Fig. 4

Modulation of electric polarization, charge distribution, and orbital symmetry. a Experimentally layer-resolved charge distribution of 10BTO/3STO/3LTO (red circles) and reference sample 25STO/3LTO (yellow triangles) measured by STEM/EELS. It is noted the yellow solid lines are guidelines for clarity. Here the error bar indicates the standard deviation between experimental and fitting spectra. Blue shadows (in a, b) indicate the anomalous charge distribution in BTO layers. b Calculated orbitally resolved charge distribution for each TiO₂ layer in 4BTO/3STO/2LTO. Red circles indicate total projected density of states, whereas blue triangles and light-blue rhombuses label the contribution from d_xz/d_yz and d_xy orbitals, respectively. c Illustration of coexisting electric polarization and two-dimensional electron gas with theoretically proposed in-plane d_xy state as the preferential occupation. The image is plotted based on experimental Ti–O polar displacements (Fig. 3d). White solid lines schematically indicate the positions of two-dimensional electron gases, whereas cyan arrows mark the direction switching of Ti–O displacements. The strength and direction of polarization are labeled by the color map from blue to yellow