Population inversion and ultrafast terahertz nonlinearity of transient Dirac fermions in ${\mathrm{Cd}}_3{\mathrm{As}}_2$

Harmonic generation provides an efficient tool for the study of ultrafast nonlinear dynamics. We report on time-resolved optical-pump terahertz harmonic generation spectroscopic investigation of ultrafast nonlinearity in a prototypical three-dimensional Dirac semimetal, ${\mathrm{Cd}}_3{\mathrm{As}}_2$. A transient population inversion characterized by excessive nonthermal Dirac electrons and holes is found to be very sensitive and responsive to a periodic terahertz drive, leading to very efficient terahertz third-harmonic generation. Based on the Boltzmann transport theory, we analyze the terahertz field-driven kinetics of the transient Dirac fermions that is responsible for the observed strong terahertz nonlinearity.