Topological star junctions: Linear modes and solitons

We address continuous two-dimensional (2D) star-junctions formed by different numbers of Su–Schrieffer-Heeger (SSH) chains that have one common waveguide in the center of the junction. We show that by changing waveguide shifts in the dimers forming individual SSH chains, one can create a rich variety of modes in the center of the junction. Independently of the relation between non-equal bonds of the SSH chains, the in-gap modes localized in the center of the junction can be considered as topological, either representing extensions of the conventional topological edge stages or being modes induced by a defect at one of the SSH chain edges. Degeneracy of the eigenvalues and structure of the localized modes of fully 2D junctions depend on their symmetry and number of chains, and are different from their 1D counterparts obtained in the tight-binding approximation. In the presence of the focusing nonlinearity of the medium such states give rise to families of solitons with distinct stability properties depending on the number of chains in junction, waveguide shifts, and mode symmetry.