  Harmonic generation is a general characteristic of driven nonlinear systems,
and serves as an efficient tool for investigating the fundamental principles
that govern the ultrafast nonlinear dynamics. In atomic gases, high-harmonic
radiation is produced via a three-step process of ionization, acceleration, and
recollision by strong-field infrared laser. This mechanism has been intensively
investigated in the extreme ultraviolet and soft X-ray regions, forming the
basis of attosecond research. In solid-state materials, which are characterized
by crystalline symmetry and strong interactions, yielding of harmonics has just
recently been reported. The observed high-harmonic generation was interpreted
with fundamentally different mechanisms, such as interband tunneling combined
with dynamical Bloch oscillations, intraband thermodynamics and nonlinear
dynamics, and many-body electronic interactions. Here, in a distinctly
different context of three-dimensional Dirac semimetal, we report on
experimental observation of high-harmonic generation up to the seventh order
driven by strong-field terahertz pulses. The observed non-perturbative
high-harmonic generation is interpreted as a generic feature of terahertz-field
driven nonlinear intraband kinetics of Dirac fermions. We anticipate that our
results will trigger great interest in detection, manipulation, and coherent
control of the nonlinear response in the vast family of three-dimensional Dirac
and Weyl materials.
