  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.
