Optical properties of quasi-two-dimensional objects from time dependent - density functional theory: longitudinal versus transverse dielectric functions

Comprehension of the electronic properties of nano-objects is a key to defining dedicated properties, which can be adjusted by changing their size. Beyond confinement effects, the presence of interfaces, i.e., places where there is an abrupt change of electronic density, should also play a role. Time-dependent density functional theory (TD-DFT) is a state-of-the-art ab initio formalism, in which this effect is accounted for through the so-called local field effects. In an earlier paper [Stefano Mazzei and Christine Giorgetti, Phys. Rev. B. 106, 035431 (2022)], we showed that the framework inheritated from three-dimensional crystals could not provide reliable absorption spectra. In the present paper, we propose to calculate the macroscopic average of the dielectric tensor of a quasi-two-dimensional (2D) object from the response function of the density to the total macroscopic potential, in order to avoid the use of the so-called Adler and Wiser formula. We evidence that the inclusion of the interfaces in the thickness of the slab causes the response function to move sharply for the out-of-plane component from the bulk absorption resonance to the plasmon one. This shows that the longitudinal-longitudinal contraction of the dielectric tensor is no longer equal to the transverse-transverse one in a quasi-2D object, for the out-of-plane perturbation. Nevertheless, we also show that the macroscopic average of the dielectric tensor of an ultra-thin slab calculated within the longitudinal formalism of TD-DFT depicts the properties of the transverse reflectance and transmittance spectra of a thin slab.