Fig. 1: Tetragonal domains in STO and electronic structure of GAO/STO heterostructures.

a A schematic showing structural twin domains of STO below 105 K. Three types of domains with c axis along [100], [010], and [001] have been marked with X (blue), Y (purple), and Z (red) respectively^16,39. b Schematic to depict coexistence of strain field (ϵ) and polarization (P) within the domain wall. For the sake of simplicity, we have only shown the component which is perpendicular to the domain wall. A spontaneous strain field arises due to inherent ferroelasticity, which also varies in sign across the domain wall⁵⁵. Further, the maximum value of polarization appears at the domain wall. Within a domain wall, both polarization and strain field are coupled. Additionally, one domain wall can also interact with the neighboring one via either dipole-dipole interaction or through coupled strain fields^24,25. c Temperature-dependent sheet resistance (R_S) in the cooling cycle (ramp rate = 3 K/min) for GAO/STO heterostructures with different thicknesses, demonstrating a metal-to-insulator transition with lowering the film thickness. Inset shows the hysteresis in R_S vs. T plot between heating and cooling run for the 15 uc GAO/STO sample. The hysteresis for other metallic samples have been shown in Supplementary Fig. S4. d Measured Ti 2p core level spectrum of a metallic GAO/STO sample using HAXPES. Fitting of the spectra reveals the presence of Ti³⁺ and Ti²⁺ in the sample, in addition to Ti⁴⁺. A charge transfer shake-up satellite peak⁷⁰ was also included in the fitting. e Residual of the fitting, testifying the excellent matching with the measured spectrum.