Аннотация: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 with hybrid boundaries, whose order of discrete rotational sym-
metry differs from that of the unit cells of the constituent honeycomb lattice. Such HOTI has hybrid
edges that by itself include multiple corners, each of which can support effectively 0D corner states of
topological origin. We demonstrate that while in small-size structures such corner states can couple,
resembling edge states, increasing lattice size makes such strongly confined states independent. New types of corner states demonstrated here coexist in the bandgap with conventional topological corner states, but feature different symmetry. They are protected by the discrete rotational symmetry and explained by the fractional spectral charge arising due to the “filling anomaly”. We also show that linear corner states give rise to rich families of stable hybrid corner solitons bifurcating from them in the presence of focusing nonlinearity of the material. Such new types of solitons are observed in hy-brid HOTI inscribed in transparent nonlinear dielectric using fs-laser writing technique. Our results expand the class of HOTIs and open the way to observation of topological states with new internal structure and symmetry.