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

Effect of spin-orbit coupling on the high harmonics from the topological Dirac semimetal Na3Bi