## 3 Results and Discussions  
In Figure 1a, a representative cross-sectional bright-field TEM image of the TiO\({}_{2}\)/LAO heterostructure taken in the [010] zone axis of the substrate is shown. The TiO\({}_{2}\) film has a good crystalline quality and shows the typical modulated structure of the reduced anatase structure reported in earlier works [17; 27; 28]. The TiO\({}_{2}\)/LAO interfaces appear sharp and atomically flat. The corresponding selected area electron diffraction (SAED) pattern shown in Figure 1b indicates very good crystalline matching between the TiO\({}_{2}\) film and the LAO substrate with a TiO\({}_{2}\) (001)\(\parallel\) LAO (001) epitaxial relationship. To gain more insight into the atomic structure of the TiO\({}_{2}\)/LAO interface, we performed advanced STEM-HAADF experiments with a C\({}_{\rm s}\)-corrected microscope, since HAADF provides the atomic sites of heavy elements, which enable us to visualize oxide interfaces [29; 30; 31]. A representative STEM-HAADF image of the TiO\({}_{2}\)/LAO heterostructure is shown in Figure 2a. The predominant signal in the film comes from the typical dumbbell structure of TiO\({}_{2}\) anatase, while the signal of the substrate is dominated by the heaviest La ions (labels are superimposed to the image for ease of visualization). In Figure 2b, an enlarged view of the interface region is provided and marked with a cyan-colored dashed box. The atomic stacking in the vicinity of the interface is strikingly different from both the substrate and the film. This can be better appreciated from the magnified image of Figure 2b, where extra atoms (marked with white arrows) can be identified with a relative distance of half of the unit cell of anatase along the [100] direction. According to the general strategy reported in the literature [32], we evaluated the possibility of a TiO\({}_{2}\) on AlO\({}_{2}\)- and LaO-terminated LAO substrate to reproduce the interfacial structure of our experimental data. In both cases, we cannot reproduce the presence of extra spots that are clearly evident in our experimental data, as well as in the reported literature [33]. We, therefore, evaluated the possibility of other structural phases based on the element present at the film/substrate interface and spacings compatible with the experimental data. Among these, a good candidate is represented by Ti\({}_{2}\)AlO\({}_{4}\), which has lattice parameters of a = 5.66 A, b = 6.08 A, and c = 8.13 A for the conventional unit-cell belonging to the 'Imma' (74) [PERSON] space-group [34]. Moreover, since the 2 DEG is known to occur in O-deficient anatase [16], we performed DFT calculations starting from an O-deficient anatase structure and considering two different possible interfacial terminations of the LAO substrate, namely AlO\({}_{2}\) and LaO. All the parameters used for the calculation are provided in the materials and methods section. At first, to identify the interfacial termination of LAO substrate, the bulk unit cells of LAO and Ti\({}_{2}\)AlO\({}_{4}\) were relaxed using DFT as implemented in the Quantum Espresso  
Figure 1: (**a**) Cross-sectional TEM image of the TiO\({}_{2}\)/LAO interface. (**b**) The SAED patterns at the TiO\({}_{2}\)/LAO interface correspond to [010] zone-axis. Figure 2: (**a**) A cross-sectional STEM-HAADF image of the interface TiO\({}_{2}\)/LaAlO\({}_{3}\) viewed along the [010] direction. [PERSON], blue, and yellow solid circles indicate La, Al, and Ti columns, respectively. (**b**) The interface is marked by a dashed cyan-colored box pointed with cyan arrows. The white arrows point at the extra atoms at the first interfacial layer. software suite [24]. With the optimized coordinates, surface slabs were built along [001] and [110] for LAO and Ti\({}_{2}\)AlO\({}_{4}\), respectively. The lattice parameters for the (2 \(\times\) 2) LAO [001] surface slab were optimized to be a = b = 7.55 A and those for (1 \(\times\) 1) Ti\({}_{2}\)AlO\({}_{4}\) (110) were optimized to be a = 8.13 A and b = 8.31 A.