  Nonlinear optics is an increasingly important field for scientific and
technological applications, owing to its relevance and potential for optical
and optoelectronic technologies. Currently, there is an active search for
suitable nonlinear material systems with efficient conversion and small
material footprint. Ideally, the material system should allow for
chip-integration and room-temperature operation. Two-dimensional materials are
highly interesting in this regard. Particularly promising is graphene, which
has demonstrated an exceptionally large nonlinearity in the terahertz regime.
Yet, the light-matter interaction length in two-dimensional materials is
inherently minimal, thus limiting the overall nonlinear-optical conversion
efficiency. Here we overcome this challenge using a metamaterial platform that
combines graphene with a photonic grating structure providing field
enhancement. We measure terahertz third-harmonic generation in this
metamaterial and obtain an effective third-order nonlinear susceptibility with
a magnitude as large as 3$\cdot$10$^{-8}$m$^2$/V$^2$, or 21 esu, for a
fundamental frequency of 0.7 THz. This nonlinearity is 50 times larger than
what we obtain for graphene without grating. Such an enhancement corresponds to
third-harmonic signal with an intensity that is three orders of magnitude
larger due to the grating. Moreover, we demonstrate a field conversion
efficiency for the third harmonic of up to $\sim$1% using a moderate field
strength of $\sim$30 kV/cm. Finally we show that harmonics beyond the third are
enhanced even more strongly, allowing us to observe signatures of up to the
9$^{\rm th}$ harmonic. Grating-graphene metamaterials thus constitute an
outstanding platform for commercially viable, CMOS compatible, room
temperature, chip-integrated, THz nonlinear conversion applications.
