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<p>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.</p>

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Topological transition enabled by composite symmetry-breaking paths in trefoil-knot honeycomb lattices

  • 期刊论文

  • 发表日期：

    2026年2月28日

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  • Tai Ren,
  • Xiuhui Hou,
  • Tingting Wang,
  • Zhiwei Zhu,
  • Kai Zhang,
  • Zichen Deng

摘要

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.