Observation of Topologically Distinct Corner States in "Bearded" Photonic Kagome Lattices

Kagome lattices represent an archetype of intriguing physics, attracting a great deal of interest in different branches of natural sciences, recently in the context of topological crystalline insulators. Here, two distinct classes of corner states in breathing Kagome lattices (BKLs) with "bearded" edge truncation are demonstrated, unveiling their topological origin. The in-phase corner states are found to exist only in the topologically nontrivial regime, characterized by a nonzero bulk polarization. In contrast, the out-of-phase corner states appear in both topologically trivial and nontrivial regimes, either as bound states in the continuum or as in-gap states depending on the lattice dimerization conditions. Furthermore, the out-of-phase corner states are highly localized, akin to flat-band compact localized states, and they manifest both real- and momentum-space topology. Experimentally, both types of corner states are observed in laser-written photonic bearded-edge BKLs, corroborated by numerical simulations. The results not only deepen the current understanding of topological corner modes in BKLs but also provide new insight into their physical origins, which may be applied to other topological BKL platforms beyond optics. Two classes of topological corner states in breathing photonic Kagome lattices with "bearded" edge truncation are reported, featuring distinctive phase structures and topological protection. It is found that the in-phase corner states originate exclusively from momentum-space topology. Instead, the out-of-phase corner states manifest both momentum- and real-space topology, exhibiting properties that are different from typical higher-order topological insulators.image