Nonlinear nano-imaging of electronic coherence in gated graphene

The Dirac cone band structure and zero energy band gap of graphene allow for a multitude of resonant nonlinear optical interaction pathways not possible in conventional materials. Further, gate voltage Fermi level (Ef) tuning enables switching and controlling the nonlinear conversion efficiency. However, underlying spatial heterogeneities, including selection rules and electronic coherence, are yet poorly understood, and expected to be in part fundamentally distinct in the optical near-field regime. Here we apply ultrafast nonlinear nanoscopy in adiabatic nano-focusing on gated ultra-clean graphene devices. We investigate the graphene response in four-wave mixing (FWM) as a function of gate voltage changing Ef. Due to Pauli blocking, the far-field FWM intensity is only expected to change for Fermi level shifts about 0.8 eV from the neutrality point under our experimental conditions. In contrast, we observe a different near-field gate dependency with Ef ~0.4 eV, suggesting a new nonlinear nano-optics regime with non-local enhancement and associated with a quantum Doppler effect.