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Effective Ionic Valence and Local Magnetic Moment in Kagome Superconductors

Ruoshi Jiang1,2, Zi-Jian Lang1, Yuzki Oey3, Andrea Capa Salinas3, Stephen D. Wilson3, Yongwei Li4, Ilya Shipulin5,4, Yiwen Zhang4, Deng Hu6 et al.

Zhiwei Wang6,7, Hans-Henning Klauss8, Zurab Guguchia9, Vadim Grinenko4,†, and Wei Ku1,10,11,*

  • *Contact author: weiku@sjtu.edu.cn
  • †Contact author: vadim.grinenko@sjtu.edu.cn

Phys. Rev. X 16, 031064 – Published 10 September, 2026

DOI: https://doi.org/10.1103/t5nf-jksr

Abstract

In order to understand the unexpected similarity and the correlated behavior in kagome superconductor families AV3Sb5 (A=K,Rb,Cs) and ATi3Bi5 (A=Rb,Cs), we investigate the Hartree-scale local electronic structure of these systems. Our result indicates that V and Ti ions are both of 2+ valence such that the corresponding itinerant carrier densities are similar, and the difference in electron count is instead reflected in their quantum fluctuating ionic magnetic moments. However, due to the frustrated lattice geometry of these materials, such local moments are difficult to experimentally observe via standard probes. For verification, we systematically introduce nonmagnetic Sn impurities to locally relieve the geometric frustration and experimentally demonstrate the existence of well-defined local magnetic moments via magnetic susceptibility and muon spin rotation or relaxation (μSR) measurements. All experiments discover a systematic increase of magnetic susceptibility upon increasing nonmagnetic impurity level. Our discovered ionic moments suggest a paradigm shift from the existing itinerant carrier-only picture to one incorporating strong correlation from local ionic spins. The associated interatomic and local-itinerant correlations offer a solid ground for the emergence of the observed rich correlated behavior in this new family of superconducting materials.

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References (145)

  1. B. R. Ortiz, L. C. Gomes, J. R. Morey, M. Winiarski, M. Bordelon, J. S. Mangum, Iain W. H. Oswald, Jose 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).
  2. Mingu Kang, Shiang Fang, Jeong-Kyu Kim, Brenden Ortiz, Sae Hee Ryu, Jimin Kim, Jonggyu Yoo, Giorgio Sangiovanni, Domenico Sante, Byeong-Gyu Park, Chris Jozwiak, Aaron Bostwick, Eli Rotenberg, Efthimios Kaxiras, Stephen Wilson, Jae-Hoon Park, and Riccardo Comin, Twofold van Hove singularity and origin of charge order in topological kagome superconductor CsV3Sb5, Nat. Phys. 18, 301 (2022).
  3. H. Chen et al., Roton pair density wave in a strong-coupling kagome superconductor, Nature (London) 599, 222 (2021).
  4. Rustem Khasanov, Debarchan Das, Ritu Gupta, Charles Mielke, Matthias Elender, Qiangwei Yin, Zhijun Tu, Chunsheng Gong, Hechang Lei, Ethan T. Ritz, Rafael M. Fernandes, Turan Birol, Zurab Guguchia, and Hubertus Luetkens, Time-reversal symmetry broken by charge order in CsV3Sb5, Phys. Rev. Res. 4, 023244 (2022).
  5. Yuxiao Jiang, Jiaxin Yin, M. Denner, Nana Shumiya, Brenden Ortiz, Gang Xu, Z. Guguchia, Junyi He, Md Shafayat Hossain, Xiaoxiong Liu, Jacob Ruff, Linus Kautzsch, Songtian Zhang, Guoqing Chang, Ilya Belopolski, Qi Zhang, Tyler Cochran, Daniel Multer, Maksim Litskevich, and M. Zahid Hasan, Unconventional chiral charge order in kagome superconductor KV3Sb5, Nat. Mater. 20, 1353 (2021).
  6. Ying Xiang, Qing Li, Yongkai Li, Wei Xie, Huan Yang, Zhiwei Wang, Yugui Yao, and Hai-Hu Wen, Twofold symmetry of c-axis resistivity in topological kagome superconductor CsV3Sb5 with in-plane rotating magnetic field, Nat. Commun. 12, 6727 (2021).
  7. Noah Ratcliff, Lily Hallett, Brenden R. Ortiz, Stephen D. Wilson, and John W. Harter, Coherent phonon spectroscopy and interlayer modulation of charge density wave order in the kagome metal CsV3Sb5, Phys. Rev. Mater. 5, L111801 (2021).
  8. Ece Uykur, Brenden R. Ortiz, Stephen D. Wilson, Martin Dressel, and Alexander A. Tsirlin, Optical detection of the density-wave instability in the kagome metal KV3Sb5, npj Quantum Mater. 7, 16 (2022).
  9. B. R. Ortiz, Samuel M. L. Teicher, L. Kautzsch, P. M. Sarte, N. Ratcliff, J. Harter, Jacob P. C. Ruff, R. Seshadri, and S. D. Wilson, Fermi surface mapping and the nature of charge-density-wave order in the kagome superconductor CsV3Sb5, Phys. Rev. X 11, 041030 (2021).
  10. Cong Li, Xianxin Wu, Hongxiong Liu, Craig Polley, Qinda Guo, Yang Wang, Xinloong Han, Maciej Dendzik, Magnus H. Berntsen, Balasubramanian Thiagarajan, Youguo Shi, Andreas P. Schnyder, and Oscar Tjernberg, Coexistence of two intertwined charge density waves in a kagome system, Phys. Rev. Res. 4, 033072 (2022).
  11. Rui Lou, Alexander Fedorov, Qiangwei Yin, Andrii Kuibarov, Zhijun Tu, Chunsheng Gong, Eike F. Schwier, Bernd Büchner, Hechang Lei, and Sergey Borisenko, Charge-density-wave-induced peak-dip-hump structure and the multiband superconductivity in a kagome superconductor CsV3Sb5, Phys. Rev. Lett. 128, 036402 (2022).
  12. Haoxiang Li, T. T. Zhang, T. Yilmaz, Y. Y. Pai, C. E. Marvinney, A. Said, Q. W. Yin, C. S. Gong, Z. J. Tu, E. Vescovo, C. S. Nelson, R. G. Moore, S. Murakami, H. C. Lei, H. N. Lee, B. J. Lawrie, and H. Miao, Observation of unconventional charge density wave without acoustic phonon anomaly in kagome superconductors AV3Sb5(A=Rb,Cs), Phys. Rev. X 11, 031050 (2021).
  13. Hailan Luo, Qiang Gao, Hongxiong Liu, Yuhao Gu, Dingsong Wu, Changjiang Yi, Junjie Jia, Shilong Wu, Xiangyu Luo, Yu Xu, Lin Zhao, Qingyan Wang, Hanqing Mao, Guodong Liu, Zhihai Zhu, Youguo Shi, Kun Jiang, Jiangping Hu, Zuyan Xu, and X. J. Zhou, Electronic nature of charge density wave and electron-phonon coupling in kagome superconductor KV3Sb5, Nat. Commun. 13, 273 (2022).
  14. Hong Li, He Zhao, Brenden R. Ortiz, Takamori Park, Mengxing Ye, Leon Balents, Ziqiang Wang, Stephen D. Wilson, and Ilija Zeljkovic, Rotation symmetry breaking in the normal state of a kagome superconductor KV3Sb5, Nat. Phys. 18, 265 (2022).
  15. Linpeng Nie, Sun Kuanglv, Wanru Ma, Dianwu Song, Lixuan Zheng, Zuowei Liang, Ping Wu, Fanghang Yu, Jian Li, Min Shan, Dan Zhao, Shunjiao Li, Baolei Kang, Zhimian Wu, Yanbing Zhou, Kai Liu, Ziji Xiang, Jianjun Ying, and Xianhui Chen, Charge-density-wave-driven electronic nematicity in a kagome superconductor, Nature (London) 604, 59 (2022).
  16. Shangfei Wu, Brenden R. Ortiz, Hengxin Tan, Stephen D. Wilson, Binghai Yan, Turan Birol, and Girsh Blumberg, Charge density wave order in the kagome metal AV3Sb5 (A=Cs,Rb,K), Phys. Rev. B 105, 155106 (2022).
  17. Li Yu, Chennan Wang, Yuhang Zhang, Mathias Sander, Shunli Ni, Zouyouwei Lu, Sheng Ma, Zhengguo Wang, Zhen Zhao, Hui Chen, Kun Jiang, Yan Zhang, Haitao Yang, Fang Zhou, Xiaoli Dong, Steven L. Johnson, Michael J. Graf, Jiangping Hu, Hong-Jun Gao, and Zhongxian Zhao, Evidence of a hidden flux phase in the topological kagome metal CsV3Sb5, arXiv:2107.10714.
  18. Takamori Park, Mengxing Ye, and Leon Balents, Electronic instabilities of kagome metals: Saddle points and Landau theory, Phys. Rev. B 104, 035142 (2021).
  19. Yu-Ping Lin and Rahul 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).
  20. 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).
  21. Hengxin Tan, Yizhou Liu, Ziqiang Wang, and Binghai Yan, Charge density waves and electronic properties of superconducting kagome metals, Phys. Rev. Lett. 127, 046401 (2021).
  22. Morten H. Christensen, Turan Birol, Brian M. Andersen, and Rafael M. Fernandes, Theory of the charge density wave in AV3Sb5 kagome metals, Phys. Rev. B 104, 214513 (2021).
  23. Chandan Setty, Haoyu Hu, Lei Chen, and Qimiao Si, Electron correlations and t-breaking density wave order in a Z2 kagome metal, arXiv:2105.15204.
  24. Xilin Feng, Yi Zhang, Kun Jiang, and Jiangping Hu, Low-energy effective theory and symmetry classification of flux phases on the kagome lattice, Phys. Rev. B 104, 165136 (2021).
  25. Sen Zhou and Ziqiang Wang, Chern Fermi pocket, topological pair density wave, and charge-4e and charge-6e superconductivity in kagome superconductors, Nat. Commun. 13, 7288 (2022).
  26. Rina Tazai, Youichi Yamakawa, Seiichiro Onari, and Hiroshi Kontani, Mechanism of exotic density-wave and beyond-migdal unconventional superconductivity in kagome metal AV3Sb5 (A=K,Rb,Cs), Sci. Adv. 8, eabl4108 (2022).
  27. Alaska Subedi, Hexagonal-to-base-centered-orthorhombic 4q charge density wave order in kagome metals KV3Sb5,RbV3Sb5 and CsV3Sb5, Phys. Rev. Mater. 6, 015001 (2022).
  28. Zhonghao Liu, Ningning Zhao, Qiangwei Yin, Chunsheng Gong, Zhijun Tu, Man Li, Wenhua Song, Zhengtai Liu, Dawei Shen, Yaobo Huang, Kai Liu, Hechang Lei, and Shancai Wang, Charge-density-wave-induced bands renormalization and energy gaps in a kagome superconductor RbV3Sb5, Phys. Rev. X 11, 041010 (2021).
  29. N. Shumiya et al., Intrinsic nature of chiral charge order in the kagome superconductor RbV3Sb5, Phys. Rev. B 104, 035131 (2021).
  30. Qi Wang, Pengfei Kong, Wujun Shi, Cuiying Pei, Chenhaoping Wen, Lingling Gao, Yi Zhao, Qiangwei Yin, Yueshen Wu, Gang Li, Hechang Lei, Jun Li, Yulin Chen, Shichao Yan, and Yanpeng Qi, Charge density wave orders and enhanced superconductivity under pressure in the kagome metal CsV3Sb5, Adv. Mater. 33, 2102813 (2021).
  31. Xilin Feng, Kun Jiang, Ziqiang Wang, and Jiangping Hu, Chiral flux phase in the kagome superconductor AV3Sb5, Sci. Bull. 66, 1384 (2021).
  32. X. Wu, T. Schwemmer, T. Müller, A. Consiglio, G. Sangiovanni, D. Di Sante, Y. Iqbal, W. Hanke, A. P. Schnyder, M. M. Denner, M. H. Fischer, T. Neupert, and R. Thomale, Nature of unconventional pairing in the kagome superconductors AV3Sb5 (A=K,Rb,Cs), Phys. Rev. Lett. 127, 177001 (2021).
  33. C. Mielke III, D. Das, J.-X. Yin, H. Liu, R. Gupta, Y.-X. Jiang, M. Medarde, X. Wu, H. C. Lei, J. J. Chang, P. Dai, Q. Si, H. Miao, R. Thomale, T. Neupert, Y. Shi, R. Khasanov, M. Z. Hasan, H. Luetkens, and Z. Guguchia, Time-reversal symmetry breaking charge order in a kagome superconductor, Nature (London) 602, 245 (2022).
  34. Zuowei Liang, Xingyuan Hou, Fan Zhang, Wanru Ma, Ping Wu, Zongyuan Zhang, Fanghang Yu, J.-J. Ying, Kun Jiang, Lei Shan, Zhenyu 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).
  35. Lixuan Zheng, Zhimian Wu, Ye Yang, Linpeng Nie, Min Shan, Kuanglv Sun, Dianwu Song, Fanghang Yu, Jian Li, Dan Zhao, Shunjiao Li, Baolei Kang, Yanbing Zhou, Kai Liu, Ziji Xiang, Jianjun Ying, Zhenyu Wang, Tao Wu, and Xianhui Chen, Emergent charge order in pressurized kagome superconductor CsV3Sb5, Nature (London) 611, 682 (2022).
  36. Yuxin Wang, Tao Wu, Zheng Li, Kun Jiang, and Jiangping Hu, Structure of the kagome superconductor CsV3Sb5 in the charge density wave state, Phys. Rev. B 107, 184106 (2023).
  37. Zhengguo Wang, Sheng Ma, Yuhang Zhang, Haitao Yang, Zhen Zhao, Yi Ou, Yu Zhu, Shunli Ni, Zouyouwei Lu, Hui Chen, Kun Jiang, Li Yu, Yan Zhang, Xiaoli Dong, Jiangping Hu, Hong-Jun Gao, and Zhongxian Zhao, Distinctive momentum dependent charge-density-wave gap observed in CsV3Sb5 superconductor with topological kagome lattice, arXiv:2104.05556.
  38. F. H. Yu, T. Wu, Z. Y. Wang, B. Lei, W. Z. Zhuo, J. J. Ying, and X. H. Chen, Concurrence of anomalous Hall effect and charge density wave in a superconducting topological kagome metal, Phys. Rev. B 104, L041103 (2021).
  39. Xiaoxiang Zhou, Yongkai Li, Xinwei Fan, Jiahao Hao, Yaomin Dai, Zhiwei Wang, Yugui Yao, and Hai-Hu Wen, Origin of charge density wave in the kagome metal CsV3Sb5 as revealed by optical spectroscopy, Phys. Rev. B 104, L041101 (2021).
  40. Ge He, Leander Peis, Emma Frances Cuddy, Zhen Zhao, Dong Li, Ramona Stumberger, Brian Moritz, Haitao Yang, Hong-Jun Gao, Thomas Peter Devereaux, and Rudi Hackl, Anharmonic strong-coupling effects at the origin of the charge density wave in CsV3Sb5, Nat. Commun. 15, 1895 (2024).
  41. He Zhao, Hong Li, Brenden R. Ortiz, Samuel M. L. Teicher, Takamori Park, Mengxing Ye, Ziqiang Wang, Leon Balents, Stephen D. Wilson, and Ilija Zeljkovic, Cascade of correlated electron states in the kagome superconductor CsV3Sb5, Nature (London) 599, 216 (2021).
  42. Z. Guguchia et al., Tunable unconventional kagome superconductivity in charge ordered RbV3Sb5 and KV3Sb5, Nat. Commun. 14, 153 (2023).
  43. Ritu Gupta, Debarchan Das, Charles Mielke III, Ethan Ritz, Fabian Hotz, Qiangwei Yin, Zhijun Tu, Chunsheng Gong, Hechang Lei, Turan Birol, Rafael Fernandes, Z. Guguchia, Hubertus Luetkens, and Rustem Khasanov, Two types of charge order with distinct interplay with superconductivity in the kagome material CsV3Sb5, Commun. Phys. 5, 232 (2022).
  44. Huazhou Li, Siyuan Wan, Han Li, Qing Li, Qiangqiang Gu, Huan Yang, Yongkai Li, Zhiwei Wang, Yugui Yao, and Hai-Hu Wen, No observation of chiral flux current in the topological kagome metal CsV3Sb5, Phys. Rev. B 105, 045102 (2022).
  45. Qiangwei Yin, Zhijun Tu, Chunsheng Gong, Yang Fu, Shaohua Yan, and Hechang Lei, Superconductivity and normal-state properties of kagome metal RbV3Sb5 single crystals, Chin. Phys. Lett. 38, 037403 (2021).
  46. Feng Du, Shuaishuai Luo, Brenden R. Ortiz, Ye Chen, Weiyin Duan, Dongting Zhang, Xin Lu, Stephen D. Wilson, Yu Song, and Huiqiu Yuan, Pressure-induced double superconducting domes and charge instability in the kagome metal KV3Sb5, Phys. Rev. B 103, L220504 (2021).
  47. Fanghang Yu, Donghui Ma, Weizhuang Zhuo, Shiqiu Liu, Xikai Wen, Bin Lei, Jianjun Ying, and Xianhui Chen, Unusual competition of superconductivity and charge-density-wave state in a compressed topological kagome metal, Nat. Commun. 12, 3645 (2021).
  48. C. C. Zhu, X. F. Yang, W. Xia, Q. W. Yin, L. S. Wang, C. C. Zhao, D. Z. Dai, C. P. Tu, B. Q. Song, Z. C. Tao, Z. J. Tu, C. S. Gong, H. C. Lei, Y. F. Guo, and S. Y. Li, Double-dome superconductivity under pressure in the V-based kagome metals AV3Sb5 (A=Rb and K), Phys. Rev. B 105, 094507 (2022).
  49. Yanpeng Song, Tianping Ying, Xu Chen, Xu Han, Xianxin Wu, Andreas P. Schnyder, Yuan Huang, Jian-Gang Guo, and Xiaolong Chen, Enhancement of superconductivity in hole-doped CsV3Sb5 thin films, Phys. Rev. Lett. 127, 237001 (2021).
  50. Weiyin Duan, Zhiyong Nie, Shuaishuai Luo, Fanghang Yu, Brenden R. Ortiz, Lichang Yin, Hang Su, Feng Du, An Wang, Ye Chen, Xin Lu, Jianjun Ying, Stephen D. Wilson, Xianhui Chen, Yu Song, and Huiqiu Yuan, Nodeless superconductivity in the kagome metal CsV3Sb5, Sci. China Phys. Mech. Astron. 64, 107462 (2021).
  51. Chao Mu, Qiangwei Yin, Zhijun Tu, Chunsheng Gong, Hechang Lei, Zheng Li, and Jianlin Luo, S-wave superconductivity in kagome metal CsV3Sb5 revealed by 121/123Sb NQR and 51V NMR measurements, Chin. Phys. Lett. 38, 077402 (2021).
  52. Kosuke Nakayama, Yongkai Li, Takemi Kato, Min Liu, Zhiwei Wang, Takashi Takahashi, Yugui Yao, and Takafumi Sato, Carrier injection and manipulation of charge-density wave in kagome superconductor CsV3Sb5, Phys. Rev. X 12, 011001 (2022).
  53. Thanh Nguyen and Mingda Li, Electronic properties of correlated kagome metals AV3Sb5 (A=K,Rb, and Cs): A perspective, J. Appl. Phys. 131, 060901 (2022).
  54. D. W. Song, L. X. Zheng, F. H. Yu, J. Li, L. P. Nie, M. Shan, D. Zhao, S. J. Li, B. L. Kang, Z. M. Wu, Y. B. Zhou, K. L. Sun, K. Liu, X. G. Luo, Z. Y. Wang, J. J. Ying, X. G. Wan, T. Wu, and X. H. Chen, Orbital ordering and fluctuations in a kagome superconductor CsV3Sb5, Sci. China Phys. Mech. Astron. 65, 247462 (2022).
  55. Andrea N. Capa Salinas, Brenden R. Ortiz, Calvin Bales, Jonathan Frassineti, Vesna F. Mitrović, and Stephen D. Wilson, Electron-hole asymmetry in the phase diagram of carrier-tuned CsV3Sb5, Front. Electron. Mater. 3, 1257490 (2023).
  56. Shuo-Ying Yang, Yaojia Wang, Brenden R. Ortiz, Defa Liu, Jacob Gayles, Elena Derunova, Rafael Gonzalez-Hernandez, Libor Smejkal, Yulin Chen, Stuart S. P. Parkin, Stephen D. Wilson, Eric S. Toberer, Tyrel McQueen, and Mazhar N. Ali, Giant, unconventional anomalous Hall effect in the metallic frustrated magnet candidate, KV3Sb5, Sci. Adv. 6, eabb6003 (2020).
  57. Dong Chen, Bin He, Mengyu Yao, Yu Pan, Haicheng Lin, Walter Schnelle, Yan Sun, Johannes Gooth, Louis Taillefer, and Claudia Felser, Anomalous thermoelectric effects and quantum oscillations in the kagome metal CsV3Sb5, Phys. Rev. B 105, L201109 (2022).
  58. Xinrun Mi, Wei Xia, Long Zhang, Yuhan Gan, Kunya Yang, Aifeng Wang, Yisheng Chai, Yanfeng Guo, Xiaoyuan Zhou, and Mingquan He, Multiband effects in thermoelectric and electrical transport properties of kagome superconductors AV3Sb5(A=K,Rb,Cs), New J. Phys. 24, 093021 (2022).
  59. J. Nie, X. Yang, X. Zhang, X. Liu, W. Xia, D. Dai, C. Zhao, C. Tu, X. Kong, X. Jin, Yanfeng Guo, and S. Li, Pressure-induced double-dome superconductivity in kagome metal CsTi3Bi5, Chin. Phys. Lett. 42, 070713 (2025).
  60. Haitao Yang, Yuhan Ye, Zhen Zhao, Jiali Liu, Xin-Wei Yi, Yuhang Zhang, Hongqin Xiao, Jinan Shi, Jing-Yang You, Zihao Huang, Bingjie Wang, Jing Wang, Hui Guo, Xiao Lin, Chengmin Shen, Wu Zhou, Hui Chen, Xiaoli Dong, Gang Su, Ziqiang Wang, and Hong-Jun Gao, Superconductivity and nematic order in a new titanium-based kagome metal CsTi3Bi5 without charge density wave order, Nat. Commun. 15, 9626 (2024).
  61. Yong Hu, Congcong Le, Yuhang Zhang, Zhen Zhao, Jiali Liu, Junzhang Ma, Nicholas C. Plumb, Milan Radovic, Hui Chen, Andreas P. Schnyder, Xianxin Wu, Xiaoli Dong, Jiangping Hu, Haitao Yang, Hong-Jun Gao, and Ming Shi, Non-trivial band topology and orbital-selective electronic nematicity in a titanium-based kagome superconductor, Nat. Phys. 19, 1827 (2023).
  62. Hong Li, Siyu Cheng, Brenden R. Ortiz, Hengxin Tan, Dominik Werhahn, Keyu Zeng, Dirk Johrendt, Binghai Yan, Ziqiang Wang, Stephen D. Wilson, and Ilija Zeljkovic, Electronic nematicity without charge density waves in titanium-based kagome metal, Nat. Phys. 19, 1591 (2023).
  63. Chunyu Guo, Glenn Wagner, Carsten Putzke, Dong Chen, Kaize Wang, Ling Zhang, Martin Gutierrez-Amigo, Ion Errea, Maia G. Vergniory, Claudia Felser, Mark H. Fischer, Titus Neupert, and Philip J. W. Moll, Correlated order at the tipping point in the kagome metal CsV3Sb5, Nat. Phys. 20, 579 (2024).
  64. H. Yang et al., Titanium doped kagome superconductor CsV3−xTixSb5 and two distinct phases, Science bulletin 67, 2176 (2022).
  65. Haitao Yang, Zhen Zhao, Xin-Wei Yi, Jiali Liu, Jing-Yang You, Yuhang Zhang, Hui Guo, Xiao Lin, Chengmin Shen, Hui Chen, Xiaoli Dong, Gang Su, and Hong-Jun Gao, Titanium-based kagome superconductor CsTi3Bi5 and topological states, arXiv:2209.03840.
  66. B. R. Ortiz, Samuel M. L. Teicher, Y. Hu, J. L. Zuo, P. M. Sarte, E. C. Schueller, A. M. Milinda 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).
  67. P. W. Anderson, More is different, Science 177, 393 (1972).
  68. Elbio Dagotto, Complexity in strongly correlated electronic systems, Science 309, 257 (2005).
  69. Eric M Kenney, Brenden R Ortiz, Chennan Wang, Stephen D Wilson, and Michael J Graf, Absence of local moments in the kagome metal KV3Sb5 as determined by muon spin spectroscopy, J. Phys. Condens. Matter 33, 235801 (2021).
  70. KA Chao, J Spalek, and AM Oles, Kinetic exchange interaction in a narrow s-band, J. Phys. C 10, L271 (1977).
  71. Steven White, Numerical canonical transformation approach to quantum many-body problems, J. Chem. Phys. 117, 7472 (2002).
  72. Ruoshi Jiang, Zi-Jian Lang, Tom Berlijn, and Wei Ku, Variation of carrier density in semimetals via short-range correlation: A case study with nickelate NdNiO2, Phys. Rev. B 108, 155126 (2023).
  73. Ruoshi Jiang, Jinning Hou, Zhiyu Fan, Zi-Jian Lang, and Wei Ku, Pressure driven fractionalization of ionic spins results in cupratelike high-Tc superconductivity in La3Ni2O7, Phys. Rev. Lett. 132, 126503 (2024).
  74. Yajian Hu, Soichiro Yamane, Giordano Mattoni, Kanae Yada, Keito Obata, Yongkai Li, Yugui Yao, Zhiwei Wang, Jingyuan Wang, Camron Farhang, Jing Xia, Yoshiteru Maeno, and Shingo Yonezawa, Time-reversal symmetry breaking in charge density wave of CsV3Sb5 detected by polar Kerr effect, arXiv:2208.08036.
  75. Yishuai Xu, Zhuoliang Ni, Yizhou Liu, Brenden R. Ortiz, Qinwen Deng, Stephen D. Wilson, Binghai Yan, Leon Balents, and Liang Wu, Three-state nematicity and magneto-optical Kerr effect in the charge density waves in kagome superconductors, Nat. Phys. 18, 1470 (2022).
  76. T. Asaba, A. Onishi, Y. Kageyama, T. Kiyosue, K. Ohtsuka, S. Suetsugu, Y. Kohsaka, T. Gaggl, Y. Kasahara, H. Murayama, K. Hashimoto, R. Tazai, H. Kontani, Brenden Ortiz, S. Wilson, Qing Li, H. Wen, T. Shibauchi, and Y. Matsuda, Evidence for an odd-parity nematic phase above the charge-density-wave transition in a kagome metal, Nat. Phys. 20, 40 (2024).
  77. Chunyu Guo, Carsten Putzke, Sofia Konyzheva, Xiangwei Huang, Martin Gutierrez-Amigo, Ion Errea, Dong Chen, Maia Vergniory, Claudia Felser, Mark Fischer, Titus Neupert, and P. Moll, Switchable chiral transport in charge-ordered kagome metal CsV3Sb5, Nature (London) 611, 461 (2022).
  78. Xuebo Zhou, Hongxiong Liu, Wei Wu, Kun Jiang, Youguo Shi, Zheng Li, Yu Sui, Jiangping Hu, and Jianlin Luo, Anomalous thermal Hall effect and anomalous Nernst effect of CsV3Sb5, Phys. Rev. B 105, 205104 (2022).
  79. Z. Wang et al., Electronic nature of chiral charge order in the kagome superconductor CsV3Sb5, Phys. Rev. B 104, 075148 (2021).
  80. H. Miao, H. X. Li, W. R. Meier, A. Huon, H. N. Lee, A. Said, H. C. Lei, B. R. Ortiz, S. D. Wilson, J. X. Yin, M. Z. Hasan, Z. Wang, H. Tan, and B. Yan, Geometry of the charge density wave in the kagome metal AV3Sb5, Phys. Rev. B 104, 195132 (2021).
  81. M. Wenzel, B. R. Ortiz, S. D. Wilson, M. Dressel, A. A. Tsirlin, and E. Uykur, Optical study of RbV3Sb5: Multiple density-wave gaps and phonon anomalies, Phys. Rev. B 105, 245123 (2022).
  82. Q. Wu, Z. X. Wang, Q. M. Liu, R. S. Li, S. X. Xu, Q. W. Yin, C. S. Gong, Z. J. Tu, H. C. Lei, T. Dong, and N. L. Wang, Simultaneous formation of two-fold rotation symmetry with charge order in the kagome superconductor CsV3Sb5 by optical polarization rotation measurement, Phys. Rev. B 106, 205109 (2022).
  83. R. Sarkar, P. Schlender, V. Grinenko, E. Haeussler, Peter J. Baker, T. Doert, and H.-H. Klauss, Quantum spin liquid ground state in the disorder free triangular lattice NaYbS2, Phys. Rev. B 100, 241116(R) (2019).
  84. Yuesheng Li, Devashibhai Adroja, Pabitra K. Biswas, Peter J. Baker, Qian Zhang, Juanjuan Liu, Alexander A. Tsirlin, Philipp Gegenwart, and Qingming Zhang, Muon spin relaxation evidence for the U(1) quantum spin-liquid ground state in the triangular antiferromagnet YbMgGaO4, Phys. Rev. Lett. 117, 097201 (2016).
  85. Yong Hu, Xianxin Wu, Brenden R. Ortiz, Sailong Ju, Xinloong Han, Junzhang Ma, Nicholas C. Plumb, Milan Radovic, Ronny Thomale, Stephen D. Wilson, Andreas P. Schnyder, and Ming Shi, Rich nature of van Hove singularities in kagome superconductor CsV3Sb5, Nat. Commun. 13, 2220 (2022).
  86. Aurland K. Watkins, Dirk Johrendt, Vojtech Vlcek, Stephen D. Wilson, and Ram Seshadri, Fidelity and variability in the interlayer electronic structure of the kagome superconductor CsV3Sb5, Phys. Rev. Mater. 8, 054204 (2024).
  87. Jianzhou Zhao, Weikang Wu, Yilin Wang, and Shengyuan A. Yang, Electronic correlations in the normal state of the kagome superconductor KV3Sb5, Phys. Rev. B 103, L241117 (2021).
  88. Min Liu, Zhiwei Wang, and Jin-Jian Zhou, Weak electronic correlations in the kagome superconductor AV3Sb5(A=K,Rb,Cs), Phys. Rev. B 105, 235130 (2022).
  89. See Supplemental Material at http://link.aps.org/supplemental/10.1103/t5nf-jksr for details of (1) atomic Wannier orbitals as basis for H(Hartree), (2) reproducible DFT+U band structures under various magnetic structures, (3) computing density of states in the noncollinear Curie-paramagnetic phase, (4) leading parameters of tii′mm′ for H(Hartree) in Eq. (A1), (5) insensitivity of effective V2+ ionic valence to long-range magnetic order, (6) magnetization measurements on Sn-doped CsV3Sb5−xSnx single crystals, which includes Refs. [90].
  90. Yuzki M. Oey, Brenden R. Ortiz, Farnaz Kaboudvand, Jonathan Frassineti, Erick Garcia, Rong Cong, Samuele Sanna, Vesna F. Mitrović, Ram Seshadri, and Stephen D. Wilson, Fermi level tuning and double-dome superconductivity in the kagome metal CsV3Sb5−xSnx, Phys. Rev. Mater. 6, L041801 (2022).
  91. V. S. Maryasin and M. E. Zhitomirsky, Triangular antiferromagnet with nonmagnetic impurities, Phys. Rev. Lett. 111, 247201 (2013).
  92. Ellen Häußler, Jörg Sichelschmidt, Michael Baenitz, Eric C. Andrade, Matthias Vojta, and Thomas Doert, Diluting a triangular-lattice spin liquid: Synthesis and characterization of NaYb1−xLuxS2 single crystals, Phys. Rev. Mater. 6, 046201 (2022).
  93. Matthias Vojta, Chiranjeeb Buragohain, and Subir Sachdev, Quantum impurity dynamics in two-dimensional antiferromagnets and superconductors, Phys. Rev. B 61, 15152 (2000).
  94. Vadim Grinenko, Konstantin Kikoin, Stefan-Ludwig Drechsler, Günter Fuchs, Konstantin Nenkov, Sabine Wurmehl, Franziska Hammerath, Guillaume Lang, Hans-Joachim Grafe, Bernhard Holzapfel, Jeroen van den Brink, Bernd Büchner, and Ludwig Schultz, As vacancies, local moments, and Pauli limiting in LaFeAs1−δO0.9F0.1 superconductors, Phys. Rev. B 84, 134516 (2011).
  95. N. F. Mott, The mobility edge since 1967, J. Phys. C 20, 3075 (1987).
  96. N. F. Mott, Impurity band conduction. experiment and theory: The metal-insulator transition in an impurity band, J. Phys. (Paris), Colloq. 37, C4-301 (1976).
  97. Robert Freedman and J. A. Hertz, Theory of a Fermi glass, Phys. Rev. B 15, 2384 (1977).
  98. K. A. Müller, T. Penney, M. W. Shafer, and W. J. Fitzpatrick, Pauli paramagnetism in a Fermi glass, Phys. Rev. Lett. 47, 138 (1981).
  99. Hiroshi Kamimura, Theoretical model on the interplay of disorder and electron correlations, Prog. Theor. Phys. Suppl. 72, 206 (1982).
  100. Y. M. Oey, F. Kaboudvand, B. R. Ortiz, R. Seshadri, and S. D. Wilson, Tuning charge density wave order and superconductivity in the kagome metals KV3Sb5−xSnx and RbV3Sb5−xSnx, Phys. Rev. Mater. 6, 074802 (2022).
  101. V. Grinenko, R. Sarkar, P. Materne, S. Kamusella, A. Yamamshita, Y. Takano, Y. Sun, T. Tamegai, D. V. Efremov, S.-L. Drechsler, J.-C. Orain, T. Goko, R. Scheuermann, H. Luetkens, and H.-H. Klauss, Low-temperature breakdown of antiferromagnetic quantum critical behavior in FeSe, Phys. Rev. B 97, 201102(R) (2018).
  102. M. Fujihala, K. Morita, R. Mole, S. Mitsuda, T. Tohyama, S. Yano, D. Yu, S. Sota, T. Kuwai, A. Koda, H. Okabe, H. Lee, S. Itoh, T. Hawai, T. Masuda, H. Sagayama, A. Matsuo, K. Kindo, S. Ohira-Kawamura, and K. Nakajima, Gapless spin liquid in a square-kagome lattice antiferromagnet, Nat. Commun. 11, 3429 (2020).
  103. Zhaoyang Shan, Pabitra K. Biswas, Sudeep K. Ghosh, T. Tula, Adrian D. Hillier, Devashibhai Adroja, Stephen Cottrell, Guang-Han Cao, Yi Liu, Xiaofeng Xu, Yu Song, Huiqiu Yuan, and Michael Smidman, Muon spin relaxation study of the layered kagome superconductor CsV3Sb5, Phys. Rev. Res. 4, 033145 (2022).
  104. Y. Aoki, A. Tsuchiya, T. Kanayama, S. R. Saha, H. Sugawara, H. Sato, W. Higemoto, A. Koda, K. Ohishi, K. Nishiyama, and R. Kadono, Time-reversal symmetry-breaking superconductivity in heavy-fermion PrOs4Sb12 detected by muon-spin relaxation, Phys. Rev. Lett. 91, 067003 (2003).
  105. B. R. Ortiz, P. M. Sarte, E. M. Kenney, M. J. Graf, Samuel M. L. Teicher, R. Seshadri, and S. D. Wilson, Superconductivity in the Z2 kagome metal KV3Sb5, Phys. Rev. Mater. 5, 034801 (2021).
  106. Yang Fu, Ningning Zhao, Zheng Chen, Qiangwei Yin, Zhijun Tu, Chunsheng Gong, Chuanying Xi, Xiangde Zhu, Yuping Sun, Kai Liu, and Hechang Lei, Quantum transport evidence of topological band structures of kagome superconductor CsV3Sb5, Phys. Rev. Lett. 127, 207002 (2021).
  107. Yeahan Sur, Kwang-Tak Kim, Sukho Kim, and Kee Kim, Optimized superconductivity in the vicinity of a nematic quantum critical point in the kagome superconductor Cs(V1−xTix)3Sb5, Nat. Commun. 14, 3899 (2023).
  108. Shunli Ni, Sheng Ma, Yuhang Zhang, Jie Yuan, Haitao Yang, Zouyouwei Lu, Ningning Wang, Jianping Sun, Zhen Zhao, Dong Li, Shaobo Liu, Hua Zhang, Hui Chen, Kui Jin, Jinguang Cheng, Li Yu, Fang Zhou, Xiaoli Dong, Jiangping Hu, Hong-Jun Gao, and Zhongxian Zhao, Anisotropic superconducting properties of kagome metal CsV3Sb5, Chin. Phys. Lett. 38, 057403 (2021).
  109. Ritu Gupta, Debarchan Das, Charles Hillis Mielke III, Zurab Guguchia, Toni Shiroka, Christopher Baines, Marek Bartkowiak, Hubertus Luetkens, Rustem Khasanov, Qiangwei Yin, Zhijun Tu, Chunsheng Gong, and Hechang Lei, Microscopic evidence for anisotropic multigap superconductivity in the CsV3Sb5 kagome superconductor, npj Quantum Mater. 7, 49 (2022).
  110. Yixuan Liu, Yuan Wang, Yongqing Cai, Zhanyang Hao, Xiao-Ming Ma, Le Wang, Cai Liu, Jian Chen, Liang Zhou, Jinhua Wang, Shanmin Wang, Hongtao He, Yi Liu, Shengtao Cui, Bing Huang, Jianfeng Wang, Chaoyu Chen, and Jia-Wei Mei, Doping evolution of superconductivity, charge order, and band topology in hole-doped topological kagome superconductors Cs(V1−xTix)3Sb5, Phys. Rev. Mater. 7, 064801 (2023).
  111. J. Luo, Z. Zhao, Y. Z. Zhou, J. Yang, A. F. Fang, H. T. Yang, H. J. Gao, R. Zhou, and Guo-qing Zheng, Possible star-of-David pattern charge density wave with additional modulation in the kagome superconductor CsV3Sb5, npj Quantum Mater. 7, 30 (2022).
  112. Yu-Ting Tam, Dao-Xin Yao, and Wei Ku, Itinerancy-enhanced quantum fluctuation of magnetic moments in iron-based superconductors, Phys. Rev. Lett. 115, 117001 (2015).
  113. Jinning Hou, Yuting Tan, and Wei Ku, Chemical disorder induced electronic orders in correlated metals: Rekindled failed-order scenario, Phys. Rev. B 109, 195126 (2024).
  114. Shuhua Liang, Gonzalo Alvarez, Cengiz Şen, Adriana Moreo, and Elbio Dagotto, Anisotropy of electrical transport in pnictide superconductors studied using Monte Carlo simulations of the spin-fermion model, Phys. Rev. Lett. 109, 047001 (2012).
  115. Weicheng Lv, Frank Krüger, and Philip Phillips, Orbital ordering and unfrustrated (π,0) magnetism from degenerate double exchange in the iron pnictides, Phys. Rev. B 82, 045125 (2010).
  116. Su-Peng Kou, Tao Li, and Zheng-Yu Weng, Coexistence of itinerant electrons and local moments in iron-based superconductors, Europhys. Lett. 88, 17010 (2009).
  117. Yujie Lan, Yuhao Lei, Congcong Le, Brenden R. Ortiz, Nicholas C. Plumb, Milan Radovic, Xianxin Wu, Ming Shi, Stephen D. Wilson, and Yong Hu, Common sublattice-pure van Hove singularities in the kagome superconductors AV3Sb5 (A=K,Rb,Cs), Phys. Rev. Lett. 136, 016401 (2026).
  118. Wei Zhang, Tsz Fung Poon, Chun Wai Tsang, Wenyan Wang, X. Liu, J. Xie, S. T. Lam, Shanmin Wang, Kwing To Lai, A. Pourret, G. Seyfarth, G. Knebel, Wing Chi Yu, and Swee K. Goh, Large Fermi surface in pristine kagome metal CsV3Sb5 and enhanced quasiparticle effective masses, Proc. Natl. Acad. Sci. U.S.A. 121, e2322270121 (2024).
  119. Patrick A. Lee, Naoto Nagaosa, and Xiao-Gang Wen, Doping a Mott insulator: Physics of high-temperature superconductivity, Rev. Mod. Phys. 78, 17 (2006).
  120. Ying Zhou, Long Chen, Xuecong Ji, Chen Liu, Ke Liao, Zhongnan Guo, Jia’ou Wang, Hongming Weng, and Gang Wang, Physical properties, electronic structure, and strain-tuned monolayer of the weak topological insulator RbTi3Bi5 with kagome lattice, arXiv:2301.01633.
  121. Rina Tazai, Youichi Yamakawa, and Hiroshi Kontani, Charge-loop current order and Z3 nematicity mediated by bond order fluctuations in kagome metals, Nat. Commun. 14, 7845 (2023).
  122. Morten H. Christensen, Turan Birol, Brian M. Andersen, and Rafael M. Fernandes, Loop currents in AV3Sb5 kagome metals: Multipolar and toroidal magnetic orders, Phys. Rev. B 106, 144504 (2022).
  123. P. W. Anderson and H. Hasegawa, Considerations on double exchange, Phys. Rev. 100, 675 (1955).
  124. Clarence Zener, Interaction between the d-shells in the transition metals. II. ferromagnetic compounds of manganese with perovskite structure, Phys. Rev. 82, 403 (1951).
  125. Wei-Guo Yin, Chi-Cheng Lee, and Wei Ku, Unified picture for magnetic correlations in iron-based superconductors, Phys. Rev. Lett. 105, 107004 (2010).
  126. Ruoshi Jiang, Zhiyu Fan, Bartomeu Monserrat, and Wei Ku, Pressure-induced trans-proximate correlation in La4Ni3O10 and possible routes to enhance its superconductivity, arXiv:2505.13442.
  127. Dominik Werhahn, Brenden R. Ortiz, Aurland K. Hay, Stephen D. Wilson, Ram Seshadri, and Dirk Johrendt, The kagome metals RbTi3Bi5 and CsTi3Bi5, Z. Naturforsch. B 77, 757 (2022).
  128. P. Blaha, K. Schwarz, P. Sorantin, and S. B. Trickey, Full-potential, linearized augmented plane wave programs for crystalline systems, Comput. Phys. Commun. 59, 399 (1990).
  129. David J. Singh, Planewaves, Pseudopotentials and the LAPW Method (Springer, New York, 2006).
  130. V. I. Anisimov, I. V. Solovyev, M. A. Korotin, M. T. Czyżyk, and G. A. Sawatzky, Density-functional theory and NiO photoemission spectra, Phys. Rev. B 48, 16929 (1993).
  131. A. I. Liechtenstein, V. I. Anisimov, and J. Zaanen, Density-functional theory and strong interactions: Orbital ordering in Mott-Hubbard insulators, Phys. Rev. B 52, R5467 (1995).
  132. Wei Ku, H. Rosner, W. E. Pickett, and R. T. Scalettar, Insulating ferromagnetism in La4Ba2Cu2O10: An ab initio Wannier function analysis, Phys. Rev. Lett. 89, 167204 (2002).
  133. Nicola Marzari and David Vanderbilt, Maximally localized generalized Wannier functions for composite energy bands, Phys. Rev. B 56, 12847 (1997).
  134. J. C. Slater, Quantum Theory of Molecules and Solids (McGraw-Hill, New York, 1974).
  135. Vladimir I Anisimov, F Aryasetiawan, and A I Lichtenstein, First-principles calculations of the electronic structure and spectra of strongly correlated systems: The LDA+U method, J. Phys. Condens. Matter 9, 767 (1997).
  136. Wei-Guo Yin, Dmitri Volja, and Wei Ku, Orbital ordering in LaMnO3: Electron-electron versus electron-lattice interactions, Phys. Rev. Lett. 96, 116405 (2006).
  137. Zi-Jian Lang, Ruoshi Jiang, and Wei Ku, Strongly correlated doped hole carriers in the superconducting nickelates: Their location, local many-body state, and low-energy effective Hamiltonian, Phys. Rev. B 103, L180502 (2021).
  138. Ruoshi Jiang, Fangyuan Gu, and Wei Ku, ‘Interaction annealing’ to determine effective quantized valence and orbital structure: An illustration with ferro-orbital order in WTe2, npj Comput. Mater. 12, 39 (2026).
  139. Wei Ku, Tom Berlijn, and Chi-Cheng Lee, Unfolding first-principles band structures, Phys. Rev. Lett. 104, 216401 (2010).
  140. Kristjan Haule, Chuck-Hou Yee, and Kyoo Kim, Dynamical mean-field theory within the full-potential methods: Electronic structure of CeIrIn5, CeCoIn5, and CeRhIn5, Phys. Rev. B 81, 195107 (2010).
  141. A. Maisuradze, R. Khasanov, A. Shengelaya, and H. Keller, Comparison of different methods for analyzing μSR line shapes in the vortex state of type-II superconductors, J. Phys. Condens. Matter 21, 075701 (2009).
  142. A. Suter and B. M. Wojek, Musrfit: A free platform-independent framework for μSR data analysis, Phys. Procedia 30, 69 (2012).
  143. V. Grinenko et al., Split superconducting and time-reversal symmetry-breaking transitions in Sr2RuO4 under stress, Nat. Phys. 17, 748 (2021).
  144. V. Grinenko, R. Sarkar, K. Kihou, C. H. Lee, I. Morozov, S. Aswartham, B. Büchner, P. Chekhonin, W. Skrotzki, K. Nenkov, R. Hühne, K. Nielsch, S. L. Drechsler, V. L. Vadimov, M. A. Silaev, P. A. Volkov, I. Eremin, H. Luetkens, and H.-H. Klauss, Superconductivity with broken time-reversal symmetry inside a superconducting s-wave state, Nat. Phys. 16, 789 (2020).
  145. R. S. Hayano, Y. J. Uemura, J. Imazato, N. Nishida, T. Yamazaki, and R. Kubo, Zero- and low-field spin relaxation studied by positive muons, Phys. Rev. B 20, 850 (1979).

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