Electronically Inactive Intercalated La$_2$NiO$_4$ Layer in Superconducting La$_5$Ni$_3$O$_{11}$

The recent discovery of superconductivity in La$_5$Ni$_3$O$_{11}$ extends the family of superconducting Ruddlesden--Popper nickelates beyond La$_3$Ni$_2$O$_7$. Unlike conventional members of a single Ruddlesden--Popper series, La$_5$Ni$_3$O$_{11}$ contains an intercalated La$_2$NiO$_4$ layer between La$_3$Ni$_2$O$_7$ blocks, raising the question of whether this additional layer participates in the low-energy electronic structure. Here, we combine density functional theory, Wannier-based tight-binding modeling, and rotationally invariant slave-boson calculations to investigate the electronic role of the intercalated layer. We find that realistic electronic parameters place the La$_2$NiO$_4$ layer in gapped insulating regimes rather than a paramagnetic metallic state. Furthermore, realistic interlayer hybridization fails to generate any appreciable La$_2$NiO$_4$-derived spectral weight at the Fermi level. Our results demonstrate that the low-energy electronic structure of La$_5$Ni$_3$O$_{11}$ is governed primarily by the La$_3$Ni$_2$O$_7$ block, with the intercalated La$_2$NiO$_4$ layer remaining electronically inactive. This establishes a minimal low-energy description of La$_5$Ni$_3$O$_{11}$ and provides a unified framework for understanding superconductivity in intercalated Ruddlesden--Popper nickelates.