Topological phases and type-II edge state in two-leg-coupled Su-Schrieffer-Heeger chains
Tianqi Luo(罗天琦)1,2, Xin Guan(关欣)3,†, Jingtao Fan(樊景涛)1,2,‡, Gang Chen(陈刚)1,2,4, and Suo-Tang Jia(贾锁堂)1,2
1 State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China; 2 Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China; 3 Taiyuan Institute, Taiyuan University, Taiyuan 030006, China; 4 Collaborative Innovation Center of Light Manipulations and Applications, Shandong Normal University, Jinan 250358, China
Abstract Topological quantum states have attracted great attention both theoretically and experimentally. Here, we show that the momentum-space lattice allows us to couple two Su-Schrieffer-Heeger (SSH) chains with opposite dimerizations and staggered interleg hoppings. The coupled SSH chain is a four-band model which has sublattice symmetry similar to the SSH4. Interestingly, the topological edge states occupy two sublattices at the same time, which can be regarded as a one-dimension analogue of the type-II corner state. The analytical expressions of the edge states are also obtained by solving the eigenequations. Finally, we provide a possible experimental scheme to detect the topological winding number and corresponding edge states.
Fund: Project partially supported by the National Natural Science Foundation of China (Grant Nos. 12034012, 12074232, and 11804204) and 1331KSC.
Corresponding Authors:
Xin Guan, Jingtao Fan
E-mail: guanxin810712@163.com;bkxyfjt@163.com
Cite this article:
Tianqi Luo(罗天琦), Xin Guan(关欣), Jingtao Fan(樊景涛), Gang Chen(陈刚), and Suo-Tang Jia(贾锁堂) Topological phases and type-II edge state in two-leg-coupled Su-Schrieffer-Heeger chains 2022 Chin. Phys. B 31 014208
[1] Von Klitzing K, Dorda G and Pepper M 1980 Phys. Rev. Lett.45 494 [2] Thouless D J, Kohmoto M, Nightingale M P and Dennijs M 1982 Phys. Rev. Lett.49 405 [3] Simon B 1983 Phys. Rev. Lett.51 2167 [4] Hasan M Z and Kane C L 2010 Rev. Mod. Phys.82 3045 [5] Qi X L and Zhang S C 2011 Rev. Mod. Phys.83 1057 [6] Chiu C K, Teo J C Y, Schnyder A P and Ryu S 2016 Rev. Mod. Phys.88 035005 [7] Bernevig B A and Hughes T L Topological Insulators and Topological Superconductors (Princeton: Princeton University Press) [8] Bansil A, Lin H and Das T 2016 Rev. Mod. Phys.88 021004 [9] Armitage N P, Mele E J and Vishwanath A 2018 Rev. Mod. Phys.90 015001 [10] Bzdušek T, Wu Q, Rüegg A, Sigrist M and Soluyanov A A 2016 Nature538 75 [11] Wang Z, Sun Y, Chen X Q, Franchini C, Xu G, Weng H, Dai X and Fang Z 2012 Phys. Rev. B85 195320 [12] Burkov A A, Hook M D and Balents L 2011 Phys. Rev. B84 235126 [13] Benalcazar W A, Bernevig B A and Hughes T L 2017 Science357 61 [14] Benalcazar W A, Bernevig B A and Hughes T L 2017 Phys. Rev. B96 245115 [15] 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 [16] Prodan E, Hughes T L and Bernevig B A 2010 Phys. Rev. Lett.105 115501 [17] Mondragon-Shem I, Hughes T L, Song J and Prodan E 2014 Phys. Rev. Lett.113 046802 [18] Yang Y B, Li K, Duan L M and Xu Y 2021 Phys. Rev. B103 085408 [19] Yao S and Wang Z 2018 Phys. Rev. Lett.121 086803 [20] Yao S, Song F and Wang Z 2018 Phys. Rev. Lett.121 136802 [21] Zhang K, Yang Z S and Fang Chen 2020 Phys. Rev. Lett.125 126402 [22] Okuma N, Kawabata K, Shiozaki K and Sato M 2020 Phys. Rev. Lett.124 086801 [23] Goldman N, Satija I, Nikolic P, Bermudez A, MartinDelgado M A, Lewenstein M and Spielman I B 2010 Phys. Rev. Lett.105 255302 [24] Jotzu G, Messer M, Desbuquois R, Lebrat M, Uehlinger T, Greif D and Esslinger T 2014 Nature 515 7526 [25] Junemann J, Piga A, Ran S J, Lewenstein M, Rizzi M and Bermudez A 2017 Phys. Rev. X7 031057 [26] Konig M, Wiedmann S, Brune C, et al. 2007 Science318 5851 [27] Ueda K, Fujioka J, Takahashi Y, et al. 2012 Phys. Rev. Lett.109 136402 [28] Xie B Y, Wang H F, Wang H X, Zhu X Y, Jiang J H, Lu M H and Chen Y F 2018 Phys. Rev. B98 205147 [29] Mittal S, Orre V V, Zhu G, Gorlach M A, Poddubny A and Hafezi M 2019 Nat. Photon.13 692 [30] Ni X, Weiner M, Alù A and Khanikaev A B 2019 Nat. Mater.18 113 [31] Wei Q, Zhang X, Deng W, Lu J, Huang X, Yan M, Chen G, Liu Z and Jia S 2021 Nat. Mater.20 812 [32] Yang Z Z, Chen J H, Peng Y Y, et al. 2020 Chin. Phys. B29 104302 [33] Pei D L, Yang T, Chen M, et al. 2019 Chin. Phys. B28 124301 [34] Guo B, Shi K G, Qin H L, et al. 2020 Chin. Phys. B29 097403 [35] Roushan P, Neill C, Chen Y, Kolodrubetz M, et al. 2014 Nature515 241 [36] Cai W, Han J, Mei F, et al. 2019 Phys. Rev. Lett.123 080501 [37] Wang D W, Liu R B, Zhu S Y and Scully M O 2015 Phys. Rev. Lett.114 043602 [38] Gadway B 2015 Phys. Rev. A92 043606 [39] Chen L, Wang P, Meng Z, Huang L, Cai H, Wang D W, Zhu S Y and Zhang J 2018 Phys. Rev. Lett.120 193601 [40] Cai H, Liu J, Wu J, He Y, Zhu S Y, Zhang J X and Wang D W 2019 Phys. Rev. Lett.122 023601 [41] He Y Y, Mao R S, Cai H, Zhang J X, Li Y Q, Yuan L Q, Zhu S Y and Wang D W 2021 Phys. Rev. Lett.126 103601 [42] Scully M O, Fry E S, Ooi C H and Wdkiewicz K 2006 Phys. Rev. Lett.96 010501 [43] An Fangzhao Alex, Meier E J and Gadway Bryce 2017 Sci. Adv.3 e1602685 [44] Meier E J, et al. 2018 Science362 929 [45] Xie D, Gou W, Xiao T, et al. 2019 npj Quantum Inf.5 55 [46] Li L, Umer M and Gong J 2018 Phys. Rev. B98 205422 [47] Li C, Li S, Zhang G and Song Z 2017 Phys. Rev. B96 125418 [48] Zhang S L and Zhou Q 2017 Phys. Rev. A95 061601(R) [49] Maffei Maria, et al. 2018 New J. Phys.20 013023 [50] Cardano F, et al. 2017 Nat. Comm.8 15516
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