Extended Data Fig. 1: Analytical mapping of Ruddlesden–Popper faults.

a, Raw HAADF-STEM image of the Nd_0.85Sr_0.15NiO₂ film on SrTiO₃ substrate shown in Fig. 1a (left) and a magnified view of the region marked by the red dashed box (right). For the magnified view, atomic overlays are shown to illustrate the half-unit-cell displacement induced by the Ruddlesden-Popper-type stacking faults (RP faults), resulting in the reduced cation contrast. b, Composite of the compressive strain measured on the [101] and [\(\bar{1}\)01] pseudocubic lattice fringes for the HAADF-STEM image in a. The infinite-layer film appears as a region of large compressive strain compared to the substrate because of the shortened c-axis lattice constant. Ruddlesden–Popper type faults in the film are highlighted as regions of local expansion (bright lines) within the film. The highlighted boundaries are used to annotate the vertical Ruddlesden–Popper regions, shown as black (yellow) boxes here (in Fig. 1a). c, Identical strain mapping of the [101] and [\(\bar{1}\)01] pseudocubic lattice fringes for the HAADF-STEM image of the Nd_0.85Sr_0.15NiO₂ film on LSAT substrate (Fig. 1b). The circles in b and c illustrate the coarsening length scale of the Fourier-based analysis. Scale bars, 5 nm.