We study topologically-protected four-wave mixing (FWM) interactions in a plasmonic metasurface consisting of a periodic array of nanoholes in a graphene sheet, which exhibits a wide topological bandgap at terahertz frequencies upon the breaking of time-reversal symmetry by a static magnetic field. We demonstrate that due to the significant nonlinearity enhancement and large lifetime of graphene plasmons in specific configurations, a net gain of FWM interaction of plasmonic edge states within the topological bandgap can be achieved with pump power of less than 10 nW. In particular, we find that the effective waveguide nonlinearity coefficient is about 1.1x10^13 1/(Wm), i.e., more than ten orders of magnitude larger than that of commonly used, highly nonlinear silicon photonic nanowires. These findings could pave a new way for developing ultra-low-power-consumption, highly-integrated and robust active photonic systems at deep-subwavelength scale for applications in quantum communications and information processing.
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