  In this work, we performed extensive first-principles simulations of
high-harmonic generation in the topological Diract semimetal Na3Bi using a
time-dependent density functional theory framework, focusing on the effect of
spin-orbit coupling (SOC) on the harmonic response. We also derived a general
analytical model describing the microscopic mechanism of strong-field dynamics
in presence of spin-orbit coupling, starting from a locally U(1)xSU(2)
gauge-invariant Hamiltonian. Our results reveal that SOC: (i) affects the
strong-field ionization by modifying the bandstructure of Na3Bi, (ii) modifies
the electron velocity, making each spin channel to react differently to the
pump laser field, (iii) changes the emission timing of the emitted harmonics.
Moreover, we show that the SOC affects the harmonic emission by directly
coupling the charge current to the spin currents, paving the way to the
high-harmonic spectroscopy of spin currents in solids.
