Topologically enhanced nonlinear optical response of graphene nanoribbon heterojunctions

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.