| CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES |
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In-Plane Magnetization-Induced Corner States in Bismuthene |
| Bin Han1,2, Junjie Zeng1,2, and Zhenhua Qiao1,2* |
1ICQD, Hefei National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China, Hefei 230026, China
2CAS Key Laboratory of Strongly Coupled Quantum Matter Physics, and Department of Physics, University of Science and Technology of China, Hefei 230026, China
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| Cite this article: |
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Bin Han, Junjie Zeng, and Zhenhua Qiao 2022 Chin. Phys. Lett. 39 017302 |
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Abstract We theoretically demonstrate that the electronic second-order topological insulator with robust corner states, having a buckled honeycomb lattice, can be realized in bismuthene by inducing in-plane magnetization. Based on the $sp^3$ Slater–Koster tight-binding model with parameters extracted from first-principles results, we show that spin-helical edge states along zigzag boundaries are gapped out by the in-plane magnetization whereas four robust in-gap electronic corner states at the intersection between two zigzag boundaries arise. By regulating the orientation of in-plane magnetization, we show different position distribution of four corner states with different energies. Nevertheless, it respects some spatial symmetries and thus can protect the higher-order topological phase. Combined with the Kane–Mele model, we discuss the influence of the magnetization orientation on the position distribution of corner states.
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Received: 27 October 2021
Published: 29 December 2021
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| PACS: |
73.43.Nq
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(Quantum phase transitions)
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71.20.-b
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(Electron density of states and band structure of crystalline solids)
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73.43.-f
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(Quantum Hall effects)
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| [1] | Kane C L and Mele E J 2005 Phys. Rev. Lett. 95 146802 |
| [2] | Bernevig B A, Hughes T L, and Zhang S C 2006 Science 314 1757 |
| [3] | Hasan M Z and Kane C L 2010 Rev. Mod. Phys. 82 3045 |
| [4] | Qi X L and Zhang S C 2011 Rev. Mod. Phys. 83 1057 |
| [5] | Ren Y, Qiao Z, and Niu Q 2016 Rep. Prog. Phys. 79 066501 |
| [6] | Benalcazar W A, Bernevig B A, and Hughes T L 2017 Phys. Rev. B 96 245115 |
| [7] | Benalcazar W A, Bernevig B A, and Hughes T L 2017 Science 357 61 |
| [8] | Song Z, Fang Z, and Fang C 2017 Phys. Rev. Lett. 119 246402 |
| [9] | Ezawa M 2018 Phys. Rev. B 97 155305 |
| [10] | Schindler F, Brzezińska M, Benalcazar W A, Iraola M, Bouhon A, Tsirkin S S, Vergniory M G, and Neupert T 2019 Phys. Rev. Res. 1 033074 |
| [11] | Benalcazar W A, Li T, and Hughes T L 2019 Phys. Rev. B 99 245151 |
| [12] | Li T, Zhu P, Benalcazar W A, and Hughes T L 2020 Phys. Rev. B 101 115115 |
| [13] | van Miert G and Ortix C 2018 Phys. Rev. B 98 081110 |
| [14] | Langbehn J, Peng Y, Trifunovic L, von Oppen F, and Brouwer P W 2017 Phys. Rev. Lett. 119 246401 |
| [15] | Wieder B J and Bernevig B A 2018 arXiv:1810.02373 [cond-mat.mes-hall] |
| [16] | Wang Z, Wieder B J, Li J, Yan B, and Bernevig B A 2019 Phys. Rev. Lett. 123 186401 |
| [17] | Zhang W, Xie X, Hao H, Dang J, Xiao S, Shi S, Ni H, Niu Z, Wang C, Jin K, Zhang X, and Xu X 2020 Light: Sci. & Appl. 9 109 |
| [18] | Xie B Y, Su G X, Wang H F, Su H, Shen X P, Zhan P, Lu M H, Wang Z L, and Chen Y F 2019 Phys. Rev. Lett. 122 233903 |
| [19] | Chen X D, Deng W M, Shi F L, Zhao F L, Chen M, and Dong J W 2019 Phys. Rev. Lett. 122 233902 |
| [20] | Ota Y, Liu F, Katsumi R, Watanabe K, Wakabayashi K, Arakawa Y, and Iwamoto S 2019 Optica 6 786 |
| [21] | Peterson C W, Benalcazar W A, Hughes T L, and Bahl G 2018 Nature 555 346 |
| [22] | Mittal S, Orre V V, Zhu G, Gorlach M A, Poddubny A, and Hafezi M 2019 Nat. Photon. 13 692 |
| [23] | Hassan A E, Kunst F K, Moritz A, Andler G, Bergholtz E J, and Bourennane M 2019 Nat. Photon. 13 697 |
| [24] | Zangeneh-Nejad F and Fleury R 2019 Phys. Rev. Lett. 123 053902 |
| [25] | Yang Y, Jia Z, Wu Y, Xiao R C, Hang Z H, Jiang H, and Xie X C 2020 Sci. Bull. 65 531 |
| [26] | Zhang X, Wang H X, Lin Z K, Tian Y, Xie B, Lu M H, Chen Y F, and Jiang J H 2019 Nat. Phys. 15 582 |
| [27] | Ni X, Weiner M, Alù A, and Khanikaev A B 2019 Nat. Mater. 18 113 |
| [28] | Xue H, Yang Y, Gao F, Chong Y, and Zhang B 2019 Nat. Mater. 18 108 |
| [29] | Fan H, Xia B, Tong L, Zheng S, and Yu D 2019 Phys. Rev. Lett. 122 204301 |
| [30] | Zhang X, Lin Z K, Wang H X, Xiong Z, Tian Y, Lu M H, Chen Y F, and Jiang J H 2020 Nat. Commun. 11 65 |
| [31] | Zhang Z, Long H, Liu C, Shao C, Cheng Y, Liu X, and Christensen J 2019 Adv. Mater. 31 1904682 |
| [32] | Lin Z K, Wu S Q, Wang H X, and Jiang J H 2020 Chin. Phys. Lett. 37 074302 |
| [33] | Liu B, Zhao G, Liu Z, and Wang Z F 2019 Nano Lett. 19 6492 |
| [34] | Park M J, Kim Y, Cho G Y, and Lee S B 2019 Phys. Rev. Lett. 123 216803 |
| [35] | Sheng X L, Chen C, Liu H, Chen Z, Yu Z M, Zhao Y X 1 and Yang S A 2019 Phys. Rev. Lett. 123 256402 |
| [36] | Su Z, Kang Y, Zhang B, Zhang Z, and Jiang H 2019 Chin. Phys. B 28 117301 |
| [37] | Lee E, Kim R, Ahn J, and Yang B J 2020 npj Quantum Mater. 5 1 |
| [38] | Ren Y, Qiao Z, and Niu Q 2020 Phys. Rev. Lett. 124 166804 |
| [39] | Chen C, Song Z, Zhao J Z, Chen Z, Yu Z M, Sheng X L, and Yang S A 2020 Phys. Rev. Lett. 125 056402 |
| [40] | Wang K T, Ren Y, Xu F, Wei Y, and Wang J 2021 Sci. Chin. Phys. Mech. & Astron. 64 257811 |
| [41] | Qiao Z, Yang S A, Feng W, Tse W K, Ding J, Yao Y, Wang J, and Niu Q 2010 Phys. Rev. B 82 161414 |
| [42] | Tse W K, Qiao Z, Yao Y, MacDonald A H, and Niu Q 2011 Phys. Rev. B 83 155447 |
| [43] | Sui Q, Zhang J, Jin S, Xia Y, and Li G 2020 Chin. Phys. Lett. 37 097301 |
| [44] | Zhong P, Ren Y, Han Y, Zhang L, and Qiao Z 2017 Phys. Rev. B 96 241103 |
| [45] | Thouless D J, Kohmoto M, Nightingale M P, and den Nijs M 1982 Phys. Rev. Lett. 49 405 |
| [46] | Kohmoto M 1985 Ann. Phys. 160 343 |
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