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 addr...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.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.12232015 and12572106)the National Key R&D Program of China(Nos.2024YFB3408700,2024YFB3408701,2024YFB3408703)the Natural Science Foundation of Shaanxi Province of China(No.2023-JC-YB-073)。
文摘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.
