标题： 层状 Lindhard 金属和奇异金属中等离子体模式的比较分析 显示英文标题

标题： Comparative analysis of plasmon modes in layered Lindhard metals and strange metals

摘要： 神秘的奇异金属仍然是21世纪科学中最重要的未解问题之一。 理解这种物质相需要动量和能量分辨的动态电荷敏感度， $\chi(q,\omega)$，尤其是在有限动量下。 非弹性电子散射 (EELS)，在透射（T-EELS）或反射（R-EELS）几何结构中进行，是研究 $\chi(q,\omega)$的强大探针。 对于典型的奇异金属Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$，T-EELS、R-EELS和红外（IR）光谱在 $q \sim 0$处一致，都显示出接近1 eV的强烈阻尼等离子体。 在较大的$q$时，EELS 结果显示出未解决的差异。 由于 IR 数据具有高度可重复性，因此使用 IR 数据来计算在适度的$q$下预期的 EELS 响应是有利的。 基于先前的 R-EELS 工作 [J. Chen\textit{等.}, Phys. Rev. B.\textbf{109}, 045108 (2024)]，我们将这种方法扩展到有限金属层堆栈的 T-EELS，将一个“教科书”式的 Lindhard 金属与一种奇异金属进行比较。 在 Lindhard 情况下，低$q$响应由因层间库仑耦合产生的寿命较长的驻波等离子体模式主导，其面内色散类似于层状金属中众所周知的 Fetter 模式。 这种行为仅依赖于几何结构和库仑相互作用的长程性质，对层细节不敏感。 在较大的$q$时，响应反映了单个层的微观特性。 对于奇异金属，基于 IR 数据的计算预测了一个高度阻尼的等离子体，其色散较弱且没有明显表面模式。 虽然我们的结果在低$q$时与 IR 和 R-EELS 相符，但在大$q$时并未再现任何已发表的 EELS 光谱，突显出未解决的差异，需要进一步的实验研究。 显示英文摘要

摘要： The enigmatic strange metal remains one of the central unsolved problems of 21st century science. Understanding this phase of matter requires knowledge of the momentum- and energy-resolved dynamic charge susceptibility, $\chi(q,\omega)$, especially at finite momentum. Inelastic electron scattering (EELS), performed in either transmission (T-EELS) or reflection (R-EELS) geometries, is a powerful probe of $\chi(q,\omega)$. For the prototypical strange metal Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$, T-EELS, R-EELS, and infrared (IR) spectroscopy agree at $q \sim 0$, all revealing a highly damped plasmon near 1 eV. At larger $q$, however, EELS results show unresolved discrepancies. Since IR data are highly reproducible, it is advantageous to use IR data to calculate what the expected EELS response should be at modest $q$. Building on prior R-EELS work [J. Chen \textit{et al.}, Phys. Rev. B. \textbf{109}, 045108 (2024)], we extend this approach to T-EELS for finite stacks of metallic layers, comparing a "textbook" Lindhard metal to a strange metal. In the Lindhard case, the low-$q$ response is dominated by long-lived, standing wave plasmon modes arising from interlayer Coulomb coupling, with in-plane dispersions that resemble the well-known Fetter modes of layered metals. This behavior depends only on the geometry and the long-ranged nature of the Coulomb interaction, and is largely insensitive to layer details. At larger $q$, the response reflects the microscopic properties of individual layers. For the strange metal, calculations based on IR data predict a highly damped plasmon with weak dispersion and no distinct surface mode. While our results match IR and R-EELS at low $q$, they do not reproduce any published EELS spectra at large $q$, highlighting unresolved discrepancies that demand further experimental investigation.