标题： 利用量子几何增强晶体的超极化率 显示英文标题

标题： Enhancing the Hyperpolarizability of Crystals with Quantum Geometry

摘要： 我们证明，通过非平凡的拓扑不变量和量子几何，可以增强并理解晶体中的高阶电极化率，使用一维$\pi$-共轭链作为代表性模型系统。 首先，我们表明这些链的晶体对称性保护的拓扑结构对其量子度量和超极化率施加了一个下限。 其次，我们采用数值模拟来揭示在各种一维晶体中非线性、由量子几何驱动的光学响应的可调性，其中带拓扑结构可以被外部控制。 第三，我们提出一种半经典图像以提供对这些效应的直观理解。 我们的发现为原本难以解释的巨大大超极化率实验观测提供了坚实的解释，并为设计具有增强非线性光学性质的任意维度拓扑材料提供了指导方针。 显示英文摘要

摘要： We demonstrate that higher-order electric susceptibilities in crystals can be enhanced and understood through nontrivial topological invariants and quantum geometry, using one-dimensional $\pi$-conjugated chains as representative model systems. First, we show that the crystalline-symmetry-protected topology of these chains imposes a lower bound on their quantum metric and hyperpolarizabilities. Second, we employ numerical simulations to reveal the tunability of nonlinear, quantum geometry-driven optical responses in various one-dimensional crystals in which band topology can be externally controlled. Third, we develop a semiclassical picture to deliver an intuitive understanding of these effects. Our findings offer a firm interpretation of otherwise elusive experimental observations of colossal hyperpolarizabilities and establish guidelines for designing topological materials of any dimensionality with enhanced nonlinear optical properties.