Realization of Topological Corner States in Tailored Photonic Graphene

Higher-order topological semimetals (HOTSMs) represent a novel type of gapless topological phase, hosting boundary states with dimensions at least two lower than those of their bulk geometry. Such nontrivial boundary states have been predicted and observed in three-dimensional (3D) gapless topological systems, representing features of the HOTSMs. However, their two-dimensional (2D) analogs, represented especially by the corner states in monolayer graphene-like structures, have thus far remained only a theoretical exploration. Here, we experimentally demonstrate nontrivial corner states in specially tailored photonic graphene hosting Dirac points, manifesting the HOTSM-like property in a 2D photonic setting. Such corner states in the otherwise gapless system exhibit distinct phase structures depending on the lattice corner and edge geometry, and are completely degenerate with the zero-energy edge states. Remarkably, we find that these “gapless” corner states remain intact at zero-energy even in a finite-sized graphene lattice, protected by chiral symmetry. Unlike corner states in higher-order topological insulators or topological crystalline insulators with certain rotational symmetry, these corner states are localized exclusively to one corner without any coupling to the bulk or other corners, despite long-distance propagation.