Topological states constructed by two different trivial quantum wires
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.
- V. L. Berezinskii, JETP 32, 473 (1971a).
- V. L. Berezinskii, JETP 34, 610 (1971b).
- J. M. Kosterlitz and D. J. Thouless, J. Phys. C Solid State Phys. 5, L124–L126 (1972).
- J. M. Kosterlitz and D. J. Thouless, J. Phys. C: Solid State Phys. 6, 1181 (1973).
- J. M. Kosterlitz, J. Phys. C: Solid State Phys 7, 1046 (1974).
- B. A. Bernevig and T. L. Hughes, Topological insulators and topological superconductors (Princeton university press, 2013).
- R. Moessner and J. E. Moore, Topological Phases of Matter (Cambridge University Press, 2021).
- M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. 82, 3045 (2010).
- X.-L. Qi and S.-C. Zhang, Rev. Mod. Phys. 83, 1057 (2011).
- S. R. Elliott and M. Franz, Rev. Mod. Phys. 87, 137 (2015).
- X.-G. Wen, Rev. Mod. Phys. 89, 041004 (2017).
- M. Ezawa, Phys. Rev. Research 2, 033397 (2020).
- A. M. Cook and J. E. Moore, Commun. Phys. 5, 262 (2022).
- J. Song and E. Prodan, Phys. Rev. B 89, 224203 (2014).
- Z.-W. Zuo and D. Kang, Phys. Rev. A 106, 013305 (2022).
- S.-J. Choi and B. Trauzettel, Phys. Rev. B 107, 245409 (2023).
- M. Jangjan and M. V. Hosseini, Sci. Rep. 10, 14256 (2020).
- J. C. Y. Teo and C. L. Kane, Phys. Rev. B 89, 085101 (2014).
- J. Klinovaja and D. Loss, Eur. Phys. J. B 87, 171 (2014).
- E. Sagi and Y. Oreg, Phys. Rev. B 90, 201102 (2014).
- T. Meng, Phys. Rev. B 92, 115152 (2015).
- L. Zhou, Entropy 22, 746 (2020).
- V. M. M. Alvarez and M. D. Coutinho-Filho, Phys. Rev. A 99, 013833 (2019).
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.