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.Nonlinear metamaterials is a rapidly developing field of fundamental interest with significant technological implications spanning from microwave through the visible spectral ranges [1][2][3][4][5][6][7]. As with tunable and reconfigurable metamaterials [8,9], the combination of the metamaterial structure with the local environment is crucial. This is because significant nonlinearities result from local field enhancement within the active region of the subwavelength metamaterial elements which, in the case of split ring resonators, are the capacitive gaps. While the active volume of the enhanced gaps is small in comparison to the unit cell volume, the field enhancement can dominate volumetric effects leading to global nonlinearities enhanced by two to four orders of magnitude [5]. This, in turn, results in useful nonlinear effects at low incident fields.Advances in nonlinear metamaterials coincide with the development of high-field terahertz sources capable of generating electric fields sufficient to induce significant nonlinearities in conventional matter [10][11][12][13][14]. For example, in doped GaAs, highly nonlinear effects such as velocity saturation and impact ionization have been observed [11,14] at peak electric fields of several hundred kV/cm. Further, with metamaterial THz field enhancement to MV/cm fields an insulator-metal phase transition has been induced in vanadium dioxide, a prototypical correlated electron material [7].In this letter, we experimentally demonstrate a nonlinear response in metamaterial split ring resonators (SRRs) on n-type GaAs and semi-insulating (SI) GaAs at terahertz frequencies. The nonlinear response arises from THz electric field-induced carrier dynamics that increase or decrease the substrate conductivity upon which the SRR arrays are fabricated. This modifies the SRR electromagnetic response as a function of field strength. For peak incident THz fields (E in ) from ∼20-160 kV/cm, mobility saturation by intervalley scattering (IVS) dominates leading (for doped GaAs) to a conductivity decrease and a corresponding increase in the metamaterial oscillator strength. In this regime, e...