  We study the nonlinear optical properties of heterojunctions made of graphene
nanoribbons (GNRs) consisting of two segments with either the same or different
topological properties. By utilizing a quantum mechanical approach that
incorporates distant-neighbor interactions, we demonstrate that the presence of
topological interface states significantly enhances the second- and third-order
nonlinear optical response of GNR heterojunctions that are created by merging
two topologically inequivalent GNRs. Specifically, GNR heterojunctions with
topological interface states display third-order harmonic hyperpolarizabilities
that are more than two orders of magnitude larger than those of their similarly
sized counterparts without topological interface states, whereas the
secondorder harmonic hyperpolarizabilities exhibit a more than ten-fold
contrast between heterojunctions with and without topological interface states.
Additionally, we find that the topological state at the interface between two
topologically distinct GNRs can induce a noticeable red-shift of the quantum
plasmon frequency of the heterojunctions. Our results reveal a general and
profound connection between the existence of topological states and an enhanced
nonlinear optical response of graphene nanostructures and possible other
photonic systems.
