Abstract We propose a new generalized Su-Schrieffer-Heeger model with hierarchical long-range hopping based on a one-dimensional tetratomic chain. The properties of the topological states and phase transition, which depend on the cointeraction of the intracell and intercell hoppings, are investigated using the phase diagram of the winding number. It is shown that topological states with large positive/negative winding numbers can readily be generated in this system. The properties of the topological states can be verified by the ring-type structures in the trajectory diagram of the complex plane. The topological phase transition is strongly related to the opening (closure) of an energy bandgap at the center (boundaries) of the Brillouin zone. Finally, the non-zero-energy edge states at the ends of the finite system are revealed and matched with the bulk-boundary correspondence.
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11405100), the Natural Science Basic Research Program in Shaanxi Province of China (Grant Nos. 2022JZ-02, 2020JM-507, and 2019JM-332), the Doctoral Research Fund of Shaanxi University of Science and Technology in China (Grant Nos. 2018BJ-02 and 2019BJ-58), and the Youth Innovation Team of Shaanxi Universities.
Corresponding Authors:
Guan-Qiang Li
E-mail: liguanqiang@sust.edu.cn
Cite this article:
Guan-Qiang Li(李冠强), Bo-Han Wang(王博涵), Jing-Yu Tang(唐劲羽), Ping Peng(彭娉), and Liang-Wei Dong(董亮伟) Topological properties of tetratomic Su-Schrieffer-Heeger chains with hierarchical long-range hopping 2023 Chin. Phys. B 32 077102
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