  We report on terahertz high-harmonic generation in a Dirac semimetal as a
function of the driving-pulse ellipticity and on a theoretical study of the
field-driven intraband kinetics of massless Dirac fermions.Very efficient
control of third-harmonic yield and polarization state is achieved in
electron-doped Cd$_3$As$_2$ thin films at room temperature. The observed
tunability is understood as resulting from terahertz-field driven intraband
kinetics of the Dirac fermions. Our study paves the way for exploiting
nonlinear optical properties of Dirac matter for applications in signal
processing and optical communications.
