## 3 Results and Discussions
For building the surface slab, surface energy convergence was tested against the surface slab thickness to ensure bulk-like behavior for the substrate. To mimic the atomic stacking of the experimental image of Figure 2b, at first, a two-layer surface slabs were built by seven layers (2 \(\times\) 2) LAO (001) and five layers of (1 \(\times\) 1) Ti\({}_{2}\)AlO\({}_{4}\) (110) with two types of LAO surface terminations: AlO\({}_{2}\) and LaO termination. For building this heterostructure, (1 \(\times\) 1) Ti\({}_{2}\)AlO\({}_{4}\) (110) was strained to twice the substrate lattice parameter of a = b = 7.55 A. In Figure 3, two types of substrate termination models for the unrelaxed configurations are shown for Ti\({}_{2}\)AlO\({}_{4}\) (110) on LAO (001). Among these two models, the most favorable termination is found to be AlO\({}_{2}\) by calculating the interface formation energy [32], although the formation energies of the two types of terminations are almost identical. By visual cues from the HAADF contrast of Figure 2b, it was confirmed that the termination is indeed AlO\({}_{2}\) termination. Based on these optimized bilayer models, a tri-layer supercell was then created to match experimental observation (Figure 4) by stitching pure anatase (without oxygen vacancies) TiO\({}_{2}\) and O-deficient anatase TiO\({}_{2}\) to one monolayer of (1 \(\times\) 1) Ti\({}_{2}\)AlO\({}_{4}\) (110) on AlO\({}_{2}\)-terminated LAO (stackings are described from the top of Figure 4). The model configurations were built along the [001] direction with seven atomic layers of LAO, one monolayer of Ti\({}_{2}\)AlO\({}_{4}\), and nine layers of anatase TiO\({}_{2}\). These layer thicknesses were sufficient to represent the bulklike properties. The DFT-relaxed interfaces of Ti\({}_{2}\)AlO\({}_{4}\)/pure-TiO\({}_{2}\) and Ti\({}_{2}\)AlO\({}_{4}\)/O-deficient-TiO\({}_{2}\) are shown in Figure 4a,b, respectively. The red arrows in Figure 4a,b show the force vectors due to DFT relaxation. The positions of random oxygen vacancies within the O-deficient TiO\({}_{2}\) structure are shown with magenta arrows in Figure 4c. By comparing Figure 4a,b, it is observed that the creation of the O-vacancy affects the interface rearrangement differently. The different directions of force vectors acting at the alloy layer give rise to different equilibrium distances in the interface region. The equilibrium interface layer spacings between extra-layer Ti\({}_{2}\)AlO\({}_{4}\) and TiO\({}_{2}\) are 3.1 A and 2.1 A for the configurations in Figure 4a,b, respectively. To check the structural stability of such a heterostructure, we further calculated the interface adhesion energy [32], which  
Figure 3: (**a**) A schematic of the unrelaxed AlO\({}_{2}\) terminated-LaAlO\({}_{3}\) (001)/Ti\({}_{2}\)AlO\({}_{4}\) (110) is shown; (**b**) schematic of the unrelaxed LaO terminated-LaAlO\({}_{3}\) (001)/Ti\({}_{2}\)AlO\({}_{4}\) (110). The legends for the atom types are given in the inset. confirms that the heterostructure model of Figure 4b is dynamically more stable than the pure anatase model (Figure 4a). In addition, the force acting on atoms (red arrows) presented in Figure 4b shows that the region near the interface (marked with the magenta-colored dashed box) favors bonding with O-deficient TiO\({}_{2}\). In order to compare the interface models with the experimental evidences, STEM-HAADF simulations were performed for both these (Figure 4) geometry-optimized structures using QSTEM software [26]. The optimized coordinates were repeated along the electron-beam direction to create a model thickness of 19 nm, consistent with previously calculated model thickness [17]. The simulated STEM-HAADF images of AlO\({}_{2}\)-terminated LaAlO\({}_{3}\)/Ti\({}_{2}\)AlO\({}_{4}\)/pure-TiO\({}_{2}\) and LaAlO\({}_{3}\)/Ti\({}_{2}\)AlO\({}_{4}\)/O-deficient-TiO\({}_{2}\) are shown in Figure 5a,b, respectively.