Energy ratio controlled gate-tuning four-wave mixing in monolayer graphene.

Monolayer graphene, with a gapless conical electronic band structure, demonstrates scale invariance, showing universal linear optical responses. The impacts of this feature on nonlinear optical responses remain unclear. Our work reveals that the gate-tunable difference-frequency four-wave mixing (DFM) responses in monolayer graphene are significantly influenced by the energy ratios between excitation photons. This effect arises from scale invariance, rather than their absolute energies. Through theoretical analysis, we show that these energy ratios critically impact the DFM response relative to the chemical potential by tailoring the sequence, magnitude, and phase of resonant channels involved. Our findings deepen the understanding of the gate-tuning behavior in the nonlinear optical responses from materials featuring Dirac cones, paving the way for innovative nonlinear photonic applications.