Applied Mathematics and Mechanics >
Topological transition enabled by composite symmetry-breaking paths in trefoil-knot honeycomb lattices
Received date: 2025-11-07
Revised date: 2026-01-15
Online published: 2026-03-02
Supported by
Project supported by the National Natural Science Foundation of China (Nos. 12232015 and 12572106), the National Key R&D Program of China (Nos. 2024YFB3408700, 2024YFB3408701, and 2024YFB3408703), and the Natural Science Foundation of Shaanxi Province of China (No. 2023-JC-YB-073)
Copyright
Topological phases are governed by lattice symmetries, yet how different symmetry-breaking paths (SBPs) affect topological transitions remains insufficiently understood. Most existing studies rely on a single SBP, and address only one bandgap, limiting independent control of multiple gaps. Here, we investigate multiple isolated Dirac points in a trefoil-knot-modified honeycomb lattice, and show that a single SBP generally inverts all relevant Dirac points simultaneously, whereas the tailored combinations of SBPs enable selective and programmable band inversion at targeted gaps. The excitation-dependent responses reveal strong modal selectivity. This capability is exploited to realize independently controllable multi-channel signal splitting, which is unattainable with a single SBP. The results enable SBPs as an effective design degree of freedom for programmable and reconfigurable topological elastic devices.
Tai REN , Xiuhui HOU , Tingting WANG , Zhiwei ZHU , Kai ZHANG , Zichen DENG . Topological transition enabled by composite symmetry-breaking paths in trefoil-knot honeycomb lattices[J]. Applied Mathematics and Mechanics, 2026 , 47(3) : 497 -508 . DOI: 10.1007/s10483-026-3364-6
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