Electron energy loss spectroscopy of thin slabs with supercell calculations

Abstract

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 connement. Time-dependent density functional theory within an ab initio formalism, is particularly suited to simulate angular resolved electron energy loss spectra, taking benet 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 new scheme called Selected-G, 1 leading to a slab potential. In this paper, we show that the standard procedure also aects 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 nite thickness. We compare our formalism to other cuto 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.

Massive and massless plasmons in germanene nanosheets

“…The above outlined electronic structures are primarily involved in the macroscopic permittivity response ϵ m of the FGe and QFGe monolayers. The other key element is the interaction generated by light-induced changes in charge density that we approximated to a truncated Coulomb potential, specific for 2D materials [40][41][42][43][44] , see Sec.II D-Sec.II E. We used the same potential, in conjunction with a plasmon pole model 47 , to correct the band energies of Fig. 1 at the level of the GW approximation [48][49][50] , as reported in Sec.…”

“…based on the 2D Coulomb potential v 2d gg ′ =2πδ gg ′ /|q + g|, with g, g ′ and G z , G ′ z respectively labeling the in-plane and out-of-plane components of G and G ′ . The advantage of v GG ′ is the deletion of redundant density-density interactions among the replicated monolayer slabs [35][36][37][38][39][40][41][42][43][44] , which provides far more accuracy to the low-momentum dielectric response of 2D materials with respect to the usual Coulomb potential v 3d…”

Massive and massless plasmons in germanene nanosheets

“…The above outlined electronic structures are primarily involved in the macroscopic permittivity response ϵ m of the FGe and QFGe monolayers. The other key element is the interaction generated by light-induced changes in charge density that we approximated to truncated Coulomb potential, specific for 2D materials [40][41][42][43][44] . The same potential was used, in conjunction with a plasmon pole model 47 , to correct the band energies of Fig.…”

“…As a routinely established framework, our TDDFT-RPA calculations [40][41][42][43][44] required a preliminary DFT step to access the ground state of FGe, QFGe on AlN, and QFGe on MoS 2 , which we reconstructed by the PW pseudopotential approach 57,58 . This involves the basis set of space functions PW k+G = Ω −1/2 e i(k+G)•r , indexed by the wave vectors k of the 1 st BZ and the reciprocal lattice vectors G, in the normalization volume Ω.…”

Massive and massless plasmons in germanene nanosheets

“…Similar features were observed in metal quantum well structures grown on graphene 29 , while a more extreme correlation of linear and flat bands was recognized in twisted sandwiched graphene 30 .Given these premises, a major issue is on the dielectric response and related plasmon modes of the QFGe sheets, as compared to freestanding germanene (FGe). In this respect, particular attention sholud be given to the role played by plasmons in extreme light trapping.Here we provide such a study, starting from a time-dependent density-functional theory 31-34 (TDDFT) approach, in the random phase approximation (RPA), with a local kernel designed for 2D systems [35][36][37][38][39][40][41][42][43][44] . Accordingly, we compute the optical absorption and energy loss function of the FGe and QFGe monolayers that allow us to explore their leading single-particle excitations (SPEs) processes and charge density modes, over the infrared (IR) to the ultraviolet (UV) range.Next, we consider the explicit inclusion of quasiparticle GW corrections [45][46][47][48][49][50] , in an RPA+GW approach.…”