Topology optimization of a second-order phononic topological insulator with dual-band corner states

Second-order phononic topological insulators (SPTIs) with topologically protected corner states offer unique routes for the realization of steering elastic waves in lower-dimension regime with robustness. However, prevailing SPTIs only host corner states within a single bandgap, restricting applications of SPTIs in multiband domain. Here, we design four new types of SPTIs with the customized dual-bandgap which supports dual-band corner states. The dual-bandgap is created by simultaneously maximizing the minimum imaginary parts of wave vectors at two desired frequencies via topology optimization. Topological trivial and nontrivial unit cells (UCs), sharing the dual-bandgap, are configured by selecting UCs from the same optimized phononic crystals (PCs) in different ways. The dual-band topological corner states are observed at the corner between the trivial and nontrivial regions. The developed four SPTIs with customized dual-band operating frequencies pave the way for multiband communications and manipulation of elastic waves with enhanced robustness.