Nonlinear frequency conversion in the terahertz regime is significant for emerging applications in high-speed communications, imaging, and sensing, yet enhancing light-matter interactions in two-dimensional materials often relies on multilayer stacking or complex resonant architectures. Here, we introduce a transmission-type nonlinear metamaterial based on a single-layer graphene architecture that enables geometry-controlled dual-frequency terahertz third-harmonic generation. By employing a rail-like graphene meta-atom, strong and spatially redistributed local electric-field hot spots are generated through geometry-induced edge confinement and narrow-gap resonances. This enables effective coupling between the enhanced electromagnetic fields and graphene’s intrinsic third-order nonlinearity, allowing dual-frequency nonlinear conversion within a single planar structure without multilayer stacking. Within the adopted fixed-temperature perturbative nonlinear surface-current framework and at an incident pump intensity of $10\mathrm{MW}/{\mathrm{cm}}^2$, the proposed structure predicts third-harmonic generation conversion efficiencies of 4.0% and 4.4% at 1.781 and 2.206 THz, respectively, together with local-field enhancement factors that are one to two orders of magnitude higher than those of bare graphene. This work demonstrates a geometry-driven strategy for controlling terahertz nonlinear responses, showing that nonlinear frequency selectivity can be engineered through geometry-induced local-field redistribution rather than structural complexity. The proposed approach provides a compact strategy for designing single-layer graphene metamaterials with controllable dual-frequency terahertz nonlinear functionality within the adopted theoretical framework.

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• Frequency conversion
• Integrated optics
• Optoelectronics
• Graphene
• Metasurfaces
• Optical sources & detectors
• High-harmonic generation
• Terahertz sources