Quantum Nature of Two-Dimensional Electron Gas Confinement at ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ Interfaces

We perform density functional calculations to understand the mechanism controlling the confinement width of the two-dimensional electron gas (2DEG) at ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ interfaces. We find that the 2DEG confinement can be explained by the formation of metal induced gap states (MIGS) in the band gap of ${\mathrm{SrTiO}}_3$. These states are formed as the result of quantum-mechanical tunneling of the charge created at the interface due to electronic reconstruction. The attenuation length of the MIGS into the insulator is controlled by the lowest-decay-rate evanescent states of ${\mathrm{SrTiO}}_3$, as determined by its complex band structure. Our calculations predict that the 2DEG is confined in ${\mathrm{SrTiO}}_3$ within about 1 nm at the interface.

Figure 1

Layer-resolved DOS on the ${\mathrm{TiO}}_2$ planes in $\mathrm{LaO}/({\mathrm{SrTiO}}_3{)}_{23}$ superlattice ($m=1$). Index $l$ denotes the ${\mathrm{TiO}}_2$ monolayer position away from the LaO monolayer placed at $l=0$. Left panels show the DOS in the vicinity of the Fermi energy ($E_F$) denoted by the vertical line. The shaded areas indicate the occupied states forming 2DEG. The dashed line demonstrates the variation of the conduction band minimum (CBM) in ${\mathrm{SrTiO}}_3$. Right panels show the DOS of the O-2s states at energies around 18 eV below $E_F$. The potential variation is indicated by the dashed line.

Figure 2

Charge on Ti sites (solid symbols) for $({\mathrm{LaAlO}}_3{)}_m/({\mathrm{SrTiO}}_3{)}_{23}$ superlattices with $m=1$ (squares), $m=3$ (circles) and $m=5$ (triangles), fitted charge distribution (solid lines), and the conduction band minimum (open squares) as a function of distance from the interface $z$. The interfacial ${\mathrm{TiO}}_2$ monolayer is placed at $z=0$ as a reference. The Fermi energy ($E_F$) is shown by a horizontal line and is related to the CBM plot only.

Figure 3

${\mathbf{k}}_{\parallel }$-resolved charge density of the $\mathrm{LaO}/({\mathrm{SrTiO}}_3{)}_{23}$ superlattice (a) and the lowest decay rate of the evanescent states in bulk ${\mathrm{SrTiO}}_3$ (b) within the two-dimensional Brillouin zone. The charge density is integrated in the energy range from $E_F-1.0\mathrm{eV}$ to $E_F$. The decay rate (in units of $2\pi /a$) is evaluated for bulk ${\mathrm{SrTiO}}_3$ at 0.2 eV below the CBM.