Electron energy loss spectroscopy of thin slabs with supercell calculations

Electron energy loss spectroscopy in the low-loss regime is widely used to access to the screening of the Coulomb potential as a function of the momentum transfer. This screening is strongly reduced for low-dimensional materials and this spectroscopy is a technique of choice to study the resulting quantum confinement. Time-dependent density-functional theory within an ab initio formalism is particularly suited to simulate angular-resolved electron energy loss spectra, taking benefit from the reciprocal space description. For an isolated object, the standard procedure based on the supercell approach dramatically fails for the out-of-plane optical response of the surface and we have proposed a scheme called Selected-G [N. Tancogne-Dejean, C. Giorgetti, and V. Véniard, Phys. Rev. B 92, 245308 (2015)PRBMDO1098-012110.1103/PhysRevB.92.245308], leading to a slab potential. In this paper, we show that the standard procedure also affects the in-plane components of the EEL spectra. Applying the Selected-G procedure, we show that the full expression of the slab potential is crucial to describe slabs of finite thickness. We compare our formalism to other cutoff procedures, and show that if they provide spectra with the correct spectral weight, allowing the good description of plasmon dispersion, the amplitude of the peaks depends on the choice of the supercell. Our results, which provide spectra independent of vacuum, will have a strong impact on the calculation of properties such as quasiparticle corrections.