Ionic relaxation contribution to the electronic reconstruction at the $n$-type ${\text{LaAlO}}_3/{\text{SrTiO}}_3$ interface

Density-functional theory calculations reveal that the compensation mechanism at the isolated $n$-type interface in ${\text{LaAlO}}_3/{\text{SrTiO}}_3$ superlattices involves both ionic and electronic degrees of freedom. Strong polar distortions screen the local electric field and reduce the band discontinuity across the interface. We find that the electronic reconstruction depends sensitively on whether structural optimization is performed within GGA (conventional exchange and correlation effects) or $\text{GGA}+U$ (which includes strong intra-atomic interactions). For a structural optimization within $\text{GGA}+U$ the excess charge is confined to the interface ${\text{TiO}}_2$ layer with a charge-ordered, orbitally polarized arrangement of ${\text{Ti}}^{3+}$ and ${\text{Ti}}^{4+}$. While the charge-ordered phase represents the ground state, optimization within GGA leads to more pronounced lattice polarization, suppression of charge order (with remaining $d_{xy}$-orbital occupation in the interface layer), and a delocalization of the excess charge extending over a few ${\text{SrTiO}}_3$ layers.

Figure 1

(Color online) Vertical displacements of ions $\Delta z$ in $\text{Å}$ in the ${\text{LAO}}_{4.5}/{\text{STO}}_{5.5}$ superlattice with respect to the bulk positions obtained within GGA (solid black line) and $\text{GGA}+U$ (red dashed line). The $x$ axis shows the distance from the interface (I) ${\text{TiO}}_2$ layer. A, B, ${\text{O}}_A$, ${\text{O}}_B$ denote the positions of ions in the layered ${\text{ABO}}_3$ perovskite lattice.

Figure 2

(Color online) Crystal structure of a ${\text{LAO}}_{4.5}/{\text{STO}}_{5.5}$ superlattice showing half of the simulation cell with atomic relaxations obtained within (a) $\text{GGA}+U$ and (b) GGA. Additionally, the charge-density distribution of the occupied $\text{Ti}3d$ states obtained for both geometries is displayed. For the geometry obtained within $\text{GGA}+U$ the $\text{Ti}3d$ occupation is confined to the interface layer with ${\text{Ti}}^{3+}$ and ${\text{Ti}}^{4+}$ arranged in a $c\left(2\times 2\right)$ manner with an occupied $d_{xy}$ orbital at the ${\text{Ti}}^{3+}$ sites. For (b) the strong polar distortions suppress charge order and delocalize the excess charge throughout the STO slab, while orbital order ($d_{xy}$ partial occupation) is retained in the interface layer.

Figure 3

(Color online) Layer-resolved density of states of a ${\text{LAO}}_{4.5}/{\text{STO}}_{5.5}$ SL obtained within $\text{GGA}+U$ with atomic positions relaxed within (a) $\text{GGA}+U$ and (b) GGA. The two topmost panels show the two Ti ions at the interface; the succeeding panels show the behavior of the Ti ions in deeper layers of the STO part of the slab. For the geometry obtained within GGA the excess charge is confined to the IF with a ${\text{Ti}}^{3+}$, ${\text{Ti}}^{4+}$ layer and rapid relaxation of the deeper layers toward bulk behavior. The structure relaxed within GGA leads to a metallic STO part, suppressed charge order and a residual orbital order $(d_{xy}$ –red/dark gray filling) at the Ti (I) sites and degenerate $t_{2g}$ states in deeper layers.

Figure 4

(Color online) Positions of $\text{O}1s$ core levels (with respect to the Fermi level, $E_v$), across the interface in the ${\text{LAO}}_{4.5}/{\text{STO}}_{5.5}$ superlattice before (dashed) and after (solid) relaxation obtained within GGA (black line) and $\text{GGA}+U$ (red/dark gray line). The $x$ axis shows the distance from the interface (I) ${\text{TiO}}_2$ layer. The Fermi levels of all systems are set to zero and only relative variations of the $\text{O}1s$ levels from layer to layer are of interest.

Figure 5

Schematic picture of the band alignment at the $n$-type interface in the ${\text{LAO}}_{4.5}/{\text{STO}}_{5.5}$ superlattice calculated using the variation of the $\text{O}1s$ core levels across the interface and the experimental band gaps ${\Delta }_{\text{STO}}=3.2\text{eV}$ and ${\Delta }_{\text{LAO}}=5.6\text{eV}$.