Broadband topological transitions in twisted elastodynamic metasurfaces

In the last decade, the connection between physics and topology has resulted in the discovery of several new phenomena. A celebrated example is the field of topological insulators [X.-L. Qi, S.-C. Zhang, <i>Rev. Mod. Phys.</i> <b>83</b>, 1057-1110 (2011)]., in which topological quantities describing the bulk medium response in reciprocal space dictate the presence of protected transport states at the boundary of a finite sample. Broken symmetries in the microscopic structure of a material play a prominent role in determining its topological features relevant to these phenomena. As another landmark phenomenon driven by broken symmetries, twistronics leverages the rotation angle between coupled layers to control in extreme ways the dispersion topology, leading to flat-band superconductivity [Y. Cao <i>et al.</i>, <i>Nature</i> <b>556</b>, 43-50 (2018)] and topological transitions for polaritons [G. Hu <i>et al.</i>, <i>Nature</i> <b>582</b>, 209-213 (2020)]. Here, we apply these concepts to elastodynamic waves, and exploit the twist degree-of-freedom to control broken symmetries in the microscopic structure of elastic metasurfaces, demonstrating extreme wave control. We predict and experimentally demonstrate topological transitions within twisted elastodynamic metasurfaces, which we harness for broadband, reconfigurable, and robust manipulation of phonons. Our twist-elastic approach opens alternative directions in microelectronics, microfluidics, and ultrasound sensing, leveraging precise multifunctional engineering of mechanical vibrations of relevance to many modern technologies.