超越局域贝里几何：电子位置的第一性原理有限动量理论
Beyond Local Berry Geometry: A First-Principles Finite-Momentum Theory of Electronic Position
AI总结：
该研究建立了有限动量下电子位置的第一性原理理论，将量子几何扩展到局域贝里极限之外，揭示了动量空间几何对非线性响应的控制作用，为预测真实材料的场驱动现象提供了通用基础。
AI中文摘要：
电子位置控制晶体如何极化以及对外场的响应，在晶体中通常通过动量空间中电子态的局域变化来描述，这种贝里框架重塑了现代凝聚态物理，但强场会驱动电子跨越有限动量范围，不同动量间的相干性成为响应的一部分。本文建立了有限动量下电子位置的第一性原理理论，保留了缺失的相干性信息，证明不等动量相干性在空间平均下仍可抵消并产生极化，形成相干偶极子；该矩阵直接从材料波函数获得，无需模型能带或拟合跃迁元。在硅中，有限动量几何确定了材料动量标度，将该标度与场驱动的动量变化对比可预测有限动量物理何时起作用；跨越该标度会强烈重组五次及更高次谐波，表明动量空间几何而非仅发射光子能量控制非线性响应。高次谐波（HHG）是首个例证，但该理论适用于驱动电子探索有限动量范围的所有情况，因此它将量子几何扩展到局域贝里极限之外，为预测真实材料中场驱动现象提供了通用基础。
英文摘要：
Electronic position controls how a crystal polarizes and responds to an external field. In crystals, it is usually described through local changes of electronic states in momentum space. This Berry framework has reshaped modern solid-state physics, but strong fields drive electrons across a finite momentum range, where coherence between different momenta becomes part of the response. Here we establish a first-principles theory of electronic position at finite momentum that retains this missing information. We show that unequal-momentum coherence can cancel under spatial averaging and still produce polarization, forming a coherence dipole. We obtain the matrix directly from material wave functions, without model bands or fitted transition elements. In Si, the finite-momentum geometry sets a material momentum scale. Comparing this scale with the momentum change driven by the field predicts when finite-momentum physics becomes active. Crossing the scale strongly reorganizes the fifth and higher harmonics, showing that momentum-space geometry, rather than emitted photon energy alone, controls the nonlinear response. HHG is the first demonstration, but the theory applies whenever driven electrons explore a finite momentum range. It therefore extends quantum geometry beyond the local Berry limit and provides a general basis for predicting field-driven phenomena in real materials.
