Numerical and experimental investigation of second-order mechanical topological insulators

Recently, higher-order topological insulators (HOTIs) as a novel frontier of topological phases of matter have been induced in mechanical systems, opening new routes to manipulate the propa-gation of elastic waves. Here, second-order mechanical topological insulators (SMTIs) imple-mented by mechanical metamaterials are systematically investigated in the rectangular lattice, the kagome lattice, the square lattice and the hexagonal lattice. The mechanical metamaterials are constructed from the generalized 2D Su-Schrieffer-Heeger (SSH) models. The topological mechanical metamaterials are characterized by the theories of topological indices and Wannier centers. With simulations and experiments, the corner states and edge states are observed in the topological mechanical metamaterials. Interestingly, the numbers of corner, edge and bulk states are respectively equal to the number of sites located at the corners, edges and bulk. This work offers an inspiring and unified model to study the higher-order topology in mechanical systems, and provides a new way for designing functional and integrated topological devices.

Automated summary

Recently, higher-order topological insulators (HOTIs) have been observed in mechanical systems, providing new possibilities for controlling the propagation of elastic waves. In this study, second-order mechanical topological insulators (SMTIs) implemented by mechanical metamaterials in different lattice structures were systematically investigated. The topological properties of these metamaterials were characterized using topological indices and Wannier centers. Both simulations and experiments confirmed the existence of corner states and edge states in these topological mechanical metamaterials. Interestingly, the number of corner, edge, and bulk states were found to be related to the number of sites located at the corresponding regions. This work presents an inspiring and unified model for studying higher-order topological effects in mechanical systems, and offers a new pathway for designing functional and integrated topological devices.