  We demonstrate nonlinear metamaterial split ring resonators (SRRs) on GaAs at
terahertz frequencies. For SRRs on doped GaAs films, incident terahertz
radiation with peak fields of ~20 - 160 kV/cm drives intervalley scattering.
This reduces the carrier mobility and enhances the SRR LC response due to a
conductivity decrease in the doped thin film. Above ~160 kV/cm, electric field
enhancement within the SRR gaps leads to efficient impact ionization,
increasing the carrier density and the conductivity which, in turn, suppresses
the SRR resonance. We demonstrate an increase of up to 10 orders of magnitude
in the carrier density in the SRR gaps on semi-insulating GaAs substrate.
Furthermore, we show that the effective permittivity can be swept from negative
to positive values with increasing terahertz field strength in the impact
ionization regime, enabling new possibilities for nonlinear metamaterials.
