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Observation of Electride-like $s$ States Coexisting with Correlated $d$ Electrons in NdNiO$_2$

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Pith's one-line read The paper claims to resolve the orbital character of the electron pocket in NdNiO2: polarization- and resonance-dependent ARPES show it arises from interstitial s states, not rare-earth 5d or 4f orbitals, establishing electride-like…

desk verdict First ARPES identification of interstitial s pocket in NdNiO2; the s assignment is solid, but 'negligible Nd' is softer than the abstract claims. read the letter →

arxiv 2507.04378 v1 pith:AIIBRE6Y submitted 2025-07-06 cond-mat.supr-con cond-mat.mtrl-scicond-mat.str-el

Chihao Li , Yutong Chen , Xiang Ding , Yezhao Zhuang , Nan Guo , Zhihui Chen , Yu Fan , Jiahao Ye
show 8 more authors
Zhitong An Suppanut Sangphet Shenglin Tang Xiaoxiao Wang Hai Huang Haichao Xu Donglai Feng Rui Peng
This is my paper
classification cond-mat.supr-concond-mat.mtrl-scicond-mat.str-el
keywords infinite-layernickelatesNdNiO2angle-resolvedphotoemissionspectroscopyinterstitialsstateselectriderare-earth4forbitalsorbital-selectiveFermisurfacechemicalpressure
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

Using polarization-dependent and resonant angle-resolved photoemission, the authors set out to settle which orbitals actually form the Fermi surface of the infinite-layer nickelate NdNiO2. They conclude that the electron-like β pocket comes from interstitial s states—electrons located in lattice voids rather than on any atom—while the large α pocket is Ni 3d$x^2-y^2$ in character. Rare-earth 5d and 4f states are found to make negligible contributions near the Fermi level, contrary to several theoretical scenarios that put Nd orbitals directly in the low-energy physics. The paper also reports that the rare-earth element acts through chemical pressure, shifting Ni-derived bands and hopping integrals. If right, this establishes electride-like behavior in a correlated oxide and redirects models of self-doping and superconductivity in nickelates.

What carries the argument

The load-bearing object is the interstitial $s$ state (sometimes called a 'zeronium' state), an electron whose wavefunction occupies the void between Ni sites along the $c$ axis created by the absence of apical oxygen, rather than an atomic orbital on Nd or Ni. Because this state is isotropic and has out-of-plane character, it produces the observed polarization dependence of the β pocket—strong intensity under horizontal linear polarization in both measurement geometries—and it is not expected to resonate at Nd absorption edges. The analysis is carried by the contrast between atomic-orbital photoemission selection rules (for $d_{xy}$, $d_{x^2-y^2}$, $d_{xz}$, $d_{yz}$) and the measured intensity pattern, together with resonant photoemission that tracks the fate of Nd 4f states.

What would settle it

A momentum-resolved ARPES measurement that sweeps the photon energy across the Nd M$_5$ or N$_4$ edge and resolves the β band would falsify the claim if the β-pocket spectral weight resonantly enhances at the Nd edge, since the paper argues Nd 4f states show no enhancement within 1 eV of E_F. Alternatively, detecting a Γ-point electron pocket under cleaner surface preparation or with higher sensitivity would falsify the absence claim.

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Extended reading notes

Core claim

The paper claims that the β electron pocket near the A point in NdNiO$_2$ is predominantly built from interstitial $s$ states delocalized in the lattice voids left by the missing apical oxygen, coexisting with strongly correlated Ni $3d_{x^2-y^2}$ electrons. This is argued from polarization-dependent ARPES: the α band follows the expected $d_{x^2-y^2}$ selection rules, whereas the β band stays strong under horizontal linear polarization regardless of in-plane sample orientation, matching an isotropic, out-of-plane interstitial $s$ orbital and excluding $d_{xy}$ and $d_{xz}/d_{yz}$ contributions. Resonant photoemission across the Nd $N_4$ and $M_5$ edges shows resonant enhancement only at deep valence states (about 3.4 and 8 eV below $E_F$), not within 1 eV of the Fermi level, so Nd 4f and 5d states are localized and do not participate in the Fermi surface. The authors further observe quantum-well states whose number scales with film thickness, indicating the interstitial electrons are uniformly distributed through the film. Comparing NdNiO$_2$ with LaNiO$_2$, they attribute small band shifts and a more rounded α pocket to chemical pressure rather than to direct rare-earth orbital involvement.

Load-bearing premise

The paper's central assignment rests on the assumption that the atomic-orbital photoemission matrix-element simulations used to judge polarization dependence correctly describe the interstitial s state, and that the absence of resonant enhancement in momentum-integrated Nd-edge spectra reliably excludes Nd 5d and 4f contributions at every point on the Fermi surface.

Editorial extensions

If this is right

  • The rare-earth 5d and 4f orbitals do not sit at the Fermi level, so theories that build superconductivity on Kondo-type hybridization or rare-earth d electrons need to be revised.
  • The small size of the β pocket gives it a low density of states, making it an unlikely source of a dominant BCS-type mechanism proposed from GW calculations.
  • Interstitial s electrons are spatially delocalized carriers that coexist with correlated Ni d electrons; their hybridizations with Ni 3d$_{3z^2-r^2}$ and $d_{x^2-y^2}$ become part of the minimal model for nickelate superconductivity.
  • Rare-earth substitution tunes the electronic structure mainly by chemical pressure, shifting the Ni 3d$_{3z^2-r^2}$ band and changing hopping integrals, which may explain the systematic increase of $T_c$ with heavier rare earths.
  • No Γ-point electron pocket is observed, disfavoring predictions of a pocket formed by hybridized Nd 5d$_{3z^2-r^2}$ and Ni 3d$_{3z^2-r^2}$ orbitals.

Reading between the lines

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

  • If the β pocket is truly interstitial, the self-doping of the NiO$_2$ planes should be re-evaluated: electron transfer may come from the lattice voids rather than from rare-earth 5d states, changing how carrier densities are assigned in transport and spectroscopy.
  • The electride-like interstitial states may generalize to other reduced oxides and infinite-layer compounds without apical oxygen; a sharp prediction is that the β-band dispersion and pocket size should respond strongly to c-axis compression, a testable pressure experiment.
  • The quantum-well states reported here imply that the interstitial electrons are coherent across the film thickness; one could exploit this by measuring their effective mass and mobility via magnetotransport in ultra-thin films, which would connect the band character to transport properties.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The manuscript reports polarization-dependent and resonant ARPES measurements on uncapped, fully reduced NdNiO2/SrTiO3 films. The authors identify the large α Fermi pocket as Ni 3d_{x^2-y^2} and the small β pocket as an interstitial s-like state, based on polarization selection rules that exclude dxy and dxz/dyz contributions. Resonant photoemission across the Nd N4 and M5 edges shows no enhancement within 1 eV of EF, which they interpret as negligible Nd 4f and 5d contributions. Additional observations include quantum well states in the β subbands and differences between NdNiO2 and LaNiO2 that are attributed to chemical pressure. The central claim is that the β pocket is electride-like interstitial s character coexisting with correlated Ni 3d electrons.

Significance. If the central claim holds, the paper would resolve a long-standing debate about the orbital origin of the electron pockets in infinite-layer nickelates and would extend the concept of electride-like interstitial states into a correlated oxide. The experimental strengths are substantial: the films are carefully characterized by REXS to rule out residual-oxygen reconstruction, the polarization-dependent measurements are performed in well-defined geometries with in-plane rotation controls, the exclusion logic for dxy and dxz/dyz is clearly presented, and the observation of multiple well-resolved quantum well states is an independent indication of homogeneous, extended states throughout the film. The comparison between NdNiO2 and LaNiO2 is also valuable. However, the strongest claim, that rare-earth 5d and 4f contributions are negligible near EF, rests on a momentum-integrated null result whose sensitivity is not quantified, and the resonant edges used primarily probe 4f final states rather than 5d states. The conclusion is therefore plausible but currently overreaches the evidence.

major comments (3)
  1. [Results, Fig. 3] The resonant photoemission across the Nd N4 (4d→4f) and M5 (3d→4f) edges enhances 4f-derived final states and is not a direct probe of Nd 5d spectral weight. The statement in the text that 'Nd states, especially the Nd 4f states, are undetectably weak' therefore cannot support the abstract's claim of 'negligible contributions from rare-earth 5d and 4f orbitals near the Fermi level.' The absence of a 4f resonance excludes only 4f weight; Nd 5d contributions could in principle be present without producing a Fano enhancement at these edges. The authors should either provide a 5d-sensitive measurement, an explicit model for why the 4f resonance would also reveal hybridized 5d weight, or soften the claim to exclude only 4f and state that 5d exclusion rests on the polarization data alone.
  2. [Results, Fig. 3(c-d) and inset] The absence of resonant enhancement within 1 eV of EF is a momentum-integrated null result with no quantified detection limit. The β pocket is a small, k-localized feature near the A point, so a modest Nd 5d or even 4f admixture (say 10–20%) in that pocket could be diluted below the noise floor after integration over the full Brillouin zone. To make the claim load-bearing, the authors should report the noise level of the integrated spectra, estimate the fractional spectral weight in the β band that would have produced a detectable enhancement, or present angle-resolved resonant spectra along A-Z-A at the resonance energies. Without such a sensitivity estimate, 'negligible contributions' is not established.
  3. [Results, Fig. 2(h-l)] The assignment of the β pocket to interstitial s states is made by exclusion, and the exclusion list is incomplete. The polarization analysis explicitly considers dxy, dx2-y2, dxz, dyz, and an isotropic interstitial s state, but theoretical proposals also include Nd 5d orbitals with other symmetries, such as 5d_{3z^2-r^2} components that could contribute near the A point. The text mentions 'Nd 5dxy' but does not systematically rule out all Nd 5d orbital characters. In addition, the simulated photoemission intensities in Fig. 2(h-l) are only described as 'adapted from ref. 43'; no details are given for the calculation (final state, polarization geometry, parameters), which makes it difficult to assess whether the predicted contrast for an interstitial s state is reliable. Please provide the simulation method and complete the symmetry analysis over all candidate orbitals.
minor comments (5)
  1. [Introduction] There is a typographical error: 'distinct form the single-band cuprates' should read 'distinct from the single-band cuprates.'
  2. [Introduction and Discussion] Several typographical errors appear: 'nicklates' in the Introduction, 'o ffer' in the Discussion, 'insu fficient' in the Discussion, and 'itinerate interstitial s orbitals' in the Results section should be corrected.
  3. [Figure 3 caption] The caption for panels (d-e) says '988 eV (on-resonance) and 981 eV (on-resonance)'; the 981 eV spectrum is presumably off-resonance and should be labeled accordingly.
  4. [Results, Fig. 3(c) inset] The inset of Fig. 3(c) is referenced to show the absence of enhancement near EF, but in the provided figure the inset is difficult to discern; enlarging it or adding a separate panel would improve clarity.
  5. [Results, Fig. 2] The statement that an isotropic interstitial s state nevertheless 'has out-of-plane character that enhances the overall intensity under LH polarization' is not self-evident; a one-sentence explanation in terms of the final-state wave function or the simulation would help the reader.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the orbital-character conclusions are drawn from independent polarization-dependent and resonant ARPES measurements, not from fitting or from a self-citation chain.

full rationale

The paper's central claim is that the β pocket in NdNiO2 arises predominantly from interstitial s states with negligible rare-earth 5d and 4f contributions. This is supported by two independent experimental pillars: polarization-dependent ARPES, which excludes dxy, dxz/dyz, and by symmetry other Ni orbitals based on measured LH/LV intensity changes; and resonant photoemission across the Nd N4 and M5 edges, where no resonant enhancement is observed within 1 eV of EF. Neither step fits a parameter to the data and then re-predicts the same quantity; there is no equation or model whose input is defined in terms of the target conclusion. The atomic-orbital photoemission simulations are cited from ref. 43, a review that includes one coauthor, but they are used as supporting standard matrix-element/selection-rule calculations, not as a source that already asserts the interstitial-s assignment. The comparison with LaNiO2 from ref. 2, also from the same group, is used for the chemical-pressure discussion and not for the β-pocket orbital assignment; the NdNiO2 data independently establish the polarization and resonance behavior. The absence of a quantified detection limit for the resonant null result is a legitimate scientific robustness concern, but it is a matter of inferential strength, not circularity: the conclusion is not forced by construction or by a self-citation chain. Therefore no circular steps are identified.

Assumptions & free parameters 1 free parameters · 3 assumptions · 0 invented entities

The paper does not introduce new physical entities. It interprets existing electronic bands in terms of the previously proposed interstitial s states concept, which is an established idea in electride materials. The study provides experimental evidence for this interpretation in a correlated oxide.

free parameters (1)
  • Inner potential V0 = 17 eV
    Used to convert photon energy to kz for the Fermi surface map in Fig. 1(a). It is a standard calibration parameter in ARPES and is not central to the orbital character claim.
assumptions (3)
  • domain assumption Photoemission matrix element selection rules for the candidate orbitals are correctly described by the atomic-orbital simulations in Fig. 2(h-l).
    The assignment of the β band to interstitial s states relies on comparing the experimental polarization dependence with simulated intensity patterns for dxy, dxz/dyz, dx2-y2, and isotropic s orbitals.
  • domain assumption Absence of 3a0 superlattice reflections in REXS confirms complete reduction and absence of residual apical oxygen in the uncapped NdNiO2 films.
    The paper argues that the absence of such signals ensures the films are fully reduced and the measured electronic structure is intrinsic to NdNiO2 (Supplementary Section I).
  • domain assumption Momentum-integrated resonant photoemission at the Nd N4 and M5 edges is sensitive enough to detect Nd 4f/5d contributions near EF if they exist.
    The conclusion of negligible Nd contribution near EF is based on the absence of resonant enhancement in integrated spectra (Fig. 3). This assumes that such integrated measurements would reveal any Nd-derived states, even if they are k-dependent.

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Cite this review

Pith. "Pith review of Observation of Electride-like $s$ States Coexisting with Correlated $d$ Electrons in NdNiO$_2$." pith.science (2026). https://pith.science/paper/AIIBRE6Y

@misc{pith2026250704378,
  author       = {Pith},
  title        = {Pith review of: Observation of Electride-like $s$ States Coexisting with Correlated $d$ Electrons in NdNiO$_2$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AIIBRE6Y}},
  note         = {Machine review of arXiv:2507.04378}
}
abstract

Despite exhibiting a similar $d_{x^2-y^2}$ band character to cuprates, infinite-layer nickelates host additional electron pockets that distinguish them from single-band cuprates. The elusive orbital origin of these electron pockets has led to competing theoretical scenarios. Here, using polarization-dependent and resonant angle-resolved photoemission spectroscopy (ARPES), we determine the orbital character of the Fermi surfaces in NdNiO$_2$. Our data reveal that the electron-like pocket arises predominantly from interstitial $s$ states, with negligible contributions from rare-earth 5$d$ and 4$f$ orbitals near the Fermi level. The observation of well-defined quantum well states indicates a uniform distribution of these interstitial electrons throughout the film thickness. By comparing with electronic structure of LaNiO$_2$, we find that the rare-earth element modulates the Ni-derived bands and hopping integrals through a chemical pressure effect. These findings clarify the role of rare-earth elements in shaping the low-energy electronic structure and establish the presence of electride-like interstitial $s$ states in a correlated oxide system, where electrons occupy lattice voids rather than atomic orbitals. The electride-like character offer new insight into the self-doping and superconductivity in infinite-layer nickelates.

Figures

Figures reproduced from arXiv: 2507.04378 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Photoemission intensity map in the [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) Photoemission intensity map of NdNiO [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a) Momentum-integrated photoemission intensity of NdNiO [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Comparison of photoemission intensity between [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

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Forward citations

Cited by 3 Pith papers

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