Avoiding the Polarization Catastrophe in ${\mathrm{LaAlO}}_3$ Overlayers on ${\mathrm{SrTiO}}_3(001)$ through Polar Distortion

A pronounced uniform polar distortion extending over several unit cells enables thin ${\mathrm{LaAlO}}_3$ overlayers on ${\mathrm{SrTiO}}_3(001)$ to counteract the charge dipole and thereby neutralize the “polarization catastrophe” that is suggested by simple ion counting. This unanticipated mechanism, obtained from density functional theory calculations, allows several unit cells of the ${\mathrm{LaAlO}}_3$ overlayer to remain insulating (hence, fully ionic). The band gap of the system, defined by occupied O $2p$ states at the surface and unoccupied Ti $3d$ states at the interface in some cases $\sim 20\AA$ distant, decreases with increasing thickness of the ${\mathrm{LaAlO}}_3$ film before an insulator-to-metal transition and a crossover to an electronic reconstruction occurs at around five monolayers of ${\mathrm{LaAlO}}_3$.

Figure 1

Side view of the relaxed structures of 1, 3, and 4 ML LAO on STO(001) showing the polar distortion. The oxygen ions are marked by light grey spheres, while the Sr-, La-, Ti-, and Al-cations are shown by large green (grey), purple (dark grey) and small blue (dark grey) and orange (grey) spheres.

Figure 2

Vertical displacements of ions $\Delta z$ in the (a) AO and (b) ${\mathrm{BO}}_2$ layers with respect to the bulk positions in Å for 1–5 MLs of LAO on STO(001) obtained within GGA. Cation/oxygen relaxations are marked by full black/open red (grey) symbols. The corresponding layer-resolved dipole moments are displayed in (c). The $x$ axis shows the distance from the interface (I) ${\mathrm{TiO}}_2$-layer.

Figure 3

Density of states for the ideal (dashed line) and relaxed (solid line, grey filling) structure of 1–5 ML LAO on STO(001). Relaxation opens a band gap, but its size decreases with each added LAO layer.

Figure 4

Layer-resolved density of states of 5 ML LAO on STO(001) with ideal (dashed line) and relaxed (grey shaded area) coordinates. The DOS for the ideal positions was shifted by 0.5 eV to align with the conduction band of the system with the relaxed atomic positions. Its Fermi level is marked with a dashed line.