Measurement of Corner-Mode Coupling in Acoustic Higher-Order Topological Insulators

Recent developments of band topology have revealed a variety of higher-order topological insulators (HOTIs). These HOTIs are characterized by a variety of different topological invariants, making them different at a fundamental level. However, despite such differences, the fact that they all sustain higher-order topological boundary modes poses a challenge to phenomenologically tell them apart. This work presents experimental measurements of the coupling effects of topological corner modes (TCMs) existing in two different types of two-dimensional acoustic HOTIs. Although both HOTIs have a similar four-site square lattice, the difference in magnetic flux per unit cell dictates that they belong to different types of topologically nontrivial phases—one lattice possesses quantized dipole moments, but the other is characterized by quantized quadrupole moment. A link between the topological invariants and the response line shape of the coupled TCMs is theoretically established and experimentally confirmed. Our results offer a pathway to distinguish HOTIs experimentally.