Conductivity models for electron energy loss spectroscopy of graphene in a scanning transmission electron microscope...

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.