Oxide superlattices with alternating $p$ and $n$ interfaces

The physics of oxide superlattices is considered for pristine (001) multilayers of the band insulators ${\text{LaAlO}}_3$ and ${\text{SrTiO}}_3$ with alternating $p$ and $n$ interfaces. A model of charged capacitor plates offers a simple paradigm to understand their dielectric properties and the insulator to metal transition (IMT) at interfaces with increasing layer thicknesses. The model is supported by first-principles results based on density-functional theory. The charge at insulating interfaces is argued and found to be as predicted from the formal ionic charges, not populations. Different relative layer thicknesses produce a spontaneous polarization of the system, and allow manipulation of the interfacial electron gas. Large piezoresistance effects can be obtained from the sensitivity of the IMT to lateral strain. Carrier densities are found to be ideal for exciton condensation.

Figure 1

Band structures of three ${\text{LaAlO}}_3/{\text{SrTiO}}_3$ superlattices with (a) 4/4, (b) 8/8, and (c) 12/12 unit-cell thicknesses.

Figure 2

Centre: DOS projected on unit-cell bilayers for the 12/12 superlattice. Left: averaged (Ref. 27) electrostatic potential energy for electrons as a function of $z$. Right: the anion-cation splitting of the ${\text{TiO}}_2$ planes in ${\text{SrTiO}}_3$ and LaO planes in ${\text{LaAlO}}_3$ (larger splitting in each material), with $\delta z=z_{\text{cation}}-z_{\text{anion}}$.

Figure 3

(Color online) Capacitor-plates model of the LAO/STO superlattice. Above, the plates are indicated by the thinner bands, and ${\sigma }_c$ indicates the charge of chemical origin attached to each, which is equal but of opposite sign for alternating interfaces. The box around the central plate indicates the surfaces for integration of Gauss’s law. The lower panel shows the net electrostatic potential $V$ for the system, which can be seen as arising from plates with ${\sigma }_{\text{net}}={\sigma }_c-P_{\text{LAO}}-P_{\text{STO}}$, the latter $P_{\text{LAO}}$ and $P_{\text{STO}}$ referring to the magnitude of the respective polarizations (notice that $V$ has opposite sign to what is shown in the left panel of Fig. 2, which is $qV$).

Figure 4

(Color online) Model band gap vs $z$ for a superlattice with equal thickness (a) the thin-film sample of Ref. 2 (b) and a superlattice with different thicknesses with (c) open and (d) periodic boundary conditions. In (a) and (c) the arrow indicates the charge transfer leading to electron (red) and hole (blue) 2D gases. In both cases the thicknesses depicted give the onset of the charge transfer, corresponding to the insulator to metal transition.