Optical response of two-dimensional systems: Insights from classical electromagnetism to ab initio calculations

Quasi-two-dimensional objects appear to be promising for the development of new optical devices since their electronic properties are expected to be governed by their size. The understanding of these properties can be achieved by means of theoretical spectroscopy based on the state-of-the-art ab initio formalisms. Time-dependent density functional theory is well suited since it accounts for the local field effects, which are expected to be large at the interfaces with vacuum. This framework allows the calculation of the response function to the external potential. For bulk materials, this quantity is related to the macroscopic dielectric function following the Adler and Wiser formula. This expression contains dimensionless quantities, while for the two-dimensional object, the physical observables should be proportional to the thickness. In this paper, we propose a mixed-space approach which allows us to calculate in a direct way the out-of-plane component and to evidence how the ambiguity on the thickness of the slab affects the calculation of the macroscopic dielectric function. The classical Lorentz model adapted to a thin slab reveals how the huge change of the induced electric field, and the arising of a transverse polarization, lead to modify the expression of the macroscopic dielectric function to get the absorption spectrum. Despite the influence of the thickness of the slab on the macroscopic dielectric function, the optical response resulting from the classical electromagnetism can be unambiguously calculated from the mixed-space simulations.