Periodic Reporting for period 4 - TopMechMat (Topological Mechanical Metamaterials)
Reporting period: 2022-08-01 to 2023-01-31
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.
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.
The main work performed towards the goal of this project was the experimental establishing of two new variants of topological bands. In a topological band, the vibrations of a material are characterized by a property that cannot be changed by small imperfections. Current research into topological condensed matter physics is exploring novel ways how this stability against imperfections is arising. It turns out, that it can always be traced back to a "knot" that is tied into the mathematical objects describing the behavior of the material. Over the last years know types of knots have been theoretically hypothesized. Our work is centered around the concrete experimental implementation of these novel knots. With this we contribute both to the further development of the theory of topological bands as well as towards the engineering of materials with novel properties. Our main results achieved so far on the fundamental side are the implementation of a higher order topological insulator as well as the first observation of a fragile topological bands. Towards applications, our key contributions have been the work on superlattices of colloidal nano-crystals as well as the design of reconfigurable metamaterials based on spiral local resonators.
The results can be summarized as follows: Six key publications highlight our principal accomplishments. In a 2018 Nature article, we utilized the preliminary version of our theoretical framework and design methodology to craft a vibrational structure that showcased a topological effect. This effect had only been predicted a year earlier and had not been observed in any other platform. In 2019, we conducted the first controlled experiment in which synthetic axial magnetic fields induced chiral Landau levels; this work was published in Nature Physics. In 2020, our research focused on the experimental characterization of the spectral flow in a fragile band, and the findings were featured in Science. Building on the insights from this Science article, we enhanced our understanding of the exotic superconductivity in twisted bi-layer graphene. This led to two publications in Physical Review Letters in 2021 and 2022, respectively.
The results can be summarized as follows: Six key publications highlight our principal accomplishments. In a 2018 Nature article, we utilized the preliminary version of our theoretical framework and design methodology to craft a vibrational structure that showcased a topological effect. This effect had only been predicted a year earlier and had not been observed in any other platform. In 2019, we conducted the first controlled experiment in which synthetic axial magnetic fields induced chiral Landau levels; this work was published in Nature Physics. In 2020, our research focused on the experimental characterization of the spectral flow in a fragile band, and the findings were featured in Science. Building on the insights from this Science article, we enhanced our understanding of the exotic superconductivity in twisted bi-layer graphene. This led to two publications in Physical Review Letters in 2021 and 2022, respectively.
The key places where we went beyond the state of the art is in the type of topology we managed to investigate with mechanical degrees of freedom. After 40 years of research on topology in condensed matter systems, there are still theoretical advances. We have shown that these advances are not merely a theoreticians dream, but can be readily observed in classical systems. This fuels the hope that such novel effects will be transferable to applications and devices useful for everyday technology. Our publication on a binary classifier for spoken words underlines the potential of mechanical metamaterials for technological applications.