Vibrational properties of solids are typically fixed by given material constants. However, by shaping the geometry of small building blocks out of which materials are built, one can enrich their behavior beyond the one given by the host material. One is speaking of a meta-(beyond) material. However, we are typically confronted with the problem, that we wish to design a property observable at the large scale of a material, not the properties of the smallest building blocks. Bridging between these small blocks that can be designed, and the large scale functional requirements is a challenge. With our work we address this challenge using concept from quantum mechanical low-temperature electron systems and apply them to the problem of vibrations in materials.
By overcoming this challenge, we will be able to provide materials engineers with design templates that allow them to fabricate a large variety of devices. Possible applications are signal filters for WiFi and 5G communications that allow for more bandwidth at lower power levels. Other applications could be enhanced vibration isolation of large industrial facilities to reduce noise emission, or in contrast, intelligent energy harvesting out of environmental noise. Just about anything that requires exquisit control of how waves travel through materials.
The overall objective is to further our basic understanding of topological band theory in the context of classical vibrations. Once we harness this design tool, the aforementioned device application could become available.
In conclusion, we have made significant strides in metamaterial design. Methodologically, we have developed a new optimization strategy for mechanical metamaterials adept at tackling the aforementioned challenges. By employing a modern evolutionary strategy (CMA-ES) to design material structures, we integrated the intricate cost functions essential for embedding large-scale functionality within microscopic material design. With this innovative, data-driven approach, we have managed to overcome various technological hurdles. As evidence, we present several scientific breakthroughs, including the first observation of a higher-order topological insulator, the first realization of band structures with an axial magnetic field, and the pioneering experimental characterization of a fragile topological system. The last discovery is especially noteworthy, as this type of topology could be central to superconductivity in twisted bi-layer graphene—a current enigma in condensed matter physics. On the application front, our project demonstrates how a passive mechanical structure, designed using our tools, can act as a binary classifier for spoken words. This last endeavor vividly illustrates the potential of mechanical metamaterials as intelligent yet passive sensors.
