Observation of nonlinear topological corner states originating from different spectral charges

Abstract: Higher-order topological insulators (HOTIs) are unique topological materials supporting edge states with the dimensionality at least by two lower than the dimensionality of the underlying structure. HOTIs were observed on lattices with different symmetries, but only in geometries, where truncation of HOTI produces a finite structure with the same order of discrete rotational symmetry as that of the unit cell, thereby setting the geometry of insulator edge. Here we experimentally demonstrate a new type of two-dimensional (2D) HOTI based on the Kekule-patterned lattice, whose order of discrete rotational symmetry differs from that of the unit cells of the constituent honeycomb lattice, with hybrid boundaries that help to produce all three possible corners that support effectively 0D corner states of topological origin, especially the one associated with spectral charge 5/6. We also show that linear corner states give rise to rich families of stable hybrid nonlinear corner states bifurcating from them in the presence of focusing nonlinearity of the material. Such new types of nonlinear corner states are observed in hybrid HOTI inscribed in transparent nonlinear dielectric using fs-laser writing technique. Our results complete the class of HOTIs and open the way to observation of topological states with new internal structure and symmetry.