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Metamaterials, Waves and Topology

Applicant Huber Sebastian
Number 182240
Funding scheme Project funding (Div. I-III)
Research institution Institut für Theoretische Physik ETH Zürich
Institution of higher education ETH Zurich - ETHZ
Main discipline Theoretical Physics
Start/End 01.01.2019 - 31.12.2022
Approved amount 318'870.00
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All Disciplines (2)

Theoretical Physics
Material Sciences

Keywords (2)

Metamaterials; Topology

Lay Summary (German)

Das verstehen von Wellen und deren Ausbreitung liegt einer Vielzahl von fundamentalen and und angewandten Problemen zugrunde. Das reicht vom Design von effizienten Antennen in mobilen Geräten über die Schallisolierung industrieller Anlagen bis hin zum Design und Verständnis zukünftiger Technologien wie einem Quantencomputer. Über das Verständnis hinaus, versuchen wir unser Wissen einzusetzen um die Ausbreitung von Wellen aktiv zu kontrollieren. Das wiederum ermöglicht Anwendungen wie Wellenleiter für die Informationsverarbeitung oder zum Nutzen von Umgebungsrauschen für die Gewinnung elektrischer Energie.
Lay summary
Wir versuchen moderne Theorien aus dem Bereich der quantenmechanischen Tieftemperaturphysik in den Bereich der klassischen Wellenphänomene zu übersetzen. Insbesondere verwenden wir Ideen der topologischen Bandtheorie um neue Materialien zu entwerfen, welche neue Vibrationeigenschaften zeigen. Dazu gehören Materialien in denen sich Schall nur in eine Richtung ausbreiten kann, oder in welchen Schall aktiv manipuliert werden kann. Aus der Theorie und der Praxis im Umgang mit elektronischen Systemen wissen wir, dass ein starkes Magnetfeld das Verhalten von Elektronen in essentieller Art und Weise beeinflussen kann. Um diese Phänomenologie auf die Physik der Vibrationen zu übersetzen suchen wir nach Möglichkeiten Materialien so zu konstruieren, damit die Vibrationen sich verhalten wie wenn sie einem Magnetfeld ausgesetzt wären. Das Verwenden von Konzepten aus der Hochenergiephysik, wie z.B. die berühmte Weyl-Gleichung, soll uns helfen dieses Ziel zu erreichen. 
Direct link to Lay Summary Last update: 20.12.2018

Responsible applicant and co-applicants


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Wave propagation is controlled by three key ingredients. First, the structure of the wave, e.g., is it a scalar, vectorial, or tensorial wave such as in acoustics, electromagnetism or in general relativity, respectively? Second, constitutive relations dictate how waves are scattered at surfaces. And finally, the parameters in the wave equation, such as the refractive index in electromagnetism, the elastic moduli for waves in solids, or the potential-landscape and particle interactions in the case of the Schrödinger equation, influence how waves are shaped when traveling through space and time. The aim of this proposal is to use concepts from modern condensed matter research to achieve control over the way waves propagate. In particular, we want to capitalize on the theory of topological band theory developed for the description of electronic low-temperature physics to steer classical waves in elastic and acoustic system.The control of wave propagation has a wide range of applications. In metamaterials research target functionalities include vibration isolation, the design of communication networks, both classical and quantum, energy harvesting, cloaking, just to name a few. On the road to a large scale quantum computing device qubits and their controlled couplings have to be carefully laid out. Given the wave nature of quantum objects, this is in essence a wave control problem.Classical waves provide an extremely versatile platform to explore fundamentally new theoretical concepts. A considerable effort of modern condensed matter theory research is concerned with the prediction of new types and classes of topological band effects. The most exciting directions include point and line degeneracies in the excitation spectrum of lattice systems that are protected by the global structure of the samples and cannot be removed by local perturbations. These so-called Weyl points, or nodal-line metals host a plethora of new phenomena such as anomalies known from high-energy physics, event-horizon physics akin the effects close to a black hole and stable non-local orbits connecting different surfaces of a finite sample. Using our research experience in topological mechanical meta- materials we propose to study effects of synthetic field on acoustic Weyl systems. We expect this research to deepen our understanding of such nodal systems and to enable new acoustic wave-guiding principles.Another promising direction includes the theoretical investigation of lattice systems on non-orientable manifolds. Most of the topological indices that are used to characterize Bloch bands depend crucially on the embedding of the lattice in space. Which of the classes of topological insulators survive the step to a non-orientable space or if there are new classes that only exist on surfaces such as the Moebius strip remains largely unclear. Motivated by the ability to implement such non-orientable structures with metamaterials using additive manufacturing techniques we aim to theoretically and experimentally explore this direction.The design of metamaterials constitutes a complicated inverse problem: Generically, we have a functionality in mind and we are presented with the challenge to find the geometry or composition of a metamaterial that exhibits this function. One approach that we established recently [A1] is based on weakly coupled units, so-called perturbative metamaterials. Here we want to bring this method, which was already successfully applied in two dimensions [A2], to the three dimensional world. This would open up the avenue to a large number of phenomena and functionalities out of reach with current methods. Second, while our algorithm originated in the realm of classical metamaterials, it is in essence a generic wave-control tool. Hence, we plan apply this method in the design of q-bit architectures, in particular the coupling of a superconducting q-bit to a multi-mode microwave stripline-resonator which would allow more compact architectures for a prospective quantum computer.In summary, we want to build on our knowledge in theoretically conceiving, designing, manufacturing and exper- imentally characterizing mechanical metamaterials to• Design,build,andcharacterizethreedimensionalmechanicalstructureswithnodalpointsintheirband-structure. • Theoretically and experimentally investigate topology on non-orientable manifolds.• Use our metamaterial design principles to contribute to the design of superconducting q-bits.