Firstly, we present a theoretical modeling of the experimental electron energy loss (EEL) spectra of free-standing films consisting of N graphene layers in a scanning transmission electron microscope (STEM) [1]. We treat the multi-layer graphene (MLG) as layered electron gas with in-plane polarizability modeled by a two-dimensional (2D), two-fluid hydrodynamic (HD) model [2] for the inter-band transitions of ʌ DQGı electrons of single-layer graphene (SLG), and find good agreement (as shown in Fig. 1) with the experimental EEL spectra [3] for N<10 graphene layers. Secondly, we present a theoretical modeling of the experimental EEL spectroscopy (EELS) data for monolayer graphene supported by Pt(111), Ru(0001), and Ni(111) substrates [4], as well as for high-quality graphene grown on peeled-off epitaxial Cu(111) foils [5]. To reproduce the experimental loss function, we use the same version of the HD model for graphene’s ʌ DQG ı HOHFWURQV in conjunction with an empirical Drude-Lorentz model for metal substrate. Finally, we present an analytical modeling of the experimental EELS data for free-standing graphene obtained by STEM using an ab initio method and the 2D, two-fluid extended HD (eHD) model [6]. We use an optical approximation based on the conductivity of graphene given in the local, i.e., frequency-dependent form derived by these two methods and find very good agreement with the EEL spectra from three independent experiments [3,7,8], especially in the case of the eHD modelMini-workshop REST in Paris : December 7-8, Paris, 2017
