Extended Data Fig. 5: Photonic and phononic band structures of Archimedean lattices constructed by DSG.
a Photonic band structure (TM mode) of the ideal and DSG-enabled (3.4.6.4) lattices calculated using COMSOL Multiphysics. The particle diameter is σ = 0.9, a and the refractive index is n = 3.0, where a denotes the characteristic bond length. While the ideal lattice exhibits no complete band gap, the lattice constructed via DSG displays a narrow but finite photonic band gap, arising from DSG-induced geometric distortions. b Photonic band structure (TM mode) of (4.82) lattices with and without helper (centre-filling) particles. The centre-filled (4.82) lattice exhibits an additional photonic band gap that is absent in the unfilled structure, demonstrating the role of DSG-compatible repulsers in tailoring optical properties. Here σ = 0.8, a and n = 3.0. c Vibrational density of states (VDOS) and dispersion relations of the (33.42) lattice under partial (DSG) and full pinning. The dispersion relations are obtained from the current–current correlation function c(k, ω), with the wavevector k averaged over 10 distinct directions (Methods). Partial DSG pinning opens a phononic band gap that is absent under full pinning, highlighting the sensitivity of vibrational spectra to symmetry-selective constraints and kinetic accessibility. Inset schematics show the corresponding lattice configurations, with pinned particles indicated by red circles. Simulation parameters: Atrap = 50kBT, Γ = 60.
