AI 中文总结
该研究通过数值计算扩展SSH模型与Rice-Mele模型的高次谐波产生谱，发现局域照射拓扑绝缘体边界时边缘态会产生偶次谐波，揭示了激光照射空间位置可调控低维纳米结构的谐波对称性。
AI 中文摘要
固体中的高次谐波产生（HHG）已成为探测量子材料对称性和拓扑性质的有力工具。本工作研究了一维固体在全局和局域光照射下，具有边缘态或带隙中间态的HHG响应。我们数值计算了含次近邻反亚晶格跃迁的Su-Schrieffer-Heeger（SSH）模型（称为扩展SSH（ESSH）模型），以及通过交错在位势打破反演对称性的一维系统Rice-Mele模型的HHG谱。通过对比全局光照射下ESSH模型与Rice-Mele模型的谱特征，分析表明，尽管带隙中间态提供了额外的跃迁路径，但产生的干涉是相消的，导致其谱特征与边缘态的谱特征不同。此外，当拓扑绝缘体的单个边界被局域光照射时，边缘态的HHG谱中奇次谐波消失，使偶次谐波在谱中占主导。我们将这种偶次谐波选择定则归因于边缘态的零能特性和系统的粒子-空穴对称性，后者强制零模响应具有偶场宇称。这些发现表明，激光照射的空间位置为控制系统对称性提供了途径，从而可在低维纳米结构中选择性地抑制或增强偶次和奇次谐波。
英文摘要
High-order harmonic generation (HHG) in solids has emerged as a powerful probe of symmetry and topological properties in quantum materials. In this work, we investigate the HHG response in one-dimensional solids with edge or midgap states under global and local illumination. We numerically compute the HHG spectrum for the Su-Schrieffer-Heeger (SSH) model with next-nearest-opposite sublattice hopping, dubbed the extended SSH (ESSH) model, and the Rice-Mele model, a one-dimensional system with broken inversion symmetry introduced via staggered on-site potentials. By contrasting the spectral features of the ESSH and Rice-Mele models under global illumination, our analysis reveals that although midgap states provide additional pathways for transitions, the resulting interference is destructive, leading to spectral features distinct from those of edge states. Furthermore, when a single boundary of the topological insulator is locally illuminated, the HHG spectrum of the edge states exhibits vanishing odd harmonics, leaving even harmonics dominant in the spectrum. We identify this even-harmonic selection rule as a consequence of the zero-energy character of the edge states and the particle-hole symmetry of the system, which enforces even field parity of the zero-mode response. These findings reveal that the spatial location of the laser illumination offers a route to control the symmetry of the system, thereby selectively suppressing or enhancing even- and odd-order harmonics in low-dimensional nanostructures.
