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The concepts of twistronics and magic angle have been widely applied beyond electrons, powering up new advancements in optics, acoustics, and heat transport. However, achieving a unidirectional or all-direction "magic angle" remains an established yet unresolved challenge in twisted bilayer metasurfaces across various disciplines. Our work proposes and validates a "twist-on-twist" paradigm to realizing unidirectional propagation and robust magic angle at arbitrary directions of the elastic out-of-plane wave. Our elastic metasurface not only exhibits a twisted configuration between the stacked bilayer but also significantly enhances out-of-plane symmetry breaking by further twisting meta-atoms in one constituent layer. Our twist-on-twist method unleashes versatile potentials of twisted thin composite materials to control the extreme propagation of topological elastic waves and even opens up new possibilities for photonic, phononic, and thermal moiré metamaterials.
Li et al. (Wed,) studied this question.