Quantum wells in polar-nonpolar oxide heterojunction systems

We address the electronic structure of quantum wells in polar-nonpolar oxide heterojunction systems focusing on the case of nonpolar ${\text{BaVO}}_3$ wells surrounded by polar ${\text{LaTiO}}_3$ barriers. Our discussion is based on a density-functional description using the local spin-density approximation with local-correlation corrections $\left(\text{LSDA}+U\right)$. We conclude that a variety of quite different two-dimensional electron systems can occur at interfaces between insulating materials depending on band lineups and on the geometrical arrangement of polarity discontinuities.

Figure 1

(Color online) Approximate charge density, electric field, and electric potential distributions in different polar-nonpolar quantum-well systems with inversion symmetry in the quantum-well center. The arrows (black on line) indicate the expected charge densities $\rho$ centered on different atomic layers; the piecewise constant thick lines (blue on line) indicate the expected electric fields $E$ between the atomic layers; and the cusped lines (red on line) indicate the expected electric potential $-V\left(z\right)$ distribution. The signs $+$ and $-$ stand for the direction of electric field $E$, the value for $\rho$, and the potential $-V\left(z\right)$.

Figure 2

(Color online) Half of the inversion symmetric unit cell. The quantum well consists of two layers of BaO and a monolayer of ${\text{VO}}_2$ and is embedded in bulk ${\text{LaTiO}}_3$. The light-orange shadowed region indicating the narrow active region in which the electronic interface reconstruction (EIR) driven by the polar discontinuity takes place. Oxygen atoms are located at the intersections of the checkered lines and form octahedra around the Ti and V atoms. The numbers specify labels for different layers. The downward arrow indicates the location of the ${\text{VO}}_2$ inversion plane.

Figure 3

(Color online) Layer-resolved $d$-projected density of states (DOS) at Ti and V sites versus energy. The layer labeling is defined in Fig. 2.

Figure 4

(Color online) Spin and layer resolved densities of states versus energy. The labels on top are layer labels as in Fig. 2. Since we allow $G$-type antifferomagnetic (AFM) order in the barrier material, there are two distinct transition-metal atoms in each layer. The DOS for majority spins and minority spins are represented by red and blue lines, respectively, and the Fermi level is marked with a horizontal dark line at $E=E_F$.

Figure 5

(Color online) Spin-resolved band structure at the Brillouin zone. The horizontal axis represents superlattice crystal momentum. The red solid lines represents the majority-spin bands, and the blue ones are the minority-spin bands. The momentum dependence along the layer direction $k_z$ is indicated in the region between the $\Gamma$ and $Z$ points. The full circle marks the $d^1$ bands for Ti atoms in LTO bulk states. The dashed circles represents the $d$ bands for V atoms in ${\text{VO}}_2$. The bands associated with EIR are flat along $k_z$ demonstrating their quasi-two-dimensional character. The shadowed blue square represents the projection of the superlattice Brillouin zone in the plane of the quantum well.

Figure 6

(Color online) Plane-averaged Hartree potential along the layer-growth direction $z$. The blue curve represents the Hartree potential experienced by electrons $-\text{eV}\left(z\right)$. The dashed line indicates the net potential variation between charge-concentration centers in each layer.

Figure 7

(Color online) Linear electron number density $\lambda \left(z\right)$ along layer-growth direction $z$. The dashed lines represent the boundaries used for the partitioning of density into contributions from different layers. The total number of electrons in each layer contributed by the $d$-character bands in Fig. 5 is indicated by the numerical values between dashed lines. In this case, the total number of electrons in the supercell is seven.

Figure 8

(Color online) Layer-resolved $d$-projected density of states at Ti and V sites versus energy.

Figure 9

(Color online) Spin and layer resolved densities of states versus energy. The labels on top are the layer labels indicated in Fig. 2. Since we allow $G$-type AFM order in the barrier material, there are two distinct transition-metal ions in each layer. The DOS for majority spins and minority spins are represented by red and blue lines, respectively.

Figure 10

(Color online) Spin-resolved band structure. The horizontal axis represents superlattice crystal momentum. The red solid lines represent the majority-spin bands, while the blue lines represent minority-spin bands. The momentum dependence along the layer direction $k_z$ is captured in the region between the $\Gamma$ and $Z$ points. The three partially occupied bands associated with EIR are flat along $k_z$, demonstrating their quasi-two-dimensional character.

Figure 11

(Color online) Plane-averaged Hartree potential along the layer-growth direction $z$. The solid dashed line indicates the net potential variation between charge-concentrated centers at each layer.

Figure 12

(Color online) Linear electron number density $\lambda \left(z\right)$ along layer-growth direction $z$. The dashed lines represent the boundaries between different layers used in constructing the layer decomposition of this charge density. The numerical numbers between dashed lines in each layers are the total number of electrons from $d$-derivative bands in Fig. 10. In this case, the total number of electrons is nine.