Switchable corner states in phononic crystals realized by inverse design

The coexistence of corner and edge states in the two-dimensional (2D) higher-order topological insulators (HOTIs) provides unprecedented approaches to manipulating waves at multiple dimensions thus attracting increasing attention. The corner states with flexible switching ability are important for localizing waves as desired, which have been achieved in hexagonal lattices but are rarely explored in square lattices. Here, we report switchable higher-order topological states realized based on square unit cells with accidental degeneracies. Inspired by the 2D SSH model in square lattices, this paper studies the elastic HOTIs in C4v-symmetric phononic crystals (PCs) with binary materials. The unit cells with precisely customized accidental degeneracies are obtained by an inverse design method. The higher-order states can be found in HOTIs constructed by nontrivial and trivial PCs as well as by two types of nontrivial PCs that exhibit band inversion. Extraordinarily, a unique type of corner state with opposite displacement polarization is observed in the HOTIs. Such corner state can be switched off as a result of the adjacent nontrivial couplings at the structural corners and can be switched back on by removing these nontrivial couplings. This intriguing property is then demonstrated in a complex waveguide to validate the switchability and tunability of the corer states. Our work opens an effective avenue for designing topological devices and extends the applications of the higher-order topological states in the elastic system.