Abstract Topological corner states of two-dimensional (2D) higher-order topological insulators (HOTIs) not only serve as a unique signature of higher-order topology, but also possess tremendous potentials in probing, confining, and manipulating particles or quasiparticles as possible carriers of information and energy. However, topological corner states are necessarily pinned to certain symmetric positions at the outer boundary of a HOTI sample, imposing strict limitations on their practical use in terms of number and positioning. Here, we propose a theoretical concept of higher-order topological point states (HOTPS) at 0D inner vacancies in 2D HOTIs that carry a fractional charge of e/2, to overcome the limitations associated with corner states. Exploiting this new concept for the HOTI phase in a Kekulé lattice, we further experimentally realize HOTPS in both acoustic and photonic metamaterials. By varying the spatial distance between a pair of vacancies, the in-gap HOTPS and their characteristic energy splitting are experimentally observed, indicating the topology-modified longer-range inter-HOTPS interaction. Our findings that inner vacancies can exhibit the same topological properties as outer corners, including bound topological states and quantized fractional charges, and can be created more controllably, introduce a new avenue in HOTI research and set the stage for wider applications.
Jiaxin Zhong (2025) studied this question.