Hole distribution and self-doping enhanced electronic correlation in hole-doped infinite-layer nickelates

Gang Li; Guang-Ming Zhang; Hongbin Qu

REVIEW 4 major objections 5 minor 61 references

Hole distribution and self-doping enhanced electronic correlation in hole-doped infinite-layer nickelates

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Doped holes in infinite-layer nickelates split evenly between Ni-d and interstitial-s orbitals, and the interstitial-s orbital deepens Ni correlation by self-doping.

desk verdict A solid DFT+DMFT study of hole distribution in infinite-layer nickelates, but the headline equal-split claim is under-quantified and the self-doping shift is a 0.10-electron difference that needs a gauge-sensitivity check. read the letter →

arxiv 2507.10364 v1 pith:H4AW6RIK submitted 2025-07-14 cond-mat.str-el cond-mat.supr-con

Hongbin Qu , Guang-Ming Zhang , Gang Li This is my paper · ORCID

classification cond-mat.str-elcond-mat.supr-con

keywords infinite-layernickelatesLa1-xSrxNiO2interstitial-sorbitalself-dopingorbital-selectiverenormalizationDFT+DMFTholedistributionsingle-bandmodel

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Where do doped holes actually go in the infinite-layer nickelate superconductor $\mathrm{La}_{1-x}\mathrm{Sr}_x\mathrm{NiO}_2$? The paper argues that they do not follow the rigid-band intuition of a cuprate: at $x=0.1$ and $0.2$, the holes are shared almost equally between the Ni-$3d_{x^2-y^2}$ orbital and the interstitial-$s$ orbital, a state located between Ni atoms. The interstitial-$s$ orbital then acts as a charge donor, feeding electrons back into Ni-$3d_{x^2-y^2}$ and pushing it closer to half-filling. That self-doping, rather than simple screening, is what strengthens the electronic correlation of the Ni-$3d_{x^2-y^2}$ band and produces the band-selective renormalization seen in ARPES. The practical upshot is that a single-band model with the right electron occupancy captures the low-energy physics, settling part of the debate over the minimal model for nickelates.

What carries the argument

The load-bearing object is the interstitial-$s$ orbital, an itinerant state centered between Ni atoms that remains metallic and nearly uncorrelated, together with the self-doping mechanism it enables. The paper's evidentiary device is a three-way comparison of hole distribution: a rigid shift of the chemical potential, an explicit supercell with one Sr substitution, and a virtual-crystal calculation downfolded to a six-band model. The first scheme puts most holes on Ni-$3d_{x^2-y^2}$; the second and third put nearly equal holes on Ni-$3d_{x^2-y^2}$ and interstitial-$s$. The mechanism is isolated in the two-band model: switching off hybridization between Ni-$3d_{x^2-y^2}$ and interstitial-$s$ lowers the Ni orbital occupancy and weakens its renormalization, and manually restoring the occupancy brings back the ARPES-like spectra. This sequence shows that the interstitial-$s$ orbital acts primarily as a charge donor rather than a screening band.

What would settle it

Recompute the orbital-resolved hole counts at $x=0.2$ while varying the orbital-downfolding windows and integration radii used to assign charge to interstitial-$s$; if a reasonable projection places substantially more holes on Ni-$3d_{x^2-y^2}$ than on interstitial-$s$, the equal-distribution and self-doping claim fails. A complementary experimental check would be orbital-resolved spectroscopy, such as O-$K$ and Ni-$L$ edge absorption on the same crystals, to see whether the inferred per-orbital hole counts match the downfolded numbers.

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Extended reading notes

Core claim

On its own terms, the paper establishes that in $\mathrm{La}_{1-x}\mathrm{Sr}_x\mathrm{NiO}_2$ the doped holes are distributed almost evenly between Ni-$3d_{x^2-y^2}$ and interstitial-$s$ orbitals, not preferentially into Ni as a rigid-band shift would predict. The interstitial-$s$ orbital is therefore not a passive spectator: it donates charge into Ni-$3d_{x^2-y^2}$, raising that orbital's electron occupancy from 0.65 toward 0.75 and thereby enhancing the correlation strength felt by the $d$ electrons. Both a six-band model with Ni-$3d$ plus interstitial-$s$ orbitals and a minimal two-band model with only Ni-$3d_{x^2-y^2}$ plus interstitial-$s$ reproduce the experimentally observed band-selective renormalization, with strong mass enhancement on Ni-$3d_{x^2-y^2}$ and no renormalization on interstitial-$s$. The conclusion is that a single-band model works for the low-energy correlated electronic structure, provided the electron occupancy is fixed by including the self-doping effect.

Load-bearing premise

The equal-sharing and self-doping conclusions depend entirely on how missing charge is assigned to Ni-$3d_{x^2-y^2}$ versus interstitial-$s$ in the downfolded and atomic-cell calculations, so a different partitioning could move holes between the two orbitals and weaken the central claim even if the overall electronic-structure calculation is sound.

Editorial extensions

If this is right

A single-band model with the self-doped electron occupancy reproduces the low-energy correlated spectra of $\mathrm{La}_{1-x}\mathrm{Sr}_x\mathrm{NiO}_2$, so single-band treatments remain viable for these nickelates.
The minimal low-energy model needs only Ni-$3d_{x^2-y^2}$ and interstitial-$s$; the other Ni-$3d$ orbitals and O-$p$ states are not required to explain the ARPES band renormalization.
The absence of renormalization on the interstitial-$s$ band does not mean it is irrelevant; it is the charge reservoir whose donation makes the Ni-$3d_{x^2-y^2}$ band more correlated.
Doping and correlation both reshape the Fermi surface, for instance by shrinking the $\beta$ pocket near $\Gamma$, which follows from the same self-doping charge transfer.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The authors do not tabulate how sensitive the equal-sharing ratio is to projection choices, so a controlled scan over orbital-downfolding windows and integration radii would tell whether the 50-50 split is robust or a projection artifact.
If the self-doping picture is correct, estimates of the effective interaction strength $U/t$ in doped nickelates should be revised relative to naive nominal-doping values, because the correlated orbital sits closer to half-filling than the nominal hole count suggests.
The same hole-partitioning analysis could be extended to Nd- and Pr-based infinite-layer nickelates and to electron-doped variants, where the interstitial-$s$ donor role may shift the effective correlation in the opposite direction.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Quick take: this is a decent DFT+DMFT paper that makes a specific claim about hole distribution in infinite-layer nickelates, but the headline number—equal holes in Ni-d_x2-y2 and interstitial-s—is not backed by a table of occupancies in the main text, and the self-doping shift that carries the argument is a 0.10-electron difference that could be sensitive to the Wannier projection. Worth a serious referee, but it needs revision, not acceptance as is.

What's new: the explicit doping-dependent hole distribution from VCA+supercell+MLWF, and the controlled comparison of two-band and six-band models against ARPES. The hybridization on/off test is a good idea: turning off s-d hybridization and then restoring the d occupancy by a chemical-potential shift isolates the self-doping mechanism. That's a clean controlled calculation. The conclusion that a single-band model works when the occupancy is correct is consistent with earlier work, and they cite it properly.

Soft spots, in order of seriousness. First, the equal-split claim is quantified graphically but never tabulated. Fig 2(c-e) shows bar charts or curves, but I can't read the actual occupancies, and there's no sensitivity analysis for the Wigner-Seitz integration radii or Wannier disentanglement. The stress-test worry is real for the absolute split. I'd be less worried about the 0.10-electron shift with hybridization on/off, because that's a differential within the same gauge, but the absolute equal split is exactly the kind of number that moves around with projection details. Second, the Hubbard U and J for the central spectra are not specified in the main text. Fig 3(g) lists a U sweep, but the DMFT spectra in Fig 2(f,g) don't state the U/J used. That's a reproducibility gap. Third, the paper has leftover Chinese annotations in the figures ('add a colorbar here', 'rerun g figure'). Presentation sloppiness that should be cleaned. Fourth, the single-band downfold is argued, not computed, but they do demonstrate two-band and six-band spectra match ARPES, so that's fair.

The citation pattern looks fine; the relevant self-doping and single-band literature is acknowledged. No circularity beyond the usual 'we interpret the occupancy shift as self-doping' which they then test with the chemical-potential restoration.

Bottom line: for a nickelate specialist, this is a useful contribution with a plausible mechanism. For a general condensed-matter reader, the missing numbers undermine the central claim. I'd send it back for a solid revision with a request for a table of occupancies, a gauge-sensitivity check, and the U/J values. That's the difference between 'conditional' and 'accept'.

Referee Report

4 major / 5 minor

Summary. This paper combines density-functional theory with dynamical mean-field theory (DFT+DMFT), using the virtual crystal approximation (VCA) for alloying, to study La1-xSrxNiO2 at x=0, 0.1, and 0.2. Its central claim is that doped holes are distributed nearly equally between the Ni-3d_x2-y2 orbital and the interstitial-s orbital, rather than following a rigid-band shift. The paper further argues that the interstitial-s orbital acts as a charge donator: it self-dopes Ni-3d_x2-y2 toward half-filling, thereby enhancing the orbital-selective renormalization observed in ARPES. Both a six-band model (Ni-3d + interstitial-s) and a two-band model (d_x2-y2 + interstitial-s) are reported to reproduce the band-selective renormalization, and the authors conclude that a single-band model with the correct Ni occupancy captures the low-energy physics.

Significance. If correct, the equal-split and self-doping scenario would materially advance the debate over the minimal model for infinite-layer nickelates: it would explain the ARPES orbital-selective renormalization, identify the microscopic role of the interstitial-s orbital, and support a single-band description with renormalized occupancy. The manuscript's strengths are its standard DFT+DMFT methodology, a VCA/supercell cross-check, controlled comparisons (hybridization on/off and chemical-potential restoration), and direct ARPES comparison without parameter fitting. The principal weakness is that the quantitative foundation of the equal-split claim, namely the orbital-resolved occupancies, is not displayed in the main text and is not tested for its sensitivity to the Wannier/projection gauge.

major comments (4)

[Results, Fig. 2(c–e)] The headline claim that holes are 'nearly equally' distributed between Ni-3d_x2-y2 and interstitial-s is not supported by any numeric table of occupancies in the main text. Figure 2(c–e) are color-scale charge-density-change plots without explicit axis values, and the text refers to Supplementary Information for the additional redistribution in the two-band model. Since the equal split is the load-bearing premise for the self-doping mechanism and the single-band conclusion, please report the actual occupancy numbers for x=0.1 and x=0.2 in all three schemes (rigid shift, supercell, VCA+MLWF), together with the precise definition of each orbital occupancy.
[Results, Fig. 2(e) and Fig. 3(b–g)] The interstitial-s occupancy is obtained from Wannier downfolding and from the missing charge in Wigner–Seitz cells; both estimates are gauge-dependent. The manuscript does not test how the occupancy difference 0.75→0.65, which is the entire basis for the 'charge donator' language, changes with Wannier spread, disentanglement window, or integration radius. Because a projection-gauge change can move a comparable amount of charge between d and s without altering the physical spectrum, the self-doping conclusion is not yet quantitatively robust. Please add a sensitivity analysis or a gauge-invariant measure (for example, the integrated d_x2-y2 spectral weight in a fixed energy window).
[Results, second scheme around Fig. 2(d)] A 2×5×2 supercell with a single Sr substitution contains 20 La sites and thus corresponds to x=0.05, not the x=0.2 discussed in the section. If the supercell is meant to realize La0.8Sr0.2NiO2, four Sr substitutions are required (or the cell size is misstated); if 5% doping was actually used, it cannot calibrate the x=0.2 equal-split claim. Please clarify or correct this mismatch.
[Fig. 3(a–g)] The identification of the self-doping effect relies on comparing occupancies in the hybridized and non-hybridized two-band models, but turning off the hybridization also changes the Wannier orbital basis, so a 0.10-electron occupancy shift is not by itself a physical observable. The chemical-potential-shift control is a useful check, but the shift is an additional free parameter, and the occupancy values are not directly measurable. Please report the quasiparticle weight Z and the occupancy for the hybridized, non-hybridized, and chemical-potential-restored models in a table, and demonstrate that the 0.65/0.75 values are stable under different localization choices.

minor comments (5)

[Fig. 2(a) and Fig. 3(g)] The figures contain unfinished Chinese editing notes ('还得在这加个colorbar...' and '在这重新跑一下g图'), and the color bar for Fig. 2(a) is missing; these artifacts must be removed before publication.
[Throughout] There are numerous typographical errors, including 'similiarity', 'predication', 'syetem', 'shits up', 'selfly-doped', 'nickletes', 'supercondutors', and 'AREPS' in the Fig. 2 caption; a thorough proofread is needed.
[Fig. 2(c–e) caption] The caption states 'Change density change estimated from (a) a rigid-band shift' but should refer to panel (c); please correct the cross-reference.
[Abstract and Results] The abstract claims hole distribution 'at various doping levels', but the detailed hole-distribution analysis shown in the main text is for x=0.2 only; please either show the x=0.1 results or qualify the claim.
[References] Some references (e.g., Refs. [56] and [63]) are arXiv preprints; if published versions now exist, they should be cited.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central claims are tested by controlled model comparisons and benchmarked against external ARPES data.

full rationale

The paper's central claims—equal hole distribution between Ni-3d_x2-y2 and interstitial-s, and self-doping enhanced correlation—are derived from DFT+DMFT calculations that are not fitted to the conclusions. The Hubbard U is taken from the literature, the ARPES spectra are used as external comparisons, and no parameter is defined in terms of the target prediction. The key controlled test in Fig. 3 turns off the d-s hybridization, observes that the Ni-d occupancy drops from 0.75 to 0.65 and that the renormalization weakens, then restores the occupancy to 0.75 by a chemical-potential shift and recovers the ARPES-consistent renormalization. This is an explicit mechanism test, not a circular construction. The equal-hole-distribution result is supported by three independent schemes (rigid-band shift, supercell charge difference, and VCA+MLWF downfolding), and the paper explicitly notes that the rigid-band expectation differs, showing that the result is not assumed from the outset. The interstitial-s occupancy is Wannier-gauge-dependent and the paper does not tabulate its sensitivity, but that is a robustness or correctness concern, not circularity, because no reduction of a prediction to its own inputs by definition or fitting can be exhibited. The self-citations (e.g., Refs. [48,51]) provide context for the single-band discussion but are not the load-bearing justification for the new quantitative claims, which rest on the calculations reported here. Therefore the honest finding is no significant circularity.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central calculations are standard DFT+DMFT, which is a domain assumption, but the quantitative hole distribution relies on a projection scheme for defining orbital occupancies, and the single-band conclusion is imported from previously published work. No fundamentally new entities or forces are introduced.

free parameters (4)

Hubbard U on Ni-3d = not stated for main spectra; Fig. 3 uses U=1.0, 3.2, 3.9, 4.3, 5.0 eV
The DMFT spectral functions in Fig. 2(f,g) depend on U but the exact value used is not reported in the main text.
Hund coupling J on Ni-3d = not stated
Multi-orbital DMFT requires a Hund coupling; its value is not given, affecting the correlation strength and orbital-selective renormalization.
Chemical potential shift in non-hybridized 2-band model = chosen to restore Ni-3d_x2-y2 occupancy to 0.75
In Fig. 3(d) the authors manually shift mu to restore occupancy 0.75; this is a control parameter rather than a fit to data.
Double-counting correction = not stated
DFT+DMFT requires a double-counting scheme (e.g., fully localized limit); the choice is not described, and it affects orbital occupancies.

assumptions (5)

domain assumption DFT+DMFT is an adequate framework for the low-energy electronic structure of infinite-layer nickelates.
The entire analysis uses DFT+DMFT with a local self-energy; the paper does not benchmark against exact methods or compare different impurity solvers.
domain assumption Virtual crystal approximation (VCA) correctly captures the effect of Sr substitution at x=0.1 and 0.2.
VCA replaces the alloy by a virtual atom; the authors verify against a 2x5x2 supercell for x=0.2, but only for band structure, not for the orbital-resolved hole counts.
domain assumption The Wannier downfolding to 6-band and 2-band models preserves the low-energy physics relevant for the d_x2-y2 and interstitial-s bands.
The paper argues other Ni-d, La-5d, and O-p orbitals contribute little, but the downfolding itself can shift occupancy; the 6-band model already redistributes holes relative to the supercell.
domain assumption Orbital-resolved occupancies can be meaningfully defined by Wigner-Seitz integration and Wannier projection.
The equal-hole-distribution claim depends on this partitioning, which is not unique.
domain assumption Prior single-band and self-doping results in refs. [40,46,52,61,62] and [48] are correct and can be used to support the conclusion.
The conclusion that a single-band model works with correct occupancy is not derived here; it is imported from cited literature.

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Cite this review

Pith. "Pith review of Hole distribution and self-doping enhanced electronic correlation in hole-doped infinite-layer nickelates." pith.science (2026). https://pith.science/paper/H4AW6RIK

@misc{pith2026250710364,
  author       = {Pith},
  title        = {Pith review of: Hole distribution and self-doping enhanced electronic correlation in hole-doped infinite-layer nickelates},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/H4AW6RIK}},
  note         = {Machine review of arXiv:2507.10364}
}

abstract

The minimal model for infinite-layer nickelates remains under debate, particularly regarding the hybridization between itinerant interstitial-$s$ and the correlated Ni-3$d_{x^2-y^2}$ orbitals, as well as the interaction between $d_{x^2-y^2}$ and other $3d$ orbitals. Additionally, how the doped holes in La$_{1-x}$Sr$_x$NiO$_2$ are distributed among different orbitals remain unresolved. Motivated by recent angle resolved photoemission spectroscopy (ARPES) experiments, we theoretically study the electronic structure of infinite-layer La$_{1-x}$Sr$_x$NiO$_2$ at various doping levels. We find that, unlike the expectation from a rigid band shift, holes are equally distributed to Ni-3$d_{x^2-y^2}$ and interstitial-$s$ orbitals. The role of interstitial-$s$ orbital is further confirmed from the renormalization of Ni-3$d_{x^2-y^2}$ band, for which the coupling between interstitial-$s$ and Ni-3$d_{x^2-y^2}$ exerts a non-negligible impact on the orbital-selective renormalization observed in ARPES. We also discuss the implication of our results to the single-band model, where the interstitial-$s$ orbital in the normal state of La$_{1-x}$Sr$_x$NiO$_2$ acts as charge donator enhancing the correlation of Ni-3$d_{x^2-y^2}$ by increasing its concentration close to half-filling.

Figures

Figures reproduced from arXiv: 2507.10364 by the authors.

**Figure 2.** (e), the main feature of the hole doping observed in supercell calculations is captured by this model, including the slight electron-doping in 𝑑𝑧 2 orbital, and the similar doping levels in Ni-3𝑑𝑥 2−𝑦 2 and interstitial-𝑠 orbitals. The Ni-3𝑑𝑥 2−𝑦 2 and interstitial-𝑠 orbitals share the majority of holes. However, compared to [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** (a) the electronic structure of the 2-band model without hybridization between Ni-3𝑑𝑥 2−𝑦 2 and interstitial-𝑠 orbitals. While the lack of hybridization does not significantly modify the band structure, the renormalization of Ni-3𝑑𝑥 2−𝑦 2 orbitals becomes less pronounced. As evident in [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

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