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 $\mathrm{\Gamma }$, 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.

中文翻译：

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固态高次谐波产生中电子-空穴再碰撞的扩展视图：全布里渊区隧穿和不完美再碰撞

我们从理论上研究了线性和椭圆极化驱动器辐照的带隙固体中高次谐波产生 (HHG) 中的电子空穴再碰撞。我们发现，在许多情况下，发射的谐波不是源自在最小带隙处产生的电子 - 空穴对，其中隧道概率最大化，而是在布里渊区 (BZ) 的扩展区域产生的对。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层次：半导体布洛赫方程的数值解、扩展的半经典再碰撞模型和量子波包方法。我们将此方法应用于具有代表性能带结构的两种通用材料类型：体系统和六边形单层系统。在大多数情况下，发现使用椭圆极化驱动器产生的带间谐波并非源自最小带隙的隧道效应$\mathrm{\Gamma }$，但来自远离它的地区。在由线性极化脉冲驱动的单层系统中，BZ 中不同对称点附近的隧道区域导致不同的谐波能量和发射剖面。我们表明，不完美的再碰撞，即电子-空穴对在空间分离的同时再碰撞，在体材料和单层材料中都很重要。我们的三个理论水平之间的极好一致性突出并描述了固体中 HHG 发射动力学背后的复杂性，并扩展了带间 HHG 的概念，因为它总是起源于在最小带隙隧道传输的轨迹。我们的工作进一步加深了对周期系统中 HHG 的基本理解，并将有益于未来的实验设计。