AI 中文总结
本文提出一种几何方法，研究金属长短时线性响应，计算金属含时量子几何张量，确定$D/\boldsymbol{\textit{S}}_1$作为电荷探针，在 kagome 金属中发现范霍夫填充响应存在差异。
AI 中文摘要
含时量子几何张量可描述束缚电子的偶极涨落，对理解绝缘体、超导体和平带的电子性质至关重要，通常被认为在以带内过程为主的金属低能描述中处于次要地位。本文重新审视该观点，强调费米面附近波函数的量子几何发挥重要作用的场景；计算金属的含时量子几何张量，解释其发散性，并与狄拉克和外尔半金属的奇异几何张量对比；确定德鲁德权重与总谱权重之比$D/\boldsymbol{\textit{S}}_1$作为束缚电荷与巡游电荷的晶格尺度探针，在 kagome 金属中量化该比值，发现尽管两个范霍夫填充的费米面相同，但响应不同。
英文摘要
The time-dependent quantum geometric tensor, which captures dipole fluctuations of bound electrons, is essential for understanding the electronic properties of insulators, superconductors, and flat bands. It is often considered subleading for low-energy descriptions of metals that are dominated by intra-band processes. Here, we revisit this perspective and highlight scenarios where the quantum geometry of the wavefunctions close to the Fermi surface plays a significant role. We compute the time-dependent quantum geometric tensor for metals, explain its divergence, and contrast it against singular geometric tensors of Dirac and Weyl semi-metals. We identify the ratio of Drude to total spectral weight, $D/\mathcal{S}_1$, as a lattice-scale probe of bound versus itinerant charge, and quantify it in the kagome metal, where the two van Hove fillings respond differently despite identical Fermi surfaces.
Comments11 pages, 2 figures
