Fig. 2: Schematic of the interfacial electric field.

a Sketch of a SrTiO₃-based heterostructure and the gating between the grounded two-dimensional electron gas (2DEG) and a backside contact. White lines show the antiferrodistortive (AFD) domain boundaries that develop below the AFD transition at T* ≈ 105 K. b Magnified view of the interfacial region at 0 V with the 2DEG (purple shading) and positively charged oxygen vacancies (blue dots) that accumulate near the interface but are still randomly distributed. c At positive gate bias (+V), the positively charged oxygen vacancies migrate toward the interface and cluster at the AFD domain boundaries. Concurrently, the 2DEG expands and some of the electrons get trapped by the oxygen vacancies which become charge neutral (gray dots). The induced polarization (magenta arrows) is perpendicular to the interface. d At negative backgate voltage (−V), the 2DEG is more strongly confined to the interface and the electrons get detrapped from the oxygen vacancies which thus regain a positive charge. The local fields have now a strong horizontal component.