Ultrafast coherent nonlinear nanooptics and nanoimaging of graphene

With its linear energy dispersion and large transition dipole matrix element, graphene is an attractive material for nonlinear optoelectronic applications. However, the mechanistic origin of its strong nonlinear response, the ultrafast coherent dynamics and the associated nanoscale phenomena have remained elusive due to a lack of suitable experimental techniques. Here, using adiabatic nanofocusing and imaging, we study the broadband four-wave mixing (FWM) response of graphene with nanometre and femtosecond spatio-temporal resolution. We detect a nonlinear signal enhancement at the edges and dependence on the number of layers from excitation areas as small as 10(4) carbon atoms. Femtosecond FWM nanoimaging and concomitant frequency-domain measurements reveal dephasing on T-2 approximate to 6 +/- 1fs timescales, which we attribute to a strong electron-electron interaction. We also identify an unusual non-local FWM response on -100-400 nm length scales, which we assign to a Doppler effect controlling the nonlinear interaction between the tip near-field momenta and the graphene electrons with high Fermi velocity. These results illustrate the distinct nonlinear nanooptical properties of graphene, expected also in related classes of two-dimensional materials, that could form the basis for improved nonlinear and ultrafast nanophotonic devices.