Structural and electronic properties of Sr(Zr,Ti)O$_3$ alloys for use in oxide heterostructures

Sr(Ti,Zr)O$_3$ alloys are promising materials for use in oxide heterostructures, however the fundamental properties of this system have not yet been characterized. Using hybrid density functional calculations, we study the electronic and structural properties of ordered SrTi$_x$Zr$_{1-x}$O$_3$ alloys at $x$=0, 0.25, 0.5, 0.75, and 1. As Ti is added to SrZrO$_3$, the lattice parameter is reduced according to Vegard's law, while the band gap shows a large bowing and is sensitive to the Ti distribution. For $x$=0.5, arranging the Ti and Zr atoms into a 1$\times$1 SrZrO$_3$/SrTiO$_3$ superlattice along the [001] direction leads to a highly dispersive single band at the conduction-band minimum (CBM) that is absent in the parent compounds, and a direct gap close to that of pure SrTiO$_3$. This is explained by the splitting of the Ti 3$d$ $t_{2g}$ states in the reduced symmetry of the superlattice, lowering the band originating from the Ti 3$d_{xy}$ orbitals. The lifting of the orbital degeneracy around the CBM suppresses scattering due to electron-phonon interactions. We propose that short-period SrZrO$_3$/SrTiO$_3$ superlattices could be exploited to engineer the band structure and improve carrier mobility compared to bulk SrTiO$_3$.