固态高次谐波产生中电子-空穴耦合的扩展观点：全布里渊区隧穿和不完全耦合
Expanded view of electron-hole recollisions in solid-state high-order harmonic generation: Full-Brillouin-zone tunneling and imperfect recollisions
摘要：
本文从理论上研究了线偏振和椭圆偏振驱动器辐照下带隙固体中高次谐波产生中的电子-空穴耦合。我们发现，在许多情况下，所发射的谐波不起源于在最小带隙处创建的电子-空穴对，其中隧穿概率最大化，而是在布里渊区（BZ）的扩展区域中创建的电子-空穴对。在这些情况下，在短轨迹和长轨迹分类方面与气相HHG的类比是不够的。我们的分析方法包括三个互补的理论水平：数值解的半导体布洛赫方程，一个扩展的半经典模型，和量子波包的方法。我们将这种方法应用于两种具有代表性的能带结构的一般材料类型：块状系统和六方单层系统。在体中，使用椭圆偏振驱动器产生的带间谐波被发现起源于隧道在最小带隙$Γ$，但从远离它的区域。在单层系统由线偏振脉冲驱动，隧道区域附近的不同对称点的BZ导致不同的谐波能量和发射轮廓。我们发现，不完美的电子-空穴对电子，而空间分离，是很重要的散装和单层材料。我们的三个层次的理论之间的良好的协议突出和表征的复杂性背后的HHG发射动力学在固体中，并扩大了带间HHG的概念总是起源于隧道在最小带隙的轨迹。我们的工作进一步加深了对周期系统中高次谐波的基本理解，并将有益于未来的实验设计。
英文摘要：
We theoretically investigate electron-hole recollisions in high-harmonic generation (HHG) in band-gap solids irradiated by linearly and elliptically polarized drivers. We find that in many cases the emitted harmonics do not originate in electron-hole pairs created at the minimum band gap, where the tunneling probability is maximized, but rather in pairs created across an extended region of the Brillouin zone (BZ). In these situations, the analogy to gas-phase HHG in terms of the short- and long-trajectory categorizations is inadequate. Our analysis methodology comprises three complementary levels of theory: the numerical solutions to the semiconductor Bloch equations, an extended semiclassical recollision model, and a quantum wave packet approach. We apply this methodology to two general material types with representative band structures: a bulk system and a hexagonal monolayer system. In the bulk, the interband harmonics generated using elliptically-polarized drivers are found to originate not from tunneling at the minimum band gap $Γ$, but from regions away from it. In the monolayer system driven by linearly-polarized pulses, tunneling regions near different symmetry points in the BZ lead to distinct harmonic energies and emission profiles. We show that the imperfect recollisions, where an electron-hole pair recollide while being spatially separated, are important in both bulk and monolayer materials. The excellent agreement between our three levels of theory highlights and characterizes the complexity behind the HHG emission dynamics in solids, and expands on the notion of interband HHG as always originating in trajectories tunnelled at the minimum band gap. Our work furthers the fundamental understanding of HHG in periodic systems and will benefit the future design of experiments.
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