Quantum confinement of the strongly correlated d-orbital electrons at complex oxide interfaces establishes an intricate orbital hierarchy, which is widely recognized as a source of emergent physics (1, 2). The most prominent example is the 2DEG induced at LAO/STO interfaces, which displays a wide range of quantum phenomena, including metal-insulator transition (3), ferromagnetism, and superconductivity (4, 5). Recent studies have shown that changing the interface orientation can modify the Ti-3d orbital hierarchy, selective occupancy, and spatial confinement of 2DEG (6). The LAO/STO (111) interface, in particular, presents an interesting playground for exploring the emergent physics of 2DEG (6–9), because its buckled honeycomb (111) lattice can induce exotic topological states (10–13) and strong magnetic reconstructions (14–16) owing to a reduced interlayer distance and strong octahedral coupling compared with that of the (001) interface. Because the crystal field adopts trigonal symmetry and the t2g states are mixed within this symmetry, the three usual orbitals transform into a1g and eg′ subbands, each with a balanced contribution from dxy, dyz, and dxz (11, 14, 17).
Another intriguing modification made by changing the interface orientation is the structural distortions of the LAO/STO heterostructure, especially AFD tilts of the AlO6 octahedron. While STO adopts an undistorted cubic phase (space group, Pm3¯m), LAO is stabilized in a rhombohedral phase (R3¯c) at room temperature with AFD tilts of the AlO6 octahedron around the pseudocubic  axis ϕabc (Fig. 1A), which corresponds to an a−a−a−-type tilt according to the Glazer notation (hereinafter, the Miller indices of LAO are indexed based on the pseudocubic crystal system). In LAO/STO (001) heterostructures, the AFD tilt pattern of LAO is expected to evolve differently from the a−a−a− pattern owing to the influence of the (tensile) epitaxial strain arising from lattice mismatch and the internal polar field arising from the polarity mismatch with the STO (18). For example, DFT calculation predicts that the tensile misfit strain acting on LAO (e.g., +2.97% in LAO/STO) stabilizes the LAO into a different phase (Imma) instead of R3¯c, which is composed of ϕab rotations (a−a−c0) with the rotation axis along the in-plane  direction (19) (see Fig. 1B). However, the AFD rotation in LAO/STO heterostructures is governed more strongly by the internal polar field; an uncompensated internal polar field within the LAO film has been shown to suppress the AFD rotation in favor of FE (polar displacement of cation and anion sublattices against one another) distortion that produces a depolarization field that compensates for the polar field (Fig. 1, B and C) (20–22). The AFD rotation evolves in the LAO/STO heterostructure only when the polar field is compensated by the formation of 2DEG above the tc (18). As such, the structural evolution of LAO/STO (001) heterostructures goes in line with the general notion that the nonpolar AFD rotation and polar FE distortion tend to compete and suppress each other in ABO3 perovskite oxides (23–26).
The FE distortion and AFD rotation evolve in a different way in the LAO/STO (111) heterostructure compared to those in the (001) counterpart. In the LAO/STO (111) heterostructure, the  rotation axis is perpendicular to the strain plane [see Fig. 1 (A and D)]. While the (001) tensile strain favors the Imma phase of LAO (19), the (111) tensile strain prefers to stabilize the out-of-plane  rotations and preserve the bulk R3¯c symmetry (27). According to the recent DFT calculations by Gu et al. (28), for perovskite oxides with a large AFD rotation angle and/or small A-site ions, the FE distortion can coexist with the AFD rotation in which A-site ions are pushed out from the strain plane to lower the repulsive interaction with neighboring oxygen ions and induce ionic polarization along the  direction (Fig. 1D). Hence, the (111) orientation of the LAO/STO heterostructure can render the cooperative evolution of AFD rotation and FE distortion, as opposed to the competitive evolution in the (001) orientation.
Given that the (competitive or cooperative) evolution of AFD rotation and FE distortion in (001) and (111) LAO/STO heterostructures is strongly influenced by the internal polar field, a question naturally arises on how this structural evolution is influenced by the formation of 2DEG. Among the various formation mechanisms (3, 29–38), the surface VO (32–34, 38) model has been receiving increasingly positive feedback as it is highly compatible with most of the experimental observations (6, 18, 39, 40). DFT calculations have shown that the formation energy of VO at the LAO surface decreases with increasing film thickness and becomes zero on reaching the tc for 2DEG formation (32–34, 37, 38, 41). VO can form spontaneously above tc and act as a donor providing electrons to the interface (32–34, 38). Moreover, VO in ABO3 perovskites is known to induce local distortion and/or rotations of BO6 octahedra (42, 43). Therefore, considering the electron donation capability and the local symmetry breaking, surface VO is expected to relieve the internal polar field and, at the…