Weak topological insulators, nodal-line semimetals, and Dirac semimetals in phononic crystal plates

Abstract

Topological phases of matter help us to modulate elastic waves at the boundaries of mechanical systems with robustness against defects. Here, we propose to realize weak topological insulator phases, nodal-line semimetal phases, and Dirac semimetal phases in 2D mechanical systems. We implement this idea by theoretical analysis of tight-binding models and numerical simulations of phononic crystal plates based on the two-dimensional Su-Schrieffer-Heeger models. The topological nature of these topological phases is characterized by the topological invariants. The edge states, the visualization feature of the weak topological insulators, are observed unambiguously in the phononic crystal plates. Particularly, the robustness of these edge states against structural defects is verified by removing four single square plates from the center. Experimentally, we realize two types of weak topological insulators in 2D mechanical systems. This study fertilizes the topological phases in mechanical systems and opens excellent avenues for manipulating elastic wave propagation.