Probing the bulk plasmon continuum of layered materials through electron energy loss spectroscopy in a reflection geometry

A periodic arrangement of two-dimensional (2D) conducting planes is known to host a (bulk) plasmon dispersion that interpolates between the typical, gapped behavior of three-dimensional (3D) metals and a gapless, acoustic regime as a function of the out-of-plane wave vector. The semi-infinite system - the configuration relevant to electron energy loss spectroscopy (EELS) in a reflection geometry, as in high-resolution EELS (HREELS) - is known to host a surface plasmon that ceases to propagate below a cutoff wave vector. As the f-sum rule requires a finite response whether there exist sharp excitations, we demonstrate that what remains in the surface loss function - the material response probed by HREELS - is the contribution from the (bulk) plasmon of the infinite system. We provide a one-to-one mapping between the plasmon continuum and the spectral weight in the surface loss function. In light of this result, we suggest that HREELS be considered a long-wavelength probe of the plasmon continuum in layered materials.