Investigation of electron correlation effects in armchair silicene nanoribbons

In this study, the electronic structure of armchair silicene nanoribbons (ASiNRs) is investigated for various widths using first-principle calculations and the framework of the density functional theory. Electronic structure of ASiNRs shows a direct band gap which is decreased  with increasing the nanoribbon's width, showing an oscillatory behavior. The effective Coulomb interaction between localized electrons plays an important role in describing the reason underlying the electronic and magnetic ordering of the material, as well as the intensity of the correlation effects. Thus, we further investigate the screening of the Coulomb interaction in ASiNRs by employing ab initio calculations in conjunction with the constrained random-phase approximation (cRPA) and determine the values of  effective on-site Coulomb interaction (Hubbard U) for them. The values of  Hubbard U parameters for ASiNRs are significant and more than the ones in pristine silicene, indicating a strong correlation effect in these compounds. According to the intensity of different quantum confinement effects in these nanoribbons, the values of  on-site Coulomb interaction parameters, similar to the previous results, turn out to be small, which vary as a function of increasing the ribbon widths. Moreover, in the edge of nanoribbon, the effective Coulomb interaction patameters are greater than the inner parts, showing   the lower screening of  the Coulomb interaction between the localized electrons in the edge of nanoribbon. Finally, the results of the study of the off-site Coulomb interaction show that the Coulomb interaction is weakly screened at short distances, while at large distances if about 12 Å, it is unscreened, which is in a good agreement with the recent studies on the  low dimensional systems. This inefficient screening at large distances can explain the existence of a remarkable quasiparticles correction in GW approximation and exciton binding energy in ASiNRs.