Coexistence of Multiple Distinct Corner-State Classes via Nearest-Neighbor Couplings Alone

Abstract

The coexistence of multiple classes of localized states, including different types of topological corner states, is highly desired; yet its realization typically requires sufficiently strong long-range couplings, bringing challenges to experimental realizations across a wide range of systems. Here, we demonstrate the emergence of multiple localized corner modes evolution under purely nearest-neighbor coupling conditions without long-range couplings, not even next-nearest-neighbour couplings, and experimentally confirm their coexistence in a single lattice. Our platform simultaneously hosts type-I and type-II corner states, corner localized bound states in the continuum, flat-band states, and edge states. We experimentally realize such lattice using topolectrical circuits, a system that can strictly exclude long-range coupling by design, enabling direct characterizations of both the energy-band spectrum and the spatial profiles of the localized eigenmode. This work demonstrates that solely modifying nearest-neighbor couplings can replace the role of long-range interactions in realizing multiple types of corner states, providing a deterministic and widely accessible route to multiple corner-state classes and rich localized states, with immediate potential for mode-division multiplexing and multimode topological devices.