Model calculations for low‐lossEELspectra of2Dmultilayer systems

Abstract

Collective electronic excitations (plasmons) in single‐layer and few‐layer graphene have been studied extensively in the past few years. In particular, the dispersion and nature of the π plasmon peak in free‐standing single‐layer graphene was investigated by means of momentum‐resolved electron energy‐loss spectroscopy (MREELS) [1‐3]. Besides, it was also studied how the transition from mono‐ to multilayer graphene changes the shape of EEL spectra. Within a layered electron‐gas (LEG) model, this transition can be modeled very precisely [4,5]. For other 2D materials such as transition metal dichalcogenides (TMDs), however, this approach may be highly inaccurate. We therefore evaluate more precise model calculations for multilayer systems. Our calculations are based on time‐dependent DFT calculations for the individual monolayers. The plane‐wave pseudopotential DFT code abinit [6] is used to simulate the ground state within local density approximation (LDA). The linear response is then calculated within random‐phase approximation (RPA) using the dp‐code [7]. Compared to the LEG model where the monolayers are assumed to be perfectly 2‐dimensional and homogeneous, we preserve the layers' microscopic structure in our calculations. We demonstrate that only by taking the finite thickness of the constituent monolayers into account, the spectra of multilayer MoS 2 can be modeled correctly (see the figure). Our calculations can be also applied to arbitrary van‐der‐Waals heterostructures. Our results are directly compared to MREEL spectra recorded with a Zeiss Libra 200 based TEM prototype (“SALVE I”, [8,2]) equipped with a monochromator and an Ω type in‐column energy filter. This allows for the verification of our calculations over a large range of energy losses (0‐40 eV) and different momentum transfers within the Brillouin zone. [9]