Topological gap states of semiconducting armchair graphene ribbons

Abstract

In semiconducting armchair graphene ribbons a tensile strain 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 of 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.