Metal-insulator transitions in GdTiO$_3$/SrTiO$_3$ superlattices

The density functional plus U (DFT+U) method is used to obtain electronic structures and metal-insulator phase diagrams of metal-insulator transition of (001) (GdTiO$_3$)$_m$/(SrTiO$_3$)$_n$ superlattices. In metallic phases, the mobile electrons are found in the SrTiO$_3$ layers, with near-interface electrons occupying $xy$-derived bands, while away from the interface the majority of electrons reside in $xz/yz$ bands. As the thickness $n$ of the SrTiO$_3$ layers decreases a metal-insulator transition occurs. Two insulating phases are found. At $n=1$ the hybridization of two TiO$_2$ layers across the SrO layer leads to a dimerized insulating state as previously proposed\footnote{Ru Chen, SungBin Lee, and Leon Balents, Phys. Rev. B {\bf 87}, 161119(R) (2013).} with relatively small U$_c \sim 2.5$ eV. For $n>1$ we find that insulating phases occur together with checkerboard charge and orbital ordering and variation of Ti-O bonds at a larger U$_c\sim3.5$eV. Inconsistencies with experiment suggest that many-body correlations are important.