, 236501 (2025).
  63. I. Mandal and R. M. Fernandes, Valley-polarized nematic order in twisted moiré systems: In-plane orbital magnetism and crossover from non-Fermi liquid to Fermi liquid, Phys. Rev. B 107, 125142 (2023).
  64. 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).
  65. D. V. Chichinadze, L. Classen, and A. V. Chubukov, Valley magnetism, nematicity, and density wave orders in twisted bilayer graphene, Phys. Rev. B 102, 125120 (2020).
  66. In our gauge choice for the orbital-to-band transformation [57] the form factors are not periodic and it is important to distinguish Q and M in the transformation to real space.
  67. In our quasi2D model, an incommensurate, out-of-plane magnetic wave vector (π/2+δ)êz that connects minority and majority spin would manifest as a q=0 FM-xy order.
  68. S. C. Holbæk, M. H. Christensen, A. Kreisel, and B. M. Andersen, Unconventional superconductivity protected from disorder on the kagome lattice, Phys. Rev. B 108, 144508 (2023).
  69. X. Wu, D. Chakraborty, A. P. Schnyder, and A. Greco, Crossover between electron-electron and electron-phonon mediated pairing on the kagome lattice, Phys. Rev. B 109, 014517 (2024).
  70. L. Wu, Y. Hu, D. Fan, D. Wang, and X. Wan, Electron-correlation-induced charge density wave in FeGe, Chin. Phys. Lett. 40, 117103 (2023).
  71. H.-Y. Ma, J.-X. Yin, M. Z. Hasan, and J. Liu, Theory for charge density wave and orbital-flux state in antiferromagnetic kagome metal FeGe, Chin. Phys. Lett. 41, 047103 (2024).
  72. H. Tan and B. Yan, Disordered charge density waves in the kagome metal FeGe, Phys. Rev. B 111, 045160 (2025).
  73. R.-Q. Fu, J. Zhan, M. Dürrnagel, H. Hohmann, R. Thomale, J. Hu, Z. Wang, S. Zhou, and X. Wu, Exotic charge density waves and superconductivity on the kagome lattice, arXiv:2405.09451.
  74. G. Kresse and J. Furthmüller, Efficiency of ab initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mater. Sci. 6, 15 (1996).
  75. G. Kresse and J. Hafner, Ab initio molecular dynamics for open-shell transition metals, Phys. Rev. B 48, 13115 (1993).
  76. G. Kresse and J. Hafner, Ab initio molecular dynamics for liquid metals, Phys. Rev. B 47, 558 (1993).
  77. G. Kresse and J. Hafner, Ab initio molecular-dynamics simulation of the liquid-metal–amorphous-semiconductor transition in germanium, Phys. Rev. B 49, 14251 (1994).
  78. 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).
  79. N. Marzari and D. Vanderbilt, Maximally localized generalized wannier functions for composite energy bands, Phys. Rev. B 56, 12847 (1997).
  80. I. Souza, N. Marzari, and D. Vanderbilt, Maximally localized wannier functions for entangled energy bands, Phys. Rev. B 65, 035109 (2001).
  81. N. Marzari, A. A. Mostofi, J. R. Yates, I. Souza, and D. Vanderbilt, Maximally localized wannier functions: Theory and applications, Rev. Mod. Phys. 84, 1419 (2012).
  82. G. Pizzi, V. Vitale, R. Arita, S. Blügel, F. Freimuth, G. Géranton, M. Gibertini, D. Gresch, C. Johnson, T. Koretsune et al., Wannier90 as a community code: New features and applications, J. Phys.: Condens. Matter 32, 165902 (2020).
  83. H. Hu, Y. Jiang, D. Călugăru, X. Feng, D. Subires, M. G. Vergniory, C. Felser, S. Blanco-Canosa, and B. A. Bernevig, Kagome materials i: Sg 191, scv _6 sn _6. Flat phonon soft modes and unconventional cdw formation: Microscopic and effective theory, Phys. Rev. B 111, 054113 (2025).
  84. C. Honerkamp and M. Salmhofer, Temperature-flow renormalization group and the competition between superconductivity and ferromagnetism, Phys. Rev. B 64, 184516 (2001).

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