  We introduce the concept of nonlinear graphene metasurfaces employing the
controllable interaction between a graphene layer and a planar metamaterial.
Such hybrid metasurfaces support two types of subradiant resonant modes,
asymmetric modes of structured metamaterial elements ("metamolecules") and
graphene plasmons exhibiting strong mutual coupling and avoided dispersion
crossing. High tunability of graphene plasmons facilitates strong interaction
between the subradiant modes, modifying the spectral position and lifetime of
the associated Fano resonances. We demonstrate that strong resonant
interaction, combined with the subwavelength localization of plasmons, leads to
the enhanced nonlinear response and high efficiency of the second-harmonic
generation.
