Electronic structures and multi-orbital models of La$_3$Ni$_2$O$_7$ thin films at ambient pressure

The recent discovery of superconductivity with a transition temperature $T_c$ exceeding 40 K in La$_3$Ni$_2$O$_7$ and (La,Pr)$_{3}$Ni$_2$O$_7$ thin films at ambient pressure marks a significant breakthrough in the field of nickelate superconductors. Using density functional theory (DFT), we propose a double-stacked two-orbital effective model for La$_3$Ni$_2$O$_7$ thin film based on the Ni$-e_g$ orbitals. Our analysis of the Fermi surface reveals three electron pockets ($\alpha,\alpha^{\prime},\beta$) and two hole pockets ($\gamma,\gamma^{\prime}$), where the additional $\alpha^{\prime}$ and $\gamma^{\prime}$ pockets arise from inter-stack interactions. Furthermore, we introduce a high-energy model that incorporates O$-p$ orbitals to facilitate future studies. Calculations of spin susceptibility within the random phase approximation (RPA) indicate that magnetic correlations are enhanced by nesting of the $\gamma$ pocket, which is predominantly derived from the Ni$-d_{z^2}$ orbital. Our results provide a theoretical foundation for understanding the electronic and magnetic properties of La$_3$Ni$_2$O$_7$ thin films.