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Harmonic generation is a general characteristic of driven nonlinear systems,and serves as an efficient tool for investigating the fundamental principlesthat govern the ultrafast nonlinear dynamics. In atomic gases, high-harmonicradiation is produced via a three-step process of ionization, acceleration, andrecollision by strong-field infrared laser. This mechanism has been intensivelyinvestigated in the extreme ultraviolet and soft X-ray regions, forming thebasis of attosecond research. In solid-state materials, which are characterizedby crystalline symmetry and strong interactions, yielding of harmonics has justrecently been reported. The observed high-harmonic generation was interpretedwith fundamentally different mechanisms, such as interband tunneling combinedwith dynamical Bloch oscillations, intraband thermodynamics and nonlineardynamics, and many-body electronic interactions. Here, in a distinctlydifferent context of three-dimensional Dirac semimetal, we report onexperimental observation of high-harmonic generation up to the seventh orderdriven by strong-field terahertz pulses. The observed non-perturbativehigh-harmonic generation is interpreted as a generic feature of terahertz-fielddriven nonlinear intraband kinetics of Dirac fermions. We anticipate that ourresults will trigger great interest in detection, manipulation, and coherentcontrol of the nonlinear response in the vast family of three-dimensional Diracand Weyl materials.

Non-perturbative high-harmonic generation in the three-dimensional Dirac semimetal Cd$_3$As$_2$