Topological Wannier Cycles for the Bulk and Edges
Ze-Lin Kong1 , Zhi-Kang Lin1* , and Jian-Hua Jiang1,2*
1 School of Physical Science and Technology, and Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, Suzhou 215006, China2 Key Lab of Advanced Optical Manufacturing Technologies of Jiangsu Province, and Key Lab of Modern Optical Technologies of Ministry of Education, Soochow University, Suzhou 215006, China
Abstract ：Topological materials are often characterized by unique edge states which are in turn used to detect different topological phases in experiments. Recently, with the discovery of various higher-order topological insulators, such spectral topological characteristics are extended from edge states to corner states. However, the chiral symmetry protecting the corner states is often broken in genuine materials, leading to vulnerable corner states even when the higher-order topological numbers remain quantized and invariant. Here, we show that a local artificial gauge flux can serve as a robust probe of the Wannier type higher-order topological insulators, which is effective even when the chiral symmetry is broken. The resultant observable signature is the emergence of the cyclic spectral flows traversing one or multiple band gaps. These spectral flows are associated with the local modes bound to the artificial gauge flux. This phenomenon is essentially due to the cyclic transformation of the Wannier orbitals when the local gauge flux acts on them. We extend topological Wannier cycles to systems with $C_{2}$ and $C_{3}$ symmetries and show that they can probe both the bulk and the edge Wannier centers, yielding rich topological phenomena.
收稿日期: 2022-03-21
Editors' Suggestion
出版日期: 2022-07-05
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43.40.+s
(Structural acoustics and vibration)
43.20.+g
(General linear acoustics)
46.40.-f
(Vibrations and mechanical waves)
46.40.Cd
(Mechanical wave propagation (including diffraction, scattering, and dispersion))
[1] Hasan M Z and Kane C L 2010 Rev. Mod. Phys. 82 3045 [2] Qi X L and Zhang S C 2011 Rev. Mod. Phys. 83 1057 [3] Benalcazar W A, Bernevig B A and Hughes T L 2017 Science 61 357 [4] Langbehn J, Peng Y, Trifunovic L, Oppen F V and Brouwer P W 2017 Phys. Rev. Lett. 119 246401 [5] Song Z, Fang Z and Fang C 2017 Phys. Rev. Lett. 119 246402 [6] Benalcazar W A, Bernevig B A and Hughes T L 2017 Phys. Rev. B 96 245115 [7] Schindler F, Cook A M, Vergniory M G, Wang Z, Parkin S S P, Bernevig B A and Neupert T 2018 Sci. Adv. 4 eaat0346 [8] Ezawa M 2018 Phys. Rev. Lett. 120 026801 [9] Miert G V and Ortix C 2018 Phys. Rev. B 98 081110 [10] Benalcazar W A, Li T and Hughes T L 2019 Phys. Rev. B 99 245151 [11] Serra-Garcia M, Peri V, Susstrunk R, Bilal O R, Larsen T, Villanueva L G and Huber S D 2018 Nature 555 342 [12] Peterson C W, Benalcazar W A, Hughes T L and Bahl G 2018 Nature 555 346 [13] Imhof S, Berger C, Bayer F, Brehm J, Molenkamp L W, Kiessling T, Schindler F, Lee C H, Greiter M, Neupert T and Thomale R 2018 Nat. Phys. 14 925 [14] Noh J, Benalcazar W A, Huang S, Collins M J, Chen K P, Hughes T L and Rechtsman M C 2018 Nat. Photon. 12 408 [15] Zhang X, Wang H X, Lin Z K, Tian Y, Xie B Y, Lu M H, Chen Y F and Jiang J H 2019 Nat. Phys. 15 582 [16] Zhang X, Xie B Y, Wang H F, Xu X, Tian Y, Jiang J H, Lu M H and Chen Y F 2019 Nat. Commun. 10 5331 [17] Xue H, Yang Y, Gao F, Chong Y and Zhang B 2019 Nat. Mater. 18 108 [18] Ni X, Weiner M, Alu A and Khanikaev A B 2019 Nat. Mater. 18 113 [19] Ota Y, Liu F, Katsumi R, Watanabe K, Wakabayashi K, Arakawa Y and Iwamoto S 2019 Optica 6 786 [20] Chen X D, Deng W M, Shi F L, Zhao F L, Chen M and Dong J W 2019 Phys. Rev. Lett. 122 233902 [21] Xie B, 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 [22] Mittal S, Orre V V, Zhu G, Gorlach M A, Poddubny A and Hafezi M 2019 Nat. Photon. 13 692 [23] Li M, Zhirihin D, Gorlach M, Ni X, Filonov D, Slobozhanyuk A, Alù A and Khanikaev A B 2020 Nat. Photon. 14 89 [24] Xue H R, Yang Y H, Liu G G, Gao F, Chong Y D and Zhang B L 2019 Phys. Rev. Lett. 122 244301 [25] 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 [26] Weiner M, Ni X, Li M, Alù A and Khanikaev A B 2020 Sci. Adv. 6 eaay4166 [27] Qi Y, Qiu C, Xiao M, He H, Ke M and Liu Z 2020 Phys. Rev. Lett. 124 206601 [28] Ni X, Li M, Weiner M, Alu A and Khanikaev A B 2020 Nat. Commun. 11 2108 [29] Wu Y, Yan M, Lin Z K, Wang H X, Li F and Jiang J H 2021 Sci. Bull. 66 1959 [30] Xie B, Wang H X, Zhang X, Zhan P, Jiang J H, Lu M and Chen Y 2021 Nat. Rev. Phys. 3 520 [31] Peterson C W, Li T, Benalcazar W A, Hughes T L and Bahl G 2020 Science 368 1114 [32] Leung S W, Liu Y, Li F F, Liang C P, Poo Y and Jiang J H 2022 arXiv:2203.00206 [physics.optics] [33] Miert G V and Ortix C 2020 npj Quantum Mater. 5 63 [34] Lin Z K, Wu Y, Jiang B, Liu Y, Wu S, Li F and Jiang J H 2022 Nat. Mater. 21 430 [35] Po H C, Vishwanath A and Watanabe H 2017 Nat. Commun. 8 50 [36] Bradlyn B, Elcoro L, Cano J, Vergniory M G, Wang Z, Felser C, Aroyo M I and Bernevig B A 2017 Nature 547 298 [37] 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 [38] Tang F, Po H C, Vishwanath A and Wan X G 2019 Nature 566 486 [39] Ran Y, Zhang Y and Vishwanath A 2009 Nat. Phys. 5 298 [40] Teo J C Y and Kane C L 2010 Phys. Rev. B 82 115120 [41] Juričić V, Mesaros A, Slager R J and Zaanen J 2012 Phys. Rev. Lett. 108 106403 [42] Juan F D, Rüegg A and Lee D H 2014 Phys. Rev. B 89 161117 [43] Slager R J, Mesaros A, Juričić V and Zaanen J 2014 Phys. Rev. B 90 241403 [44] Miert G V and Ortix C 2018 Phys. Rev. B 97 201111 [45] Queiroz R, Fulga I C, Avraham N, Beidenkopf H and Cano J 2019 Phys. Rev. Lett. 123 266802 [46] Slager R J 2019 J. Phys. Chem. Solids 128 24 [47] Roy B and Juričić V 2021 Phys. Rev. Research 3 033107 [48] Paulose J, Chen B G and Vitelli V 2015 Nat. Phys. 11 153 [49] Li F F, Wang H X, Xiong Z, Lou Q, Chen P, Wu R X, Poo Y, Jiang J H and Sajeev J 2018 Nat. Commun. 9 2462 [50] Nayak A K, Reiner J, Queiroz R, Fu H X, Shekhar C, Yan B H, Felser C, Avraham N and Beidenkopf H 2019 Sci. Adv. 5 eaax6996 [51] Qi X L, Hughes T L and Zhang S C 2008 Phys. Rev. B 78 195424 [52] Aharonov Y and Bohm D 1959 Phys. Rev. 115 485 [53] Song Z D, Elcoro L and Bernevig B A 2020 Science 367 794 [54] Gao J, Qian Y T, Jia H X, Guo Z P, Fang Z, Liu M, Weng H M and Wang Z J 2021 arXiv:2106.08035 [cond-mat.mtrl-sci]
[1]
.
[2]
.
[3]
.
[4]
.
[5]
.
[6]
.
[7]
.
[8]
.
[9]
.
[10]
.
[11]
.
[12]
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