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Abstract The acoustic properties of an acoustic crystal consisting of acoustic channels designed according to the gyroid minimal surface embedded in a 3D rigid material are investigated. The resulting gyroid acoustic crystal is characterized by a spin‐1 Weyl and a charge‐2 Dirac degenerate points that are enforced by its nonsymmorphic symmetry. The gyroid geometry and its symmetries produce multi‐fold topological degeneracies that occur naturally without the need for ad hoc geometry designs. The non‐trivial topology of the acoustic dispersion produces chiral surface states with open arcs, which manifest themselves as waves whose propagation is highly directional and remains confined to the surfaces of a 3D material. Experiments on an additively manufactured sample validate the predictions of surface arc states and produce negative refraction of waves at the interface between adjoining surfaces. The topological surface states in a gyroid acoustic crystal shed light on nontrivial bulk and edge physics in symmetry‐based compact continuum materials, whose capabilities augment those observed in ad hoc designs. The continuous shape design of the considered acoustic channels and the ensuing anomalous acoustic performance suggest this class of phononic materials with semimetal‐like topology as effective building blocks for acoustic liners and load‐carrying structural components with sound proofing functionality. 

Abstract The twist angle between a pair of stacked 2D materials has been recently shown to control remarkable phenomena, including the emergence of flat‐band superconductivity in twisted graphene bilayers, of higher‐order topological phases in twisted moiré superlattices, and of topological polaritons in twisted hyperbolic metasurfaces. These discoveries, at the foundations of the emergent field of twistronics, have so far been mostly limited to explorations in atomically thin condensed matter and photonic systems, with limitations on the degree of control over geometry and twist angle, and inherent challenges in the fabrication of carefully engineered stacked multilayers. Here, this work extends twistronics to widely reconfigurable macroscopic elastic metasurfaces consisting of LEGO pillar resonators. This work demonstrates highly tailored anisotropy over a single‐layer metasurface driven by variations in the twist angle between a pair of interleaved spatially modulated pillar lattices. The resulting quasi‐periodic moiré patterns support topological transitions in the isofrequency contours, leading to strong tunability of highly directional waves. The findings illustrate how the rich phenomena enabled by twistronics and moiré physics can be translated over a single‐layer metasurface platform, introducing a practical route toward the observation of extreme phenomena in a variety of wave systems, potentially applicable to both quantum and classical settings without multilayered fabrication requirements. 

Abstract Materials based on minimal surface geometries have shown superior strength and stiffness at low densities, which makes them promising continuous‐based material platforms for a variety of engineering applications. In this work, it is demonstrated how these mechanical properties can be complemented by dynamic functionalities resulting from robust topological guiding of elastic waves at interfaces that are incorporated into the considered material platforms. Starting from the definition of Schwarz P minimal surface, geometric parametrizations are introduced that break spatial symmetry by forming 1D dimerized and 2D hexagonal minimal surface‐based materials. Breaking of spatial symmetries produces topologically non‐trivial interfaces that support the localization of vibrational modes and the robust propagation of elastic waves along pre‐defined paths. These dynamic properties are predicted through numerical simulations and are illustrated by performing vibration and wave propagation experiments on additively manufactured samples. The introduction of symmetry‐breaking topological interfaces through parametrizations that modify the geometry of periodic minimal surfaces suggests a new strategy to supplement the load‐bearing properties of this class of materials with novel dynamic functionalities.