Effect of the additional Se layer on the electronic structure of iron-based superconductor FeSe/SrTiO$_3$

We use density functional theory to study the structure and the band structure of the monolayer FeSe deposited on the SrTiO$_3$ substrate with the additional layer of Se between them. Top of the SrTiO$_3$ is formed by the double TiO layer with and without oxygen vacancies. Several structures with different arrangements of the additional Se atoms above the double TiO layer is considered. Equilibrium structures were found and the band structures for them were obtained. Near the $Gamma=(0,0,0)$ point of the Brillouin zone, the hole Fermi surface pockets persist and, additionally, an electron pocket appears. Thus neither the presence of the additional Se layer nor the oxygen vacancies in the double TiO layer leads to the sinking of hole bands below the Fermi level near the $Gamma$ point. Necessity to include the strong electronic correlations into account is discussed.