Topological phases and type-II edge state in two-leg-coupled Su-Schrieffer-Heeger chains

doi:10.1088/1674-1056/ac3650

中国物理B ›› 2022, Vol. 31 ›› Issue (1): 14208-014208.doi: 10.1088/1674-1056/ac3650

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

收稿日期:2021-09-15 修回日期:2021-11-01 接受日期:2021-11-04 出版日期:2021-12-03 发布日期:2021-12-18
通讯作者: Xin Guan, Jingtao Fan E-mail:guanxin810712@163.com;bkxyfjt@163.com
基金资助:
Project partially supported by the National Natural Science Foundation of China (Grant Nos. 12034012, 12074232, and 11804204) and 1331KSC.

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

Received:2021-09-15 Revised:2021-11-01 Accepted:2021-11-04 Online:2021-12-03 Published:2021-12-18
Contact: Xin Guan, Jingtao Fan E-mail:guanxin810712@163.com;bkxyfjt@163.com
Supported by:
Project partially supported by the National Natural Science Foundation of China (Grant Nos. 12034012, 12074232, and 11804204) and 1331KSC.

摘要/Abstract

摘要： 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.

关键词: topological quantum states, edge state, momentum-space lattice

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.

Key words: topological quantum states, edge state, momentum-space lattice

中图分类号: (Quantum description of interaction of light and matter; related experiments)

42.50.Ct

71.23.An (Theories and models; localized states)

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[J]. 中国物理B, 2022, 31(1): 14208-014208.

参考文献

[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 Nature 538 75
[11] Wang Z, Sun Y, Chen X Q, Franchini C, Xu G, Weng H, Dai X and Fang Z 2012 Phys. Rev. B 85 195320
[12] Burkov A A, Hook M D and Balents L 2011 Phys. Rev. B 84 235126
[13] Benalcazar W A, Bernevig B A and Hughes T L 2017 Science 357 61
[14] Benalcazar W A, Bernevig B A and Hughes T L 2017 Phys. Rev. B 96 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. B 103 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. X 7 031057
[26] Konig M, Wiedmann S, Brune C, et al. 2007 Science 318 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. B 98 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. B 29 104302
[33] Pei D L, Yang T, Chen M, et al. 2019 Chin. Phys. B 28 124301
[34] Guo B, Shi K G, Qin H L, et al. 2020 Chin. Phys. B 29 097403
[35] Roushan P, Neill C, Chen Y, Kolodrubetz M, et al. 2014 Nature 515 241
[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. A 92 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 Science 362 929
[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. B 98 205422
[47] Li C, Li S, Zhang G and Song Z 2017 Phys. Rev. B 96 125418
[48] Zhang S L and Zhou Q 2017 Phys. Rev. A 95 061601(R)
[49] Maffei Maria, et al. 2018 New J. Phys. 20 013023
[50] Cardano F, et al. 2017 Nat. Comm. 8 15516

Topological phases and type-II edge state in two-leg-coupled Su-Schrieffer-Heeger chains

Topological phases and type-II edge state in two-leg-coupled Su-Schrieffer-Heeger chains

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Ningjing Yang(杨柠境), Hai Yang(杨海), and Guojun Jin(金国钧). Interface-induced topological phase and doping-modulated bandgap of two-dimensioanl graphene-like networks[J]. 中国物理B, 2023, 32(1): 17201-017201.
[2]	Jianfei Chen(陈健菲), Chaohua Wu(吴超华), Jingtao Fan(樊景涛), and Gang Chen(陈刚). Characterization of topological phase of superlattices in superconducting circuits[J]. 中国物理B, 2022, 31(8): 88501-088501.
[3]	Liu-Yong Cheng(程留永), Li-Na Zheng(郑黎娜), Ruixiang Wu(吴瑞祥), Hong-Fu Wang(王洪福), and Shou Zhang(张寿). Change-over switch for quantum states transfer with topological channels in a circuit-QED lattice[J]. 中国物理B, 2022, 31(2): 20305-020305.
[4]	Cheng-Zhi Ye(叶成芝), Lan-Yun Zhang(张蓝云), and Hai-Bin Xue(薛海斌). Quantum transport signatures of non-trivial topological edge states in a ring-shaped Su-Schrieffer-Heeger double-chain system[J]. 中国物理B, 2022, 31(2): 27304-027304.
[5]	Jianfeng Chen(陈剑锋) and Zhi-Yuan Li(李志远). Topological photonic states in gyromagnetic photonic crystals: Physics, properties, and applications[J]. 中国物理B, 2022, 31(11): 114207-114207.
[6]	Chao Zeng(曾超), Zhiwei Guo(郭志伟), Kejia Zhu(祝可嘉), Caifu Fan(范才富), Guo Li(李果), Jun Jiang(江俊), Yunhui Li(李云辉), Haitao Jiang(江海涛), Yaping Yang(羊亚平), Yong Sun(孙勇), and Hong Chen(陈鸿). Efficient and stable wireless power transfer based on the non-Hermitian physics[J]. 中国物理B, 2022, 31(1): 10307-010307.
[7]	Weijie Wang(王威杰), Xiaolong Lü(吕小龙), and Hang Xie(谢航). Floquet bands and photon-induced topological edge states of graphene nanoribbons[J]. 中国物理B, 2021, 30(6): 66701-066701.
[8]	Weijie Wang(王威杰), Xiaolong Lü(吕小龙), and Hang Xie(谢航). Erratum to “Floquet bands and photon-induced topological edge states of graphene nanoribbons”[J]. 中国物理B, 2021, 30(11): 119901-119901.
[9]	Yali Jia(贾雅利) and Zhi-Jian Li(李志坚). High winding number of topological phase in non-unitary periodic quantum walk[J]. 中国物理B, 2021, 30(10): 100301-100301.
[10]	Huiping Wang(王会平), Li Ren(任莉), Liguo Qin(秦立国), and Yueyin Qiu(邱岳寅). Edge states enhanced by long-range hopping: An analytical study[J]. 中国物理B, 2021, 30(10): 107301-107301.
[11]	郭斌, 师凯歌, 秦海浪, 周良, 陈伟强, 叶飞, 梅佳伟, 何洪涛, 潘天洛, 王干. Evidence for topological superconductivity: Topological edge states in Bi₂Te₃/FeTe heterostructure[J]. 中国物理B, 2020, 29(9): 97403-097403.
[12]	杨武庆, 李骐, 杨林鹏, 胡自翔. Neutral excitation and bulk gap of fractional quantum Hall liquids in disk geometry[J]. 中国物理B, 2019, 28(6): 67303-067303.
[13]	裴东亮, 杨洮, 陈猛, 姜恒. Underwater acoustic metamaterial based on double Dirac cone characteristics in rectangular phononic crystals[J]. 中国物理B, 2019, 28(12): 124301-124301.
[14]	张冠群, 林立, 彭海琳, 刘忠范, 康宁, 徐洪起. Coulomb-dominated oscillations in a graphene quantum Hall Fabry-Pérot interferometer[J]. 中国物理B, 2019, 28(12): 127203-127203.
[15]	邹剑飞, 康静. Distinct edge states and optical conductivities in the zigzag and armchair silicene nanoribbons under exchange and electric fields[J]. 中国物理B, 2018, 27(3): 37301-037301.