Electron-lattice instabilities suppress cuprate-like electronic structures in SrFeO${}_3$/SrTiO${}_3$ superlattices

Using {\it ab initio} density functional theory we explore the behavior of thin layers of metallic $d^4$ SrFeO${}_3$ confined between the $d^0$ dielectric SrTiO${}_3$ in a superlattice geometry. We find the presence of insulating SrTiO${}_3$ spacer layers strongly affects the electronic properties of SrFeO${}_3$: For single SrFeO${}_3$ layers constrained to their bulk cubic structure, the Fermi surface is two-dimensional, nested and resembles the hole-doped superconducting cuprates. A Jahn-Teller instability couples to an octahedral tilt mode, however, to remove this degeneracy resulting in insulating superlattices.