Planar tetra-coordinate carbon resulting in enhanced third-order nonlinear optical response of metal-terminated graphene nanoribbons

Metal-terminated graphene nanoribbons (M-GNRs) with planar tetra-coordinate carbons (PtC) are investigated theoretically for a third-order nonlinear optical (NLO) response by using the sum-over-states (SOS) method. The third order NLO polarizability, two-photon absorption (TPA) and nonlinear reflectivity are investigated within the third-harmonic generation (THG) or degenerate four-wave mixing (DFWM) processes. The origins of third order NLO polarizability and TPA are analyzed in terms of the charge transfer process, which indicates that tetra-coordinate carbons in M-GNRs have an important role in the third-order NLO response. The dynamic nonlinear reflectivity of the M-GNR presents a resonant characteristic due to the large third order NLO polarizability. Moreover, the third order NLO polarizability and TPA cross section values increase as the ribbon size increases in the low frequency region of incident light, which indicates that their NLO properties can be tailored by controlling the ribbon size. This paper aims to shed light on the design of NLO properties and understanding of the NLO response mechanisms of graphene related materials.