Edge solitons of topological insulators and fractionalized quasiparticles in two dimensions

An important characteristic of topological band insulators is the necessary presence of in-gap edge states on the sample boundary. We utilize this fact to show that when the boundary is reconnected with a twist, there are always zero-energy defect states. This provides a natural connection between novel defects in the two-dimensional $p_{x}+ip_{y}$ superconductor, the Kitaev model, the fractional quantum Hall effect, and the one-dimensional domain wall of polyacetylene.