Chiral topological phases and fractional domain wall excitations in one-dimensional chains and wires

TL;DR

This paper introduces a one-dimensional zigzag fermion chain with spin-orbit coupling, revealing multiple topological phases with fractionalized boundary excitations, and discusses potential experimental realizations.

Contribution

It identifies three topological phases in a zigzag fermion chain with spin-orbit coupling and magnetic field, featuring fractionalized zero-mode excitations at phase boundaries.

Findings

Three distinct topological phases identified.

Fractional charge excitations at phase boundaries.

Edge states with fractional charges in finite chains.

Abstract

According to the general classification of topological insulators, there exist one-dimensional chirally (sublattice) symmetric systems that can support any number of topological phases. We introduce a zigzag fermion chain with spin-orbit coupling in magnetic field and identify three distinct topological phases. Zero-mode excitations, localized at the phase boundaries, are fractionalized: two of the phase boundaries support $\pm e/2$ charge states while one of the boundaries support $\pm e$ and neutral excitations. In addition, a finite chain exhibits $\pm e/2$ edge states for two of the three phases. We explain how the studied system generalizes the Peierls-distorted polyacetylene model and discuss possible realizations in atomic chains and quantum spin Hall wires.