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Chin. Phys. B, 2026, Vol. 35(2): 027401    DOI: 10.1088/1674-1056/ae23ae
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Pressure-induced superconductivity in kagome metal CsCr3Sb5: Role of spin-orbit coupling and inter-orbital spin fluctuations

Wei Wang(王巍)1,2, Shun-Li Yu(于顺利)3,4,†, and Jian-Xin Li(李建新)3,4,‡
1 School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China;
2 Jiangsu Physical Science Research Center, Nanjing 210093, China;
3 National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China;
4 Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
Abstract  Motivated by the recent discovery of superconductivity in the kagome metal CsCr$_3$Sb$_5$ under pressure, we theoretically investigate the superconducting pairing symmetry and the impact of spin-orbit coupling (SOC) in this system. By employing an effective four-orbital tight-binding model and solving the linearized gap equation within the random phase approximation, we find that the large inter-orbital spin fluctuations enhanced by Hund's coupling promote a superconducting gap function with $E_{2g}$ symmetry. The inclusion of SOC further stabilizes this gap symmetry. Our analysis also reveals that the dx2-y2 orbital plays the dominant role in forming the superconducting pairs.
Keywords:  kagome lattice      CsCr$_3$Sb$_5$      superconductivity      spin-orbit coupling  
Received:  23 September 2025      Revised:  22 November 2025      Accepted manuscript online:  25 November 2025
PACS:  74.20.Rp (Pairing symmetries (other than s-wave))  
  75.10.Lp (Band and itinerant models)  
  71.70.Ej (Spin-orbit coupling, Zeeman and Stark splitting, Jahn-Teller effect)  
  71.10.Fd (Lattice fermion models (Hubbard model, etc.))  
Fund: This work was supported by the National Key Research and Development of China (Grant Nos. 2024YFA1408104 and 2021YFA1400400), the National Natural Science Foundation of China (Grant Nos. 12374137, 12434005, 12074175, 92165205, 12004191, and 12550405), and the Natural Science Foundation of Jiangsu Province (Grant No. BK20233001).
Corresponding Authors:  Shun-Li Yu, Jian-Xin Li     E-mail:  slyu@nju.edu.cn;jxli@nju.edu.cn

Cite this article: 

Wei Wang(王巍), Shun-Li Yu(于顺利), and Jian-Xin Li(李建新) Pressure-induced superconductivity in kagome metal CsCr3Sb5: Role of spin-orbit coupling and inter-orbital spin fluctuations 2026 Chin. Phys. B 35 027401

[1] Balents L 2010 Nature 464 199
[2] Norman M R 2016 Rev. Mod. Phys. 88 041002
[3] Wen J, Rüegg A, Wang C C J and Fiete G A 2010 Phys. Rev. B 82 075125
[4] Tang E, Mei J W and Wen X G 2011 Phys. Rev. Lett. 106 236802
[5] Yu S L and Li J X 2012 Phys. Rev. B 85 144402
[6] Kiesel M L and Thomale R 2012 Phys. Rev. B 86 121105
[7] Wang W S, Li Z Z, Xiang Y Y and Wang Q H 2013 Phys. Rev. B 87 115135
[8] Kiesel M L, Platt C and Thomale R 2013 Phys. Rev. Lett. 110 126405
[9] Kang M, Ye L, Fang S, You J S, Levitan A, Han M, Facio J I, Jozwiak C, Bostwick A, Rotenberg E, Chan M K, McDonald R D, Graf D, Kaznatcheev K, Vescovo E, Bell D C, Kaxiras E, van den Brink J, Richter M, Prasad Ghimire M, Checkelsky J G and Comin R 2020 Nat. Mater. 19 163
[10] Wu Y M, Thomale R and Raghu S 2023 Phys. Rev. B 108 L081117
[11] Chen H, Hu B, Ye Y, Yang H and Gao H J 2022 Chin. Phys. B 31 97405
[12] Neupert T, Denner M M, Yin J X, Thomale R and Hasan M Z 2022 Nat. Phys. 18 137
[13] Yin J X, Lian B and Hasan M Z 2022 Nature 612 647
[14] Wang Y, Wu H, McCandless G T, Chan J Y and Ali M N 2023 Nat. Rev. Phys. 5 635
[15] Jiang K, Wu T, Yin J X, Wang Z, Hasan M Z, Wilson S D, Chen X and Hu J 2023 Natl. Sci. Rev. 10 nwac199
[16] Wilson S D and Ortiz B R 2024 Nat. Rev. Mater. 9 420
[17] Yu F H, Wu T, Wang Z Y, Lei B, Zhuo W Z, Ying J J and Chen X H 2021 Phys. Rev. B 104 L041103
[18] Jiang Y X, Yin J X, Denner M M, Shumiya N, Ortiz B R, Xu G, Guguchia Z, He J, Hossain M S, Liu X, Ruff J, Kautzsch L, Zhang S S, Chang G, Belopolski I, Zhang Q, Cochran T A, Multer D, Litskevich M, Cheng Z J, Yang X P, Wang Z, Thomale R, Neupert T, Wilson S D and Hasan M Z 2021 Nat. Mater. 20 1353
[19] Chen H, Yang H, Hu B, Zhao Z, Yuan J, Xing Y, Qian G, Huang Z, Li G, Ye Y, Ma S, Ni S, Zhang H, Yin Q, Gong C, Tu Z, Lei H, Tan H, Zhou S, Shen C, Dong X, Yan B, Wang Z and Gao H J 2021 Nature 599 222
[20] Grandi F, Consiglio A, Sentef M A, Thomale R and Kennes D M 2023 Phys. Rev. B 107 155131
[21] Ortiz B R, Teicher S M L, Hu Y, Zuo J L, Sarte P M, Schueller E C, Abeykoon A M M, Krogstad M J, Rosenkranz S, Osborn R, Seshadri R, Balents L, He J and Wilson S D 2020 Phys. Rev. Lett. 125 247002
[22] Yin Q, Tu Z, Gong C, Fu Y, Yan S and Lei H 2021 Chin. Phys. Lett. 38 37403
[23] Ortiz B R, Sarte P M, Kenney E M, Graf M J, Teicher S M L, Seshadri R and Wilson S D 2021 Phys. Rev. Mater. 5 034801
[24] Feng X, Jiang K, Wang Z and Hu J 2021 Sci. Bull. 66 1384
[25] Liu Y, Liu Z Y, Bao J K, Yang P T, Ji L W, Wu S Q, Shen Q X, Luo J, Yang J, Liu J Y, Xu C C, Yang W Z, Chai W L, Lu J Y, Liu C C, Wang B S, Jiang H, Tao Q, Ren Z, Xu X F, Cao C, Xu Z A, Zhou R, Cheng J G and Cao G H 2024 Nature 632 1032
[26] Liu L, Li Y, Tan H, Liu Y, Shi Y, Zhai Y, Lin H, Cao G, Yan B, Zhang G M and Yang L 2024 arXiv:2411.06778 [cond-mat.str-el]
[27] Yao W, Liu S, Xu Z, Ishikawa D, Wang Z, Gao B, Xu S, Ye F, Hashimoto K, Shibauchi T, Baron A Q R and Dai P 2024 arXiv: 2410.16465 [cond-mat.str-el]
[28] Wang Z, Guo Y, Huang H Y, Xie F, Huang Y, Gao B, Oh J S, Wu H, Okamoto J, Channagowdra G, Chen C T, Ye F, Lu X, Liu Z, Ren Z, Fang Y, Wang Y, Biswas A, Zhang Y, Yue Z, Hu C, Jozwiak C, Bostwick A, Rotenberg E, Hashimoto M, Lu D, Kono J, Chu J H, Yakobson B I, Birgeneau R J, Cao G H, Fujimori A, Huang D J, Si Q, Yi M and Dai P 2025 Nat. Commun. 16 7573
[29] Li Y, Liu Y, Du X,Wu S, ZhaoW, Zhai K, Hu Y, Zhang S, Chen H, Liu J, Yang Y, Peng C, Hashimoto M, Lu D, Liu Z, Wang Y, Chen Y, Cao G and Yang L 2025 Nat. Commun. 16 3229
[30] Peng S, Han Y, Li Y, Shen J, Miao Y, Luo Y, Huai L, Ou Z, Li H, Xiang Z, Liu Z, Shen D, Hashimoto M, Lu D, Yao Y, Qiao Z, Wang Z and He J 2024 arXiv:2406.17769 [cond-mat.supr-con]
[31] Wang Y 2025 Phys. Rev. B 111 035127
[32] Xie F, Fang Y, Li Y, Huang Y, Chen L, Setty C, Sur S, Yakobson B, Valentí R and Si Q 2025 Phys. Rev. Res. 7 L022061
[33] Xu C,Wu S, Zhi G X, Cao G, Dai J, Cao C,Wang X and Lin H Q 2025 Nat. Commun. 16 3114
[34] Wang W, Yu S L and Li J X 2025 Phys. Rev. B 112 165137
[35] Wu S, Xu C, Wang X, Lin H Q, Cao C and Cao G H 2025 Nat. Commun. 16 1375
[36] Wu X, Schwemmer T, Müller T, Consiglio A, Sangiovanni G, Di Sante D, Iqbal Y, Hanke W, Schnyder A P, Denner M M, Fischer M H, Neupert T and Thomale R 2021 Phys. Rev. Lett. 127 177001
[37] Vafek O and Chubukov A V 2017 Phys. Rev. Lett. 118 087003
[38] Saito T, Yamakawa Y, Onari S and Kontani H 2015 Phys. Rev. B 92 134522
[39] Liu L, Okazaki K, Yoshida T, Suzuki H, Horio M, Ambolode L C C, Xu J, Ideta S, Hashimoto M, Lu D H, Shen Z X, Ota Y, Shin S, Nakajima M, Ishida S, Kihou K, Lee C H, Iyo A, Eisaki H, Mikami T, Kakeshita T, Yamakawa Y, Kontani H, Uchida S and Fujimori A 2017 Phys. Rev. B 95 104504
[40] Scherer D D and Andersen B M 2019 arXiv:1909.01313
[41] Rømer A T, Scherer D D, Eremin I M, Hirschfeld P J and Andersen B M 2019 Phys. Rev. Lett. 123 247001
[42] Yu S L and Li J X 2013 Chin. Phys. B 22 87411
[43] Yao Z J, Li J X and Wang Z D 2009 New J. Phys. 11 25009
[44] Grinberg M, Lesniewski T, Mahlik S and Liu R S 2017 Opt. Mater. 74 93
[45] Kresse G and Hafner J 1993 Phys. Rev. B 47 558
[46] Blöchl P E 1994 Phys. Rev. B 50 17953
[47] Perdew J P, Burke K and Ernzerhof M 1997 Phys. Rev. Lett. 78 1396
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