Topological properties of non-Hermitian Creutz ladders

doi:10.1088/1674-1056/ac3991

中国物理B ›› 2022, Vol. 31 ›› Issue (1): 10310-010310.doi: 10.1088/1674-1056/ac3991

所属专题： SPECIAL TOPIC — Non-Hermitian physics

Topological properties of non-Hermitian Creutz ladders

Hui-Qiang Liang(梁辉强) and Linhu Li(李林虎)^†

Guangdong Provincial Key Laboratory of Quantum Metrology and Sensing&School of Physics and Astronomy, Sun Yat-Sen University(Zhuhai Campus), Zhuhai 519082, China

收稿日期:2021-08-25 修回日期:2021-09-25 接受日期:2021-11-15 出版日期:2021-12-03 发布日期:2021-12-23
通讯作者: Linhu Li E-mail:lilh56@mail.sysu.edu.cn

Topological properties of non-Hermitian Creutz ladders

Hui-Qiang Liang(梁辉强) and Linhu Li(李林虎)^†

Guangdong Provincial Key Laboratory of Quantum Metrology and Sensing&School of Physics and Astronomy, Sun Yat-Sen University(Zhuhai Campus), Zhuhai 519082, China

Received:2021-08-25 Revised:2021-09-25 Accepted:2021-11-15 Online:2021-12-03 Published:2021-12-23
Contact: Linhu Li E-mail:lilh56@mail.sysu.edu.cn

摘要/Abstract

摘要： 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.

关键词: topological phases, bulk-boundary correspondence, non-Hermitian physics, Creutz ladders

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.

Key words: topological phases, bulk-boundary correspondence, non-Hermitian physics, Creutz ladders

中图分类号: (Phases: geometric; dynamic or topological)

03.65.Vf

05.50.+q (Lattice theory and statistics) 64.70.Tg (Quantum phase transitions)

Hui-Qiang Liang(梁辉强) and Linhu Li(李林虎). Topological properties of non-Hermitian Creutz ladders[J]. 中国物理B, 2022, 31(1): 10310-010310.

Hui-Qiang Liang(梁辉强) and Linhu Li(李林虎). Topological properties of non-Hermitian Creutz ladders[J]. Chin. Phys. B, 2022, 31(1): 10310-010310.

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Topological properties of non-Hermitian Creutz ladders

Topological properties of non-Hermitian Creutz ladders

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