Topological states constructed by two different trivial quantum wires

doi:10.1088/1674-1056/ad8fa3

中国物理B ›› 2025, Vol. 34 ›› Issue (1): 10306-010306.doi: 10.1088/1674-1056/ad8fa3

Topological states constructed by two different trivial quantum wires

Jing-Run Lin(林景润), Linxi Lv(吕林喜), and Zheng-Wei Zuo(左正伟)†

School of Physics and Engineering, Henan University of Science and Technology, Luoyang 471023, China

收稿日期:2024-10-11 修回日期:2024-10-31 接受日期:2024-11-07 发布日期:2024-12-24
通讯作者: Zheng-Wei Zuo E-mail:zuozw@haust.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grants Nos. 12074101 and 11604081). Z W Zuo is also sponsored by the Natural Science Foundation of Henan Province, China (Grant No. 212300410040).

Topological states constructed by two different trivial quantum wires

Jing-Run Lin(林景润), Linxi Lv(吕林喜), and Zheng-Wei Zuo(左正伟)†

School of Physics and Engineering, Henan University of Science and Technology, Luoyang 471023, China

Received:2024-10-11 Revised:2024-10-31 Accepted:2024-11-07 Published:2024-12-24
Contact: Zheng-Wei Zuo E-mail:zuozw@haust.edu.cn
About author:2025-010306-241471.pdf
Supported by:
Project supported by the National Natural Science Foundation of China (Grants Nos. 12074101 and 11604081). Z W Zuo is also sponsored by the Natural Science Foundation of Henan Province, China (Grant No. 212300410040).

摘要/Abstract

摘要： The topological states of the two-leg and three-leg ladders formed by two trivial quantum wires with different lattice constants are theoretically investigated. Firstly, we take two trivial quantum wires with a lattice constant ratio of 1:2 as an example. For the symmetric nearest-neighbor intra-chain hopping two-leg ladder, the inversion symmetry protected topological insulator phase with two degenerate topological edge states appears. When the inversion symmetry is broken, the topological insulators with one or two topological edge states of different energies and topological metals with edge states embedded in the bulk states could emerge depending on the filling factor. The topological origin of these topological states in the two-leg ladders is the topological properties of the Chern insulators and Chern metals. According to the arrangement of two trivial quantum wires, we construct two types of three-leg ladders. Each type of the three-leg ladder could be divided into one trivial subspace and one topological nontrivial subspace by unitary transformation. The topological nontrivial subspace corresponds to the effective two-leg ladder model. As the filling factor changes, the system could be in topological insulators or topological metals phases. When the two-leg ladder is constructed by two trivial quantum wires with a lattice constant ratio of 1:3 and 2:3, the system could also realize rich topological states such as the topological insulators and topological metals with the topological edge states. These rich topological states in the two-leg and three-leg ladders could be confirmed by current experimental techniques.

关键词: trivial quantum wire, topological invariant, inversion symmetric topological insulator, Chern metal

Abstract: The topological states of the two-leg and three-leg ladders formed by two trivial quantum wires with different lattice constants are theoretically investigated. Firstly, we take two trivial quantum wires with a lattice constant ratio of 1:2 as an example. For the symmetric nearest-neighbor intra-chain hopping two-leg ladder, the inversion symmetry protected topological insulator phase with two degenerate topological edge states appears. When the inversion symmetry is broken, the topological insulators with one or two topological edge states of different energies and topological metals with edge states embedded in the bulk states could emerge depending on the filling factor. The topological origin of these topological states in the two-leg ladders is the topological properties of the Chern insulators and Chern metals. According to the arrangement of two trivial quantum wires, we construct two types of three-leg ladders. Each type of the three-leg ladder could be divided into one trivial subspace and one topological nontrivial subspace by unitary transformation. The topological nontrivial subspace corresponds to the effective two-leg ladder model. As the filling factor changes, the system could be in topological insulators or topological metals phases. When the two-leg ladder is constructed by two trivial quantum wires with a lattice constant ratio of 1:3 and 2:3, the system could also realize rich topological states such as the topological insulators and topological metals with the topological edge states. These rich topological states in the two-leg and three-leg ladders could be confirmed by current experimental techniques.

Key words: trivial quantum wire, topological invariant, inversion symmetric topological insulator, Chern metal

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

03.65.Vf

73.43.-f (Quantum Hall effects) 03.65.-w (Quantum mechanics) 02.10.Ox (Combinatorics; graph theory)

Jing-Run Lin(林景润), Linxi Lv(吕林喜), and Zheng-Wei Zuo(左正伟). Topological states constructed by two different trivial quantum wires[J]. 中国物理B, 2025, 34(1): 10306-010306.

Jing-Run Lin(林景润), Linxi Lv(吕林喜), and Zheng-Wei Zuo(左正伟). Topological states constructed by two different trivial quantum wires[J]. Chin. Phys. B, 2025, 34(1): 10306-010306.

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Topological states constructed by two different trivial quantum wires

Topological states constructed by two different trivial quantum wires

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