In this work, we performed extensive first-principles simulations of high-harmonic generation in the topological Diract semimetal Na₃Bi using a first-principles time-dependent density functional theory framework, focusing on the effect of spin-orbit coupling (SOC) on the harmonic response. We also derived an analytical model describing the microscopic mechanism of strong-field dynamics in presence of spin-orbit coupling, starting from a locally U(1) × SU(2) gauge-invariant Hamiltonian. Our results reveal that SOC: (i) affects the strong-field excitation of carriers to the conduction bands by modifying the bandstructure of Na₃Bi, (ii) makes each spin channel reacts differently to the driven laser by modifying the electron velocity (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.

在这项工作中，我们使用第一性原理时间相关的密度泛函理论框架对拓扑 Diract 半金属 Na ₃ Bi 中的高次谐波产生进行了广泛的第一性原理模拟，重点是自旋轨道耦合 (SOC) 对谐波响应。我们还推导出了一个分析模型，描述了存在自旋轨道耦合的强场动力学的微观机制，从局部U (1) ×  S U (2) 规范不变哈密顿量开始。我们的结果表明 SOC： (i) 通过改变 Na _{3的能带结构来影响载流子对导带的强场激发}Bi，（ii）通过改变电子速度（iii）改变发射谐波的发射时间，使每个自旋通道对驱动激光的反应不同。此外，我们表明 SOC 通过将充电电流直接耦合到自旋电流来影响谐波发射，为固体中自旋电流的高谐波光谱铺平了道路。