Topological insulators on the square–hexagon lattice driven by next-nearest-neighbor hopping

• Published in: Journal of physics. Condensed matter 2022-07, Vol.34 (27), p.275501
• Main Authors: Wang, Guo Xiang, Zhang, Ying Zheng, Wei, Jun Hong
• Format: Article
• Language: English
• Subjects: square–hexagon lattice; tight-binding model; topological phase transition
• ISSN: 0953-8984; 1361-648X
• DOI: 10.1088/1361-648X/ac6788

We investigate the topological phase transition of the square-hexagon lattice driven by the next-nearest-neighbor (NNN) hopping. By means of the Fukui-Hatsugai method, the topological invariant can be determined. The phase diagrams in the ( , ) plane for different filling fractions are displayed, together with the size of the bulk band gap. We find the competition between and can drive the system into topological nontrivial phase, with = 1. Interestingly, for 2/5 and 3/5 filling fractions, topological nontrivial phase can be easily realized when the NNN hoppings are turned on. Besides, the phase diagrams in the plane of and ( and ) are also investigated. By numerically diagonalizing the Hamiltonian, the bulk band structures are calculated. And the topological trivial and nontrivial phase are also distinguished in terms of helical edge state. In experiments, these topological phase transitions may be realized by shaking optical lattice.