On the use of topology optimized band gap structures for the realization of second-order acoustic topological insulators with valley-selective corner states

Second-order acoustic topological insulators (SATIs) hosting corner states provide unprecedented opportunities for realizing robust transport of sound in higher dimensions. However, current SATIs are mainly designed by trial and error method based on physical intuition, seriously limiting their performances. Here, we use the topology optimized acoustic crystals (ACs) to create SATIs hosting valley-selective corner states. Instead of opening the first-order band gap by reducing the lattice symmetry from C-3v to C-3, we directly restrict the AC with C-3 symmetry and maximize its first-order band gap via topology optimization. The SATIs are created by arranging the optimized AC and its inversion-symmetric partner. Extra-wide edge states are formed at the domain between the optimized AC and its inversion-symmetric partner. Importantly, the edge gap is significantly enlarged, enabling more localized corner states. The valley-selectivity of corner states is further demonstrated.