Topological gap states of semiconducting armchair graphene ribbons

TL;DR

This paper investigates topological gap states in semiconducting armchair graphene ribbons, revealing their fractional charge and near-zero energy states induced by lattice deformation, and distinguishes them from metallic ribbons without topological states.

Contribution

It demonstrates that semiconducting armchair graphene ribbons can host topological gap states with fractional charge, showing a power-law dependence on deformation width, and clarifies the topological nature of these states.

Findings

Topological gap states have fractional charge of one-half.

Near critical deformation, states become almost degenerate with zero energy.

Metallic armchair ribbons lack topological gap states.

Abstract

In semiconducting armchair graphene ribbons a chiral lattice deformation can induce pairs of topological gap states with opposite energies. Near the critical value of the deformation potential these kink and antikink states become almost degenerate with zero energy and have a fractional charge one-half. Such a semiconducting armchair ribbon represents a one-dimensional topological insulator with nearly zero energy end states. Using data collapse of numerical results we find that the shape of the kink displays an anomalous power-law dependence on the width of the local lattice deformation. We suggest that these gap states may be probed in optical measurements. However, "metallic" armchair graphene ribbons with a gap induced by many-electron interactions have no gap states and are not topological insulators.