Visualization of Oxygen Vacancies and Self-doped Ligand Holes in La3Ni2O7-δ

The authors claim that "MEP stands out as a tool capable of determining the nanoscale stoichiometry of crystals, but such an application has not been realized in experiments so far." While the demonstration of MEP for vacancy quantification is compelling, the manuscript should address the stability of these vacancies under the electron beam. Given that La3Ni2O7-δ is sensitive to oxygen loss, please clarify if the observed vacancy distribution is intrinsic or potentially exacerbated by the high-dose 4D-STEM acquisition. A comparison of images taken at different dose rates or total fluences would significantly strengthen the claim that the observed inhomogeneity is an intrinsic property of the crystal.

Regarding the EELS analysis, the authors state that "the 528-eV peak is directly correlated to the concentration of inner apical oxygen vacancies." While the data in Figure 3a clearly show a reduction in the pre-edge peak intensity with increasing δ, the manuscript should explicitly discuss why the planar oxygen contribution to the pre-edge feature remains relatively stable despite the observed inhomogeneity. Please provide a more quantitative breakdown of the EELS spectral weight transfer to ensure that the disappearance of the peak is solely due to the filling of the O-2p band and not influenced by local changes in Ni-O hybridization or potential beam-induced reduction of the nickel valence state.

The authors state that 'the outer apical oxygen is found to be less relevant to the low-energy physics and can be safely disregarded in theoretical models.' This is a significant claim that warrants more careful justification. While the EELS data in Figure 4a and the corresponding DFT PDOS in Figure 4b show a reduced contribution from the outer apical oxygen near the Fermi energy, 'less relevant' is not synonymous with 'negligible.' The authors should clarify whether this conclusion is based solely on the density of states or if they have performed any calculations to show that removing this site does not qualitatively alter the low-energy band structure or the superconducting pairing symmetry.

Regarding the inhomogeneity, the authors note that 'the oxygen vacancies predominantly occupy the inner apical site' and that 'the oxygen content and electronic structure within the sample' are inhomogeneous. It would be beneficial to discuss the potential origin of this inhomogeneity. Is it intrinsic to the crystal growth process, or is it a result of beam damage during the STEM/EELS acquisition? Given the high-energy electron beam used for ptychography, the authors must explicitly address whether the observed vacancy distribution is representative of the bulk material or if there is any evidence of beam-induced oxygen migration, especially given the known sensitivity of nickelates to oxygen loss.

To make this work reproducible by an independent laboratory, the authors must provide a comprehensive Methods section. Currently, there is no description of the experimental setup, including the accelerating voltage, probe convergence semi-angle, probe current, step size (pixel dwell time and scan step), camera length, and the specific energy-filter slit width used for the K3 camera. Furthermore, the reconstruction algorithm for the multislice electron ptychography (MEP) must be fully documented, including the number of slices, slice thickness, starting guess, feedback parameters, number of iterations, and how aberrations (such as defocus, astigmatism, and tilt) were corrected during the reconstruction. For the DFT calculations, the authors must specify the exact parameters used in WIEN2k: the muffin-tin radii, the plane-wave cutoff, the k-point mesh, and crucially, whether a Hubbard U correction was applied to the Ni 3d states (and if so, what values of U and J were used). Without these details, the results cannot be verified or reproduced.

At an accelerating voltage typically used for such studies (e.g., 80–200 kV), the spatial delocalization of inelastic scattering for the O K-edge (~530 eV) is on the order of 1–2 Å. Given that the projected distance between the inner apical oxygen, planar oxygen, and outer apical oxygen columns along the [110] projection is extremely small (often less than 2 Å), there will be substantial spatial crosstalk between the EELS signals from adjacent columns. The authors do not address how this delocalization affects their 'site-selective' spectra in Figure 4a. To ensure the validity and reproducibility of these site-specific electronic structures, the authors must perform inelastic scattering simulations (e.g., using the PRISM algorithm or multislice inelastic scattering simulations) to quantify the extent of signal mixing between the different oxygen sites and demonstrate that the pre-edge features are indeed site-specific rather than artifacts of spatial delocalization.

The phase normalization scheme ('The average phase for the outer apical oxygens is normalized to one') implicitly assumes that the outer apical oxygen site is fully occupied (delta = 0) in all analyzed regions. If the outer apical site itself contains any vacancies, this normalization will systematically bias the calculated vacancy concentration of the inner apical site. The authors must provide a rigorous justification for this assumption. Furthermore, in Figure S10, the authors estimate the phase uncertainty to be around 6% based on the statistics of the heavy La and Ni atoms ('The estimated uncertainty in phase is around 6%'). However, because oxygen is a much lighter element, its phase signal is significantly weaker, and its signal-to-noise ratio is much lower. Therefore, the relative uncertainty for the oxygen phase must be substantially larger than that of La or Ni. The authors must perform a proper error propagation analysis that accounts for the lower scattering cross-section of oxygen to provide realistic error bars for the local vacancy concentrations.