Proposal of a One-Dimensional Electron Gas in the Steps at the ${\mathrm{LaAlO}}_3\mathrm{\text{−}}{\mathrm{SrTiO}}_3$ Interface

The two-dimensional electron gas at the interface between ${\mathrm{LaAlO}}_3$ and ${\mathrm{SrTiO}}_3$ has become one of the most fascinating and highly debated oxide systems of recent times. Here we propose that a one-dimensional electron gas can be engineered at the step edges of the ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ interface. These predictions are supported by first-principles calculations and electrostatic modeling which elucidate the origin of the one-dimensional electron gas as an electronic reconstruction to compensate a net surface charge in the step edge. The results suggest a novel route to increasing the functional density in these electronic interfaces.

Figure 1

Schematic diagram illustrating the effect of steps on the net charge of the interface. Top: Polarization argument considering LAO has a polarization, $P_0$ along the [100], [010], and [001] directions, with $P$ the total and $\tilde{P}$ the net of the stepped interface. Bottom: An equivalent picture with charge densities $\pm {\sigma }_c$ on the terrace and step edge.

Figure 2

Left: The DFT simulation cell of the LAO/STO superlattice. The two interface terrace terminations are both ${\mathrm{TiO}}_2\mathrm{\text{−}}\mathrm{LaO}$ ($n$-type), whereas the interface step termination is $n$-type along the bottom interface and $p$-type ($\mathrm{SrO}\mathrm{\text{−}}{\mathrm{AlO}}_2$) along the top interface. (gray, oxygen; dark blue, Al; light blue, La; yellow, Ti; green, Sr) Center: (001) layered density of states near the Fermi level of the stepped superlattice (solid lines) and pristine superlattice (dashed line). Right: The change in the layer density of free electrons on introduction of steps in the superlattice.

Figure 3

Top: Interface free electron density $\sigma$ as a function of the miscut angle $\theta$ for a LAO(3 unit cells)/STO film geometry. Points represent densities calculated from DFT, and lines are electrostatic modeling under various assumptions (see the text). Middle: Predicted schematic electronic phase diagram (see the text) at the $n$-type (step and terrace) terminated LAO/STO interface as a function of the miscut angle $\theta$ and the LAO thickness $d$. Bottom: An isosurface of the Ti $3d$ electron density (yellow clouds) at an $n$-type stepped LAO/STO interface. Blue and pink cages represent oxygen octahedra around Ti and Al atoms, respectively.