  We investigate high-harmonic generation in graphene heterostructures
consisting of metallic nanoribbons separated from a graphene sheet by either a
few-nanometer layer of aluminum oxide or an atomic monolayer of hexagonal boron
nitride. The nanoribbons amplify the near-field at the graphene layer relative
to the externally applied pumping, thus allowing us to observe third- and
fifth-harmonic generation in the carbon monolayer at modest pump powers in the
mid-infrared. We study the dependence of the nonlinear signals on the ribbon
width and spacer thickness, as well as pump power and polarization, and
demonstrate enhancement factors relative to bare graphene reaching 1600 and
4100 for third- and fifth-harmonic generation, respectively. Our work supports
the use of graphene heterostructures to selectively enhance specific nonlinear
processes of interest, an essential capability for the design of nanoscale
nonlinear devices.
