Figure 1: Quantitative analysis of polar catastrophe and cation intermixing in LAO/STO at atomic scale.

(a) The summed HAADF image over three individual ones (bright, cations) and a chemical map (red, Sr; green, Ti; blue, La) in 10-uc LAO/STO. Scale bar, 1 nm. (b) The HAADF blowup of a (white and red, cations), showing the Al-site displacement towards the interface (guiding white circles) and c-elongated STO (guiding white rectangles). (c) The AO- and BO₂-plane cation distributions, omitting the ±10% error bars for clarity of the figure presentation. The error bars on the surface LAO uc in 3-uc LAO/STO are larger, ±20%, as a result of the beam sensitivity of this uc and are particularly denoted. The SXRD results in refs 10, 16 are incorporated for comparison, while omitting the associated error bars also for clarity. The diffusive cation distribution in all these heterostructures indicates ubiquitous intermixing. (d) The STEM–EELS probing of the Ti³⁺ fraction (error bars, ±10%). (e) The uc-by-uc charge distributions derived from c and d, showing 2DEG in the STO and holes in the LAO of conductive heterostructures. Error bars, ±10% as deduced from c and d except for the larger error of ±20% in the surface uc of 3-uc LAO/STO due to the associated beam sensitivity. (f) The plane-specific charges in the polar-catastrophe context (grey) and in the 10-uc experiment (black) considering the uc charges in e. (g) The plane-by-plane potential variations in the polar-catastrophe model (grey) and on the presence of interfacial charges in e. The insulating 3-uc LAO/STO is free from charge at the interface, thus not shown. (h) The counterpart to g considering cation intermixing in c only without net interfacial charge (that is, charge-neutral uc). Cation intermixing grades the diverging polar-catastrophe potential and the associated interfacial-metallicity onset at 4-uc LAO is no longer satisfied.