Separation between the long- and short-range part of the Coulomb interaction in low-dimensional systems: Implications for the macroscopic screening length and collective charge excitations

Collective charge excitations directly probed in electron energy loss and inelastic x-ray scattering spectroscopies play a key role in different fields of condensed matter physics. Being induced by the long-range part of the Coulomb interaction between particles, in standard bulk systems they appear as well-defined features in the spectra associated with the zero crossing of the real part of the macroscopic dielectric function. However, this simple criterion cannot be used to identify collective excitations in low-dimensional systems where the macroscopic dielectric function is not a well-defined concept. In this work, we discuss how this problem can be traced back to the definition of the long-range Coulomb interaction, and we show how appropriate separation between long- and short-range Coulomb interactions allows one to correctly express the low-dimensional macroscopic dielectric function in terms of microscopic quantities accessible in first-principles calculations. This allows disentangling collective charge excitations in low-dimensional materials in analogy with what one does in standard bulk systems. In addition, we show how important macroscopic quantities, such as the screening length scale, can be extracted from full first-principle calculations. As an illustrative example we study the screening effects and the collective excitations in prototypical two-dimensional materials, including metals (NbSe2) and semiconductors (BN and MoS2).