CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES |
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Phononic Weyl Nodal Lines and Weyl Pairs in van der Waals Heavy Fermion Material CeSiI |
Fulei Li1,2, Tianye Yu2*, Junwen Lai2, Jiaxi Liu2, Peitao Liu2, Xing-Qiu Chen2*, and Yan Sun2* |
1School of Materials Science and Engineering, Northeastern University, Shenyang 110819, China 2Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China
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Cite this article: |
Fulei Li, Tianye Yu, Junwen Lai et al 2024 Chin. Phys. Lett. 41 107301 |
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Abstract Topological phonon is a new frontier in the field of topological materials. Different from electronic structures, phonons are bosons and most topological phonons are metallic form. Previous studies about topological phonon states were focused on three-dimensional (3D) materials. Owing to the lack of material candidates, two-dimensional (2D) and van der Waals $f$-electron-related topological phonons were rarely reported. Based on first-principles calculations, we investigate the topological phononic state in the heavy fermion material CeSiI with a layered structure. Both 3D bulk and 2D monolayers have topological nontrivial states in the rarely seen $f$ electron dominated van der Waals metal. Owing to the $PT$ and $C_{3z}$ symmetries, Weyl nodal lines with nonzero Chern numbers exist on the hinge of the Brillouin zone. Protected by $C_{3z}$ rotation symmetry, three pairs of Weyl points with $\pm \pi$ Berry phase exist at point $K$ near the frequency of 8 and 10 THz. In addition to the bulk topological charges, corresponding surface/edge states are also systematically analyzed, which gives a consistent understanding. Our results propose another interesting point in the newly discovered rear earth heavy fermion material CeSiI and are helpful for future experimental research of CeSiI topological phonons.
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Received: 11 July 2024
Published: 26 October 2024
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PACS: |
63.20.D-
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(Phonon states and bands, normal modes, and phonon dispersion)
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03.65.Vf
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(Phases: geometric; dynamic or topological)
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[1] | Kosterlitz J M 2017 Rev. Mod. Phys. 89 040501 |
[2] | Chiu C K, Teo J C Y, Schnyder A P, and Ryu S 2016 Rev. Mod. Phys. 88 035005 |
[3] | Goldman N, Budich J C, and Zoller P 2016 Nat. Phys. 12 639 |
[4] | Bradlyn B, Elcoro L, Cano J, Vergniory M G, Wang Z J, Felser C, Aroyo M I, and Bernevig B A 2017 Nature 547 298 |
[5] | Zhang T T, Jiang Y, Song Z D, Huang H, He Y Q, Fang Z, Weng H M, and Fang C 2019 Nature 566 475 |
[6] | Vergniory M G, Elcoro L, Felser C, Regnault N, Bernevig B A, and Wang Z J 2019 Nature 566 480 |
[7] | Tang F, Po H C, Vishwanath A, and Wan X G 2019 Nature 566 486 |
[8] | Konig M, Wiedmann S, Brune C, Roth A, Buhmann H, Molenkamp L W, Qi X L, and Zhang S C 2007 Science 318 766 |
[9] | Hsieh D, Qian D, Wray L, Xia Y, Hor Y S, Cava R J, and Hasan M Z 2008 Nature 452 970 |
[10] | Xia Y, Qian D, Hsieh D, Wray L, Pal A, Lin H, Bansil A, Grauer D, Hor Y S, Cava R J, and Hasan M Z 2009 Nat. Phys. 5 398 |
[11] | Slager R J, Mesaros A, Juričić V, and Zaanen J 2013 Nat. Phys. 9 98 |
[12] | Young S M, Zaheer S, Teo J C Y, Kane C L, Mele E J, and Rappe A M 2012 Phys. Rev. Lett. 108 140405 |
[13] | Wang Z J, Sun Y, Chen X Q, Franchini C, Xu G, Weng H M, Dai X, and Fang Z 2012 Phys. Rev. B 85 195320 |
[14] | Wan X G, Turner A M, Vishwanath A, and Savrasov S Y 2011 Phys. Rev. B 83 205101 |
[15] | Weng H M, Fang C, Fang Z, Bernevig B A, and Dai X 2015 Phys. Rev. X 5 011029 |
[16] | Huang S M, Xu S Y, Belopolski I, Lee C C, Chang G Q, Wang B K, Alidoust N, Bian G, Neupane M, Zhang C L, Jia S, Bansil A, Lin H, and Hasan M Z 2015 Nat. Commun. 6 7373 |
[17] | Li R H, Ma H, Cheng X Y, Wang S L, Li D Z, Zhang Z Y, Li Y Y, and Chen X Q 2016 Phys. Rev. Lett. 117 096401 |
[18] | Schoop L M, Ali M N, Straßer C, Topp A, Varykhalov A, Marchenko D, Duppel V, Parkin S S P, Lotsch B V, and Ast C R 2016 Nat. Commun. 7 11696 |
[19] | Bian G, Chang T R, Sankar R et al. 2016 Nat. Commun. 7 10556 |
[20] | Li R, Li J, Wang L, Liu J, Ma H, Song H F, Li D, Li Y, and Chen X Q 2019 Phys. Rev. Lett. 123 136802 |
[21] | Chun Po H, Vishwanath A, and Watanabe H 2017 Nat. Commun. 8 50 |
[22] | Xu Y F, Elcoro L, Song Z D, Wieder B J, Vergniory M G, Regnault N, Chen Y L, Felser C, and Bernevig B A 2020 Nature 586 702 |
[23] | Mousavi S H, Khanikaev A B, and Wang Z 2015 Nat. Commun. 6 8682 |
[24] | He C, Ni X, Ge H, Sun X C, Chen Y B, Lu M H, Liu X P, and Chen Y F 2016 Nat. Phys. 12 1124 |
[25] | Zheng F and Zhang P 2017 Comput. Phys. Commun. 210 139 |
[26] | Lu L, Fu L, Joannopoulos J D, and Soljačić M 2013 Nat. Photonics 7 294 |
[27] | Liu Y Z, Xu Y, and Duan W H 2018 Natl. Sci. Rev. 5 314 |
[28] | Zhang L and Niu Q 2015 Phys. Rev. Lett. 115 115502 |
[29] | Li J, Liu J, Baronett S A, Liu M, Wang L, Li R, Chen Y, Li D, Zhu Q, and Chen X Q 2021 Nat. Commun. 12 1204 |
[30] | Xu Y F, Vergniory M G, Ma D S, Mañes J L, Song Z D, Bernevig B A, Regnault N, and Elcoro L 2024 Science 384 eadf8458 |
[31] | Li M L, Shakoori M A, Wang R P, and Li H P 2024 Chin. Phys. Lett. 41 016302 |
[32] | Bardeen J, Cooper L N, and Schrieffer J R 1957 Phys. Rev. 108 1175 |
[33] | Zhang F and Yin L 2022 Chin. Phys. Lett. 39 060301 |
[34] | Liu H, Yu T X, Zhang Z H, and Ying T P 2024 Chin. Phys. Lett. 41 077401 |
[35] | Liu Y Z, Xu Y, Zhang S C, and Duan W H 2017 Phys. Rev. B 96 064106 |
[36] | Wang J, Yuan H, Kuang M, Yang T, Yu Z M, Zhang Z, and Wang X 2021 Phys. Rev. B 104 L041107 |
[37] | Xie C, Liu Y, Zhang Z, Zhou F, Yang T, Kuang M, Wang X, and Zhang G 2021 Phys. Rev. B 104 045148 |
[38] | Yang T, Xie C, Chen H, Wang X, and Zhang G 2022 Phys. Rev. B 105 094310 |
[39] | Zhong M, Liu Y, Zhou F, Kuang M, Yang T, Wang X, and Zhang G 2021 Phys. Rev. B 104 085118 |
[40] | Yu W W, Liu Y, Tian L, He T, Zhang X, and Liu G 2022 J. Phys.: Condens. Matter 34 155703 |
[41] | Liu G, Huang Z, Chen Z, Jin Y, He C, and Xu H 2022 Phys. Rev. B 106 054306 |
[42] | Li J, Xie Q, Ullah S, Li R, Ma H, Li D, Li Y, and Chen X Q 2018 Phys. Rev. B 97 054305 |
[43] | Xie Q, Li J, Ullah S, Li R, Wang L, Li D, Li Y, Yunoki S, and Chen X Q 2019 Phys. Rev. B 99 174306 |
[44] | Zhang T, Song Z, Alexandradinata A, Weng H, Fang C, Lu L, and Fang Z 2018 Phys. Rev. Lett. 120 016401 |
[45] | Miao H, Zhang T T, Wang L, Meyers D, Said A H, Wang Y L, Shi Y G, Weng H M, Fang Z, and Dean M P M 2018 Phys. Rev. Lett. 121 035302 |
[46] | Ding G, Zhou F, Zhang Z, Yu Z M, and Wang X 2022 Phys. Rev. B 105 134303 |
[47] | Liu Q B, Wang Z, and Fu H H 2021 Phys. Rev. B 103 L161303 |
[48] | Liu P F, Li J, Tu X H, Li H, Zhang J, Zhang P, Gao Q, and Wang B T 2021 Phys. Rev. B 103 094306 |
[49] | Zhang T, Takahashi R, Fang C, and Murakami S 2020 Phys. Rev. B 102 125148 |
[50] | Wang R, Xia B W, Chen Z J, Zheng B B, Zhao Y J, and Xu H 2020 Phys. Rev. Lett. 124 105303 |
[51] | Huang Z, Chen Z, Zheng B, and Xu H 2020 npj Comput. Mater. 6 87 |
[52] | Xia B W, Wang R, Chen Z J, Zhao Y J, and Xu H 2019 Phys. Rev. Lett. 123 065501 |
[53] | Liu J, Hou W, Wang E, Zhang S, Sun J T, and Meng S 2019 Phys. Rev. B 100 081204 |
[54] | Chen Z J, Wang R, Xia B W, Zheng B B, Jin Y J, Zhao Y J, and Xu H 2021 Phys. Rev. Lett. 126 185301 |
[55] | Jin Y, Wang R, and Xu H 2018 Nano Lett. 18 7755 |
[56] | Yang T, Gu Q, Wang P, Wu Z, and Zhang Z 2022 Appl. Phys. Lett. 121 053102 |
[57] | Zhang T T, Miao H, Wang Q, Lin J Q, Cao Y, Fabbris G, Said A H, Liu X, Lei H C, Fang Z, Weng H M, and Dean M P M 2019 Phys. Rev. Lett. 123 245302 |
[58] | Ding G, Sun T, Surucu G, Surucu O, Gencer A, and Wang X 2022 Phys. Chem. Chem. Phys. 24 17210 |
[59] | Wang J, Yuan H, Yu Z M, Zhang Z, and Wang X 2021 Phys. Rev. Mater. 5 124203 |
[60] | Li J, Xie Q, Liu J, Li R, Liu M, Wang L, Li D, Li Y, and Chen X Q 2020 Phys. Rev. B 101 024301 |
[61] | Liu G, Jin Y, Chen Z, and Xu H 2021 Phys. Rev. B 104 024304 |
[62] | Liu Q B, Fu H H, Xu G, Yu R, and Wu R 2019 J. Phys. Chem. Lett. 10 4045 |
[63] | Jin Y J, Chen Z J, Xia B W, Zhao Y J, Wang R, and Xu H 2018 Phys. Rev. B 98 220103 |
[64] | Wang R Y, Chen Z J, Huang Z Q, Xia B W, and Xu H 2021 Phys. Rev. Mater. 5 084202 |
[65] | Zheng B B, Xia B W, Wang R, Chen Z J, Zhao J Z, Zhao Y J, and Xu H 2020 Phys. Rev. B 101 100303 |
[66] | Zhou F, Zhang Z, Chen H, Kuang M, Yang T, and Wang X 2021 Phys. Rev. B 104 174108 |
[67] | Peng B, Hu Y, Murakami S, Zhang T, and Monserrat B 2020 Sci. Adv. 6 eabd1618 |
[68] | Li J, Wang L, Liu J, Li R, Zhang Z, and Chen X Q 2020 Phys. Rev. B 101 081403 |
[69] | Deng W, Lu J, Li F, Huang X, Yan M, Ma J, and Liu Z 2019 Nat. Commun. 10 1769 |
[70] | Peng B, Murakami S, Monserrat B, and Zhang T 2021 npj Comput. Mater. 7 195 |
[71] | Chen Z J, Xie Z J, Jin Y J, Liu G, and Xu H 2022 Phys. Rev. Mater. 6 034202 |
[72] | Wang X, Zhou F, Yang T, Kuang M, Yu Z M, and Zhang G 2021 Phys. Rev. B 104 L041104 |
[73] | Wang J, Yuan H, Liu Y, Zhou F, Wang X, and Zhang G 2022 Phys. Chem. Chem. Phys. 24 2752 |
[74] | Liu Q B, Wang Z Q, and Fu H H 2021 Phys. Rev. B 104 L041405 |
[75] | Xie C, Yuan H, Liu Y, and Wang X 2022 Phys. Rev. B 105 054307 |
[76] | Xie C, Yuan H, Liu Y, Wang X, and Zhang G 2021 Phys. Rev. B 104 134303 |
[77] | Posey V A, Turkel S, Rezaee M et al. 2024 Nature 625 483 |
[78] | Mathur N D, Grosche F M, Julian S R et al. 1998 Nature 394 39 |
[79] | Gegenwart P, Si Q M, and Steglich F 2008 Nat. Phys. 4 186 |
[80] | Yazdani A, da Silva Neto E H, and Aynajian P 2016 Annu. Rev. Condens. Matter Phys. 7 11 |
[81] | Löhneysen H V, Rosch A, Vojta M, and Wölfle P 2007 Rev. Mod. Phys. 79 1015 |
[82] | Stewart G R 1984 Rev. Mod. Phys. 56 755 |
[83] | Jiao L, Howard S, Ran S, Wang Z Y, Rodriguez J O, Sigrist M, Wang Z Q, Butch N P, and Madhavan V 2020 Nature 579 523 |
[84] | Kresse G and Furthmüller J 1996 Phys. Rev. B 54 11169 |
[85] | Kresse G and Furthmüller J 1996 Comput. Mater. Sci. 6 15 |
[86] | Eriksson F, Fransson E, and Erhart P 2019 Adv. Theory Simul. 2 1800184 |
[87] | Wu Q, Zhang S, Song H F, Troyer M, and Soluyanov A A 2018 Biochem. Biophys. Res. Commun. 224 405 |
[88] | Lopez Sancho M P, Lopez Sancho J M, Sancho J M L, and Rubio J 1985 J. Phys. F 15 851 |
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