Edge solitons of topological insulators and fractionalized quasiparticles in two dimensions

TL;DR

This paper explores the existence of zero-energy defect states at the edges of topological insulators when boundaries are twisted, linking various topological phenomena and fractionalized quasiparticles in two dimensions.

Contribution

It introduces a novel perspective on edge states in topological insulators, connecting them to defects in superconductors, the Kitaev model, and quantum Hall effects.

Findings

Zero-energy defect states always occur with boundary twists.

Connections established between topological insulators, superconductors, and quantum Hall systems.

Provides a unified framework for understanding fractionalized quasiparticles.

Abstract

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.