Correlation-Driven Charge Order at the Interface between a Mott and a Band Insulator

To study digital Mott insulator ${\mathrm{LaTiO}}_3$ and band insulator ${\mathrm{SrTiO}}_3$ interfaces, we apply correlated band theory within the local density approximation including a Hubbard U to ($n$, $m$) multilayers, $1\le n$, $m\le 9$ using unit cells with larger lateral periodicity. If the on-site repulsion on Ti is big enough to model the Mott insulating behavior of undistorted ${\mathrm{LaTiO}}_3$, the charge imbalance at the interface is found in all cases to be accommodated by disproportionation (${\mathrm{Ti}}^{4+}+{\mathrm{Ti}}^{3+}$), charge ordering, and ${\mathrm{Ti}}^{3+}$ $d_{xy}$-orbital ordering, with antiferromagnetic exchange coupling between the spins in the interface layer. Lattice relaxations lead to conducting behavior by shifting (slightly but importantly) the lower Hubbard band, but the charge and orbital order is robust against relaxation.

Figure 1

Segment of the (1,1) ${\mathrm{LaTiO}}_3\mathrm{\text{−}}{\mathrm{SrTiO}}_3$ multilayer, illustrating the cubic perovskite structure (unlabeled white spheres denote oxygen). An LaO layer lies in the center, bordered by two ${\mathrm{TiO}}_2$ layers, with a SrO layer at top and bottom. The lateral size of this figure corresponds to the $p(2\times 2)$ cell discussed in the text.

Figure 2

(a) Phase diagram of the Ti moments for the (1,1)-SL in a transverse $c(2\times 2)$ cell vs the on-site Coulomb repulsion strength $U$ on the Ti $3d$ orbitals. (b) Density of states (spin direction indicated by arrows) of the (1,1)-SL for different $U$ values. Disproportionation occurs in a weak first-order manner around $U\approx 5.5\mathrm{eV}$. HM FM indicates a region of half-metallic ferromagnetism before the Mott gap appears around $U\approx 6.5\mathrm{eV}$.

Figure 3

45° checkerboard charge density distribution of the occupied $3d$ states in the charge-ordered ${\mathrm{TiO}}_2$ layer in the FM (1,1) multilayer. Orbital ordering due to $d_{xy}$ orbital occupation is apparent. The positions of O, ${\mathrm{Ti}}^{3+}$, and ${\mathrm{Ti}}^{4+}$ ions are marked by white, light blue (gray), and dark blue (black) circles, respectively.

Figure 4

Layer-resolved projected $3d$ density of states at the Ti sites for a (a) structurally ideal and (b) relaxed (1,5) multilayer. The two topmost panels show ${\mathrm{Ti}}^{3+}$ and ${\mathrm{Ti}}^{4+}$ at the IF; the succeeding panels show the behavior of the Ti ion in deeper layers of the STO part of the slab. Ti $d_{xy}$ orbitals are marked red (dark gray), while the $d_{xz}$ and $d_{yz}$ are marked light gray.