Topological properties of non-Hermitian Creutz ladders

doi:10.1088/1674-1056/ac3991

Abstract We study topological properties of the one-dimensional Creutz ladder model with different non-Hermitian asymmetric hoppings and on-site imaginary potentials, and obtain phase diagrams regarding the presence and absence of an energy gap and in-gap edge modes. The non-Hermitian skin effect (NHSE), which is known to break the bulk-boundary correspondence (BBC), emerges in the system only when the non-Hermiticity induces certain unbalanced non-reciprocity along the ladder. The topological properties of the model are found to be more sophisticated than that of its Hermitian counterpart, whether with or without the NHSE. In one scenario without the NHSE, the topological winding is found to exist in a two-dimensional plane embedded in a four-dimensional space of the complex Hamiltonian vector. The NHSE itself also possesses some unusual behaviors in this system, including a high spectral winding without the presence of long-range hoppings, and a competition between two types of the NHSE, with the same and opposite inverse localization lengths for the two bands, respectively. Furthermore, it is found that the NHSE in this model does not always break the conventional BBC, which is also associated with whether the band gap closes at exceptional points under the periodic boundary condition.

Keywords: topological phases bulk-boundary correspondence non-Hermitian physics Creutz ladders

Received: 25 August 2021
Revised: 25 September 2021
Accepted manuscript online: 15 November 2021

PACS:	03.65.Vf	(Phases: geometric; dynamic or topological)
	05.50.+q	(Lattice theory and statistics)
	64.70.Tg	(Quantum phase transitions)

Corresponding Authors: Linhu Li
E-mail: lilh56@mail.sysu.edu.cn

Cite this article:

Hui-Qiang Liang(梁辉强) and Linhu Li(李林虎) Topological properties of non-Hermitian Creutz ladders 2022 Chin. Phys. B 31 010310

[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] Bernevig B A and Hughes T L 2013 Topological insulators and topological superconductors (Princeton University Press)
[4] Moiseyev N 2011 Non-Hermitian quantum mechanics (Cambridge University Press)
[5] Bender C M and Boettcher S 1998 Phys. Rev. Lett. 80 5243
[6] Bender C M 2007 Reports on Progress in Physics 70 947
[7] Rotter I 2009 J. Phys. A: Math. Theor. 42 153001
[8] Yoshida T, Peters R and Kawakami N 2018 Phys. Rev. B 98 035141
[9] Yamamoto K, Nakagawa M, Adachi K, Takasan K, Ueda M and Kawakami N 2019 Phys. Rev. Lett. 123 123601
[10] Rüter C E, Makris K G, El-Ganainy R, Christodoulides D N, Segev M and Kip D 2010 Nat. Phys. 6 192
[11] Longhi S 2018 Europhys. Lett. 120 64001
[12] Ozawa T, Price H M, Amo A, et al. 2019 Rev. Mod. Phys. 91 015006
[13] Lee T E 2016 Phys. Rev. Lett. 116 133903
[14] Martinez Alvarez V M, Barrios Vargas J E and Foa Torres L E F 2018 Phys. Rev. B 97 121401
[15] Xiong Y 2018 Journal of Physics Communications 2 035043
[16] Kunst F K, Edvardsson E, Budich J C and Bergholtz E J 2018 Phys. Rev. Lett. 121 026808
[17] Yao S and Wang Z 2018 Phys. Rev. Lett. 121 086803
[18] Yokomizo K and Murakami S 2019 Phys. Rev. Lett. 123 066404
[19] Lee C H and Thomale R 2019 Phys. Rev. B 99 201103
[20] Li L, Lee C H and Gong J 2019 Phys. Rev. B 100 075403
[21] Lee C H, Li L, Thomale R and Gong J 2020 Phys. Rev. B 102 085151
[22] Yang Z, Zhang K, Fang C and Hu J 2020 Phys. Rev. Lett. 125 226402
[23] Zhang K, Yang Z and Fang C 2020 Phys. Rev. Lett. 125 126402
[24] Okuma N, Kawabata K, Shiozaki K and Sato M 2020 Phys. Rev. Lett. 124 086801
[25] Wang K, Dutt A, Yang K Y, Wojcik C C, Vučković J and Fan S 2021 Science 371 1240
[26] Li L, Mu S, Lee C H and Gong J 2012 Preprint arXiv: 2012.08799v2
[27] Creutz M 1999 Phys. Rev. Lett. 83 2636
[28] Bermudez A, Patanè D, Amico L and Martin-Delgado M A 2009 Phys. Rev. Lett. 102 135702
[29] Sticlet D, Seabra L, Pollmann F and Cayssol J 2014 Phys. Rev. B 89 115430
[30] Hügel D and Paredes B 2014 Phys. Rev. A 89 023619
[31] Li L and Chen S 2015 Europhys. Lett. 109 40006
[32] Li L and Chen S 2015 Phys. Rev. B 92 085118
[33] Sun N and Lim L K 2017 Phys. Rev. B 96 035139
[34] Jünemann J, Piga A, Ran S J, Lewenstein M, Rizzi M and Bermudez A 2017 Phys. Rev. X 7 031057
[35] Lin Y, Hao W and Guo H 2018 Chin. Phys. B 27 010204
[36] Kang J H, Han J H and Shin Y 2020 New J. Phys. 22 013023
[37] Zhou L and Du Q 2020 Phys. Rev. A 101 033607
[38] Song F, Yao S and Wang Z 2019 Phys. Rev. Lett. 123 170401
[39] Lee E, Lee H and Yang B J 2020 Phys. Rev. B 101 121109
[40] Jin L and Song Z 2019 Phys. Rev. B 99 081103
[41] Wu H C, Jin L and Song Z 2019 Phys. Rev. B 100 155117
[42] Zhou L 2020 Entropy 22 746
[43] Zhou L, Gu Y and Gong J 2021 Phys. Rev. B 103 L041404
[44] Li L, Lee C H and Gong J 2020 Phys. Rev. Lett. 124 250402
[45] Su W P, Schrieffer J R and Heeger A J 1979 Phys. Rev. Lett. 42 1698
[46] Gong Z, Ashida Y, Kawabata K, Takasan K, Higashikawa S and Ueda M 2018 Phys. Rev. X 8 031079
[47] Kawabata K, Shiozaki K, Ueda M and Sato M 2019 Phys. Rev. X 9 041015
[48] Hatano N and Nelson D R 1996 Phys. Rev. Lett. 77 570
[49] Li L, Lee C H, Mu S and Gong J 2020 Nat. Commun. 11 5491
[50] Yi Y and Yang Z 2020 Phys. Rev. Lett. 125 186802
[51] Yin C, Jiang H, Li L, Lü R and Chen S 2018 Phys. Rev. A 97 052115
[52] Sánchez-Soto L L, Monzón J J, Barriuso A G and Cariñena J F 2012 Physics Reports 513 191
[53] Mailybaev A A, Kirillov O N and Seyranian A P 2005 Phys. Rev. A 72 014104
[54] Shen H, Zhen B and Fu L 2018 Phys. Rev. Lett. 120 146402

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