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.