Topological mechanical states in geometry-driven hyperuniform materials.

Disordered hyperuniform materials are increasingly drawing attention due to their unique physical properties, associated with global isotropy and locally broken orientational symmetry, that set them apart from traditional crystalline materials. Using a dynamic space-partitioning process, we generate disordered hyperuniform cellular structures where distinct patterns of pentagonal and heptagonal topological defects emerge within hexagonal domains. The microscopic defect dynamics are guided by local topological transitions, commonly observed in viscoelastic systems. This leads to a reduction in the system's structural entropy as hyperuniformity is attained, marked by the rise and fall of certain locally favored motifs. Further, we introduce an elastic hyperuniform material that exhibits evolving topological mechanical states in the continuum. Through vibration experiments and numerical analysis, we show energy localization around these defects, which is tied to the topological band gaps inherent to our geometry-driven material. We suggest that this robust dynamic mechanism influences a broad spectrum of disordered systems, from synthetic materials to biological structures guided by stigmergic interactions.