Corner states in a second-order acoustic topological insulator as bound states in the continuum

A second-order topological insulator is designed on a platform of a two-dimensional (2D) square lattice with all coupling coefficients having the same sign. Simulated results show the existence of two types of nontrivial corner states in this system, with one type being identified as bound states in the continuum (BIC). The non-BIC corner states are also found by surrounding a nontrivial sample by a trivial one, and interestingly, these perfectly confined corner states can be gradually delocalized and merge into edge states by tuning the intersystem coupling coefficient. Both BIC and non-BIC corner states originate from bulk dipole moments rather than quantized quadrupole moments, with the corresponding topological invariant being the 2D Zak phase. Full wave simulations based on realistic acoustic waveguide structures are demonstrated. Our proposal provides an experimentally feasible platform for the study of the interplay between BIC and a high-order topological insulator, and the evolution from corner states to edge states.