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

Abstract

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 [S. Mazzei and C. Giorgetti, Phys. Rev. B 106, 035431 (2022)], we showed that the framework inherited 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 use of the so-called Adler and Wiser formula. We evidence that the inclusion of interfaces in the thickness of the slab causes the response function for the out-of-plane component to move sharply 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 out-of-plane perturbation. Nevertheless, we also show that the macroscopic average of the dielectric tensor of an ultrathin slab calculated within the longitudinal formalism of TD-DFT depicts the properties of the transverse reflectance and transmittance spectra of a thin slab.