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Engineering non-Hermitian and topological flow of sound

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2022-07
Defense date
2022-09-08
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During the last decades, acoustic and phononic metamaterial research was focused on finding new ways to modify the flow of sound waves at will. In this project, we focus on exploring novel properties of sound by developing numerical code and theoretical methods to understand the acoustic analogy to non-Hermitian systems, topological insulators, and other exciting phenomena in condensed matter physics such as the magic angle in twisted bilayer graphene. Succinctly, we wish to translate these common notions of quantum mechanics into classical acoustics to find new properties for the case of sound. Non-Hermitian acoustic structures can be achieved by balancing acoustic loss and gain units. Commonly known as Parity-Time (PT) symmetric structures, they have neither parity symmetry nor time-reversal symmetry, but are nevertheless symmetric in the product of both. In particular, the doctoral research project aims at designing acoustic PT symmetry and demonstrating the extraordinary scattering characteristics of the acoustic PT medium based on exact theoretical predictions and numerical analysis. Hence, we investigate the possibilities to realize one-way cloaks of invisibility and broken symmetry properties with amplifying or attenuating behaviour. Topological sound combines the knowledge of topology in mathematics and electronics with sound waves. Knowing that artificial sonic lattices have been widely used to explore topological phases of sound and its properties, we propose to study the properties of Second Order Topological Insulators when non-hermiticity is involved. Deriving a semi-numerical tool that allows us to compute the spectral dependence of corner states in the presence of defects, we illustrate the limits of the topological resilience of the confined non-Hermitian acoustic states. An attractive motivation of these acoustic structures compared to their electronic counterparts, is their easy fabrication and tunability, allowing the experimental verification of this quantum analogies as well as the development of many numerical studies. Thereby, in the last part of this thesis we mimic twisted bilayer physics in a mechanical twisted bilayer configuration and also in an acoustical bilayer. Designing the mathematical models to describe the physics involved, we show how the twist angle is related to the flat band formation as happens in twisted bilayer graphene.
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Non-Hermitian acoustics, Topological acoustics, Twistronics, Moiré Lattice, Cloaking
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