Investigation of topological phonons in discrete mechanical metamaterials

The study of topological mechanical metamaterials is a new emerging field that focuses on the topological properties of artificial mechanical structures. Inspired by topological insulators, topological mechanism has attracted intensive attention in condensed matter physics and successfully connected the quantum mechanical descriptions of electrons with the classical descriptions of phonons. It has led to experiments of mechanical metamaterials possessing topological characteristics, such as topologically protected conducting edges or surfaces without back-scattering. This dissertation presents a new experimental approach for mechanically engineering topological metamaterials based on patterning magnetically coupled spinners in order to localize the propagation of vibrations and evaluate different resonant modes. The topological properties of these metamaterials originate simply from their structures regardless of their nature and require no fine tuning of parameters. Strong excitation modes can also be observed through naked eyes, ideal for the exemplification of abstract theories. In Chapter 2, robust edge modes only due to smart patterning are reported. In Chapter 3, the analog of quantum valley Hall effect (QVHE) is emulated mechanically and its suitability for metamaterial applications is also discussed. In Chapter 4, flat frequency bands localized at open edges and antiphase boundary seams of topological mechanical metamaterials are shown to be promising for other metamaterials and novel applications. In Chapter 5, current work on classical Majorana edge modes of a ladder-like system, which is a counterpart to the classic Kitaev chain, is presented. Finally, in Chapter 6, contributions, possible improvements, significant challenges, and potential applications are discussed