  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.
