Recent advancements in the energy resolution and probing capabilities of monochromated electron-beam spectroscopy instruments have made this experimental technique increasingly useful for investigating and understanding the plasmonic, photonic, and electronic properties of graphene-enhanced systems. We develop herein an empirical model for the in-plane conductivity of doped monolayer graphene, comparing with ab initio data from the terahertz (THz) to the upper range of frequencies accessible with the valence electron energy loss spectroscopy (VEELS). Along with our ab initio data, this model is employed to calculate the energy loss spectra using a relativistic formulation, allowing us to analyze the effects that different electron beam parameters have on the response of graphene in a monochromated scanning transmission electron microscope setup. In particular, we explore the effects of reducing the collection angle of scattered electrons, thereby deducing a computational procedure for extracting the real and imaginary parts of the optical conductivity of graphene layers from VEELS measurements. Our modeling ultimately provides insight into how the optoelectronic properties of graphene are expected to manifest in the VEELS obtained via monochromated beams, with the effects of graphene doping, the excitation of its plasmon-polaritons, and relativistic contributions included comprehensively.

中文翻译：

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具有高能量分辨率的扫描透射电子显微镜中石墨烯电子能量损失谱的电导率模型

单色电子束光谱仪器的能量分辨率和探测能力的最新进展使这种实验技术对于研究和理解石墨烯增强系统的等离子体、光子和电子特性越来越有用。我们在此开发了掺杂单层石墨烯的面内电导率的经验模型，与从太赫兹 (THz) 到价电子能量损失光谱 (VEELS) 可获得的频率上限的 ab initio 数据进行比较。连同我们的 ab initio 数据，该模型用于使用相对论公式计算能量损失谱，使我们能够在单色扫描透射电子显微镜设置中分析不同电子束参数对石墨烯响应的影响。特别是，我们探索了减小散射电子收集角的影响，从而推导出从 VEELS 测量中提取石墨烯层光导率实部和虚部的计算程序。我们的建模最终提供了对石墨烯的光电特性如何在通过单色光束获得的 VEELS 中表现出来的见解，石墨烯掺杂的影响、其等离子体极化子的激发和相对论的贡献全面包括在内。