Characterization and experimental demonstration of corner states of boundary-obstructed topological insulators in a honeycomb lattice

Higher-order topological insulators containing multidimensional boundary states have been extensively researched. Here, we characterize the zero-energy corner states generated in the honeycomb lattice by calculating the multiple chiral numbers topological invariant in real space with fewer symmetry constraints. By relating the concept of boundary-obstructed topological insulators which shows a gap in the bulk band, we analyze the edge states transition and the phase diagram of the zero-energy level of the hexagonal structure which are consistent with the characterization results of the sample. Crucially, we construct three samples hosting the nontrivial, phase-transition-point and trivial edge states in acoustic systems and demonstrate the higher-order band topology. Our paper demonstrates the usefulness of directly characterizing topological properties of chiral-symmetric systems by applying multiple chiral numbers.