Topology optimization of quantum spin Hall effect-based second-order phononic topological insulator

Second-order phononic topological insulators (SPTIs) featured with topological edge and corner states offer promising ways for steering elastic waves. However, existing SPTIs were mainly designed with trial-and-error procedures, limiting the achievable width of topological bandgaps for tightly confining edge and corner states. Here, we develop a topology optimization approach for designing quantum spin Hall effect-based SPTIs. By simultaneously maximizing the powers emitted by the artificially selected body forces via topology optimization, the dipolar and quadrupolar modes are excited at the desirable frequencies. As a result, topologically nontrivial and trivial phononic crystals (PCs) with a record-breaking size of the overlapped bandgap (36.14%) are created. Thereafter, SPTIs arranged by hexagon and rhombus unit cells extracted from the optimized PCs are successfully created, validating the effectiveness of the optimization results. Additionally, the spatial decay of corner states is quantitatively characterized based on the complex band theory. Our work bridges topology optimization with SPTIs and, meanwhile, enriches the mechanism of corner states.

Automated summary

A topology optimization approach was developed for designing second-order phononic topological insulators based on the quantum spin Hall effect, resulting in the creation of phononic crystals with record-breaking size of overlapped bandgap. The optimized PCs were successfully used to create SPTIs arranged by hexagon and rhombus unit cells, validating the effectiveness of the optimization results. Additionally, the spatial decay of corner states was quantitatively characterized based on complex band theory, bridging topology optimization with SPTIs and enriching the understanding of corner states.