Topological States in Ordered and Disordered Mechanical Metamaterial

Abstract

Topological mechanical metamaterials have emerged as an active research field with the rapid development of topological phases in condensed matter physics. By incorporating robust topological features and highly customizable nature, topological mechanical metamaterials offer unprecedented power to manipulate acoustic and elastic waves and show great potential in a variety of engineering applications, such as low-loss devices, high-precision sensors, and quantum information processing. In this dissertation, we explore the topological phases in ordered three-dimensional (3D) mechanical metamaterials and investigate the disorder induced topological phase transition in both one-dimensional (1D) and two-dimensional (2D) mechanical metamaterials. First, we design an elastic structure made of beam elements with an AA−stacked honeycomb lattice. The chiral interlayer couplings induce Weyl points with opposite topological charges (±1) in the bulk bands. We also demonstrate the elastic Fermi arcs, and topologically protected surface states through full-scale numerical simulations. Then, we proposed a chiral phononic crystal based on a 3D Lieb lattice that carries spin−1 Weyl points of topological charge ±2. We observe special straight-type acoustic Fermi arcs and numerically demonstrate dual-band topologically protected and collimated surface waves in the spin-1 Weyl structure. Next, we investigate the interplay between topology and disorder in a 1D spring-mass chain. Three types of topological invariants defined in real space are implemented to characterize the topological properties in disordered 1D mechanical setups. Our findings reveal that disorder can both destroy and establish a topological state, depending on the type and strength of the disorder. Finally, we extend the disorder study to 2D mechanical systems and demonstrate disorder induced topological phase transition in both discrete and continuous quantum spin Hall mechanical systems.