Pith. sign in

REVIEW 2 major objections 4 minor 101 references

Intercalating wide-gap LaXO3 layers into La2NiO4 donates electrons without disorder and places the nickelate in the optimal window for dx2-y2 superconductivity above 50 K.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

T0 review · grok-4.5

2026-07-10 05:28 UTC pith:FJNHMPUZ

load-bearing objection Clean disorder-free electron-doping route for RP nickelates with solid DFT/DMFT evidence; the >50 K Tc is a one-band extrapolation whose error bar is uncontrolled. the 2 major comments →

arxiv 2607.08553 v1 pith:FJNHMPUZ submitted 2026-07-09 cond-mat.supr-con cond-mat.mtrl-scicond-mat.str-el

Heterostructuring as Gateway to Electron Doping of Nickelate Superconductors

classification cond-mat.supr-con cond-mat.mtrl-scicond-mat.str-el
keywords nickelate superconductorselectron dopingheterostructuresRuddlesden-Popperd-wave superconductivityDMFTfirst-principles
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Chemical substitution has never cleanly electron-doped Ruddlesden-Popper nickelates, leaving half the phase diagram unexplored. This paper shows that simply inserting insulating LaXO3 blocks (X = Al, Ga, Sc) into La2NiO4 creates extra (LaO)+ layers that transfer roughly one electron per nickel into the Ni-3d orbitals. The resulting La2NiO4:La2AlO4 heterostructure sits naturally near half-filling of the dx2-y2 band. Many-body calculations on that band then predict d-wave superconductivity with Tc exceeding 50 K even at ambient pressure. The same intercalation idea also electron-dopes the bilayer superconductor La3Ni2O7, giving a general, disorder-free design route for other layered oxides.

Core claim

Intercalation of wide-band-gap LaXO3 layers into Ruddlesden-Popper nickelates supplies extra (LaO)+ units that act as clean electron donors, driving Ni toward a 3d9-δ configuration. For La2NiO4:La2AlO4 this places the dx2-y2 filling near the optimal value for high-Tc d-wave superconductivity, with DΓA, FLEX and DCA all predicting critical temperatures above 50 K.

What carries the argument

The extra (LaO)+ rocksalt layers introduced by LaXO3 intercalation transfer charge into the adjacent NiO2 planes without chemical disorder on the A or B sites.

Load-bearing premise

The predicted Tc rests on a single-band Hubbard model whose hoppings, filling and interaction are fixed by multi-orbital calculations and then treated as reliable inputs; if residual multi-orbital or interface effects matter, the high-Tc claim collapses.

What would settle it

Grow epitaxial La2NiO4:La2AlO4 by molecular-beam epitaxy or pulsed-laser deposition, measure the Hall density and low-temperature resistivity; absence of electron doping near n ≈ 0.87 or of a superconducting transition above 50 K falsifies the central claim.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • La2NiO4:La2AlO4 is predicted to be an ambient-pressure d-wave superconductor with Tc > 50 K without any further chemical doping.
  • The same intercalation electron-dopes La3Ni2O7 and can be extended to other Ruddlesden-Popper oxides including cuprates and ruthenates.
  • Disorder-free doping should stabilize fragile correlated phases that conventional substitutional doping would disrupt.
  • The reduced in-plane lattice constant weakens correlations relative to infinite-layer nickelates and thereby raises Tc.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Experimental realization of these superlattices would finally map the missing electron-doped half of the nickelate phase diagram.
  • Combining the charge-transfer doping demonstrated here with geometric quantum-well thickness control could open multigap or further elevated-Tc regimes.
  • The same intercalation strategy may solve long-standing electron-doping bottlenecks in manganites and cobaltates where tetravalent A-site substitution also fails.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. The manuscript proposes a disorder-free electron-doping route for Ruddlesden–Popper nickelates by intercalating wide-gap LaXO3 (X=Al, Ga, Sc) blocks into La2NiO4 (and analogously La3Ni2O7). Extra (LaO)+ layers donate electrons into the NiO2 planes. DFT occupations, Bader/Mulliken charges, and multi-orbital DMFT spectra consistently show ~1 e− transfer, producing a near-half-filled Ni-dx2−y2 band (n≈0.87 in the La-5d+Ni-3d model) with nearly filled dz2. Structural stability is supported by SCPH phonons, AIMD, and a convex-hull analysis. Superconductivity is then estimated from a single-band Hubbard model (Wannier hoppings t′/t=−0.20, t″/t≈0.10, filling fixed to the multi-orbital DMFT value, U set to 6t) solved by DΓA, FLEX and DCA, yielding d-wave Tc values of ~53 K (DΓA), ~100 K (FLEX) and ~127 K (DCA).

Significance. Electron doping of nickelates has remained experimentally inaccessible by conventional A-site substitution; a clean, symmetry-preserving alternative would open the unexplored electron-doped side of the phase diagram and is therefore of high interest. The charge-transfer mechanism itself is robustly documented by multiple independent DFT and DMFT diagnostics and is shown to extend to the bilayer compound La3Ni2O7. The work also supplies concrete, falsifiable structural predictions (lattice constants, Ni–O bond lengths) and open data. The quantitative Tc claim, while secondary, is obtained with established many-body methods and places the proposed heterostructure in a regime previously identified as optimal for high-Tc d-wave pairing.

major comments (2)
  1. The central quantitative claim (Tc exceeding 50 K) rests on the single-band model of Sec. IV with U fixed by hand to 6t = 2.58 eV because the frequency-dependent cRPA interaction is omitted. Multi-orbital DMFT (Fig. 2c,d and Table I) still shows residual La-5d pockets and a non-zero dz2 occupation; the paper asserts these are “minor” but never recomputes the superconducting eigenvalue with a multi-orbital vertex or with the actual cRPA U. A controlled sensitivity study (or an explicit multi-orbital estimate) is needed to place an error bar on the reported DΓA/FLEX/DCA Tc values.
  2. The text itself notes that inversion-symmetry breaking during growth “may introduce additional bands near the Fermi level o multiband pairing.” Interface reconstruction and possible intermixing are not quantified. Because the doping mechanism relies on clean (LaO)+ donation, at least a model estimate of how modest interface disorder or polarity-driven reconstruction would alter the Ni filling and the single-band character is required before the “disorder-free” claim can be taken as experimentally robust.
minor comments (4)
  1. Table I lists both DFT and DMFT occupations; the caption and surrounding text should state more clearly which filling (0.87) is fed into the subsequent DΓA/FLEX/DCA calculations and why the La-pocket contribution is absorbed only as a rigid shift of n.
  2. Fig. 4(a) uses a logarithmic fit λSC ≈ a − b ln(T) to extract Tc; the fitting window and the raw eigenvalue data should be shown or deposited so that the extrapolation can be reproduced.
  3. The hoppings quoted in Sec. IV (t′/t = −0.20, t″/t = 0.10 or 0.11) differ slightly between the main text and the SM; a single consistent set should be used throughout.
  4. Typographical inconsistencies appear in the abstract and introduction (“T c”, “d x2−y2”, missing spaces around colons in compound names). A uniform style for chemical formulas and orbital labels would improve readability.

Circularity Check

1 steps flagged

No significant circularity: doping and Tc follow from independent DFT/DMFT + established many-body solvers; U and filling are chosen inputs, not forced outputs.

specific steps
  1. self citation load bearing [Sec. IV (Simplified 3d_x2-y2 one-band Hamiltonian) and Superconductivity paragraph]
    "Nevertheless, as discussed in our earlier work [89], the omission of the frequency-dependent nature of U in our current calculations likely leads to an underestimation of its effective strength. We therefore suggest that a slightly larger value, around U=6t=2.58 eV, provides a more realistic representation... This filling was used in the DΓA, FLEX, and DCA calculations to mimic the effect of the pockets and is consistent with the optimal carrier concentration (∼0.85) predicted in a previous study [89]."

    The numerical value of U and the claim that n≈0.87 is 'optimal' rest on the authors' own prior work [89] rather than a fresh cRPA calculation or an external uniqueness theorem. This is a minor self-citation that supplies a conventional parameter choice; it does not force λ_SC=1 by construction, nor does it make the DΓA/FLEX/DCA eigenvalues tautological. The hoppings and the multi-orbital filling itself are independently computed for the new heterostructure.

full rationale

The paper's derivation chain is self-contained against external benchmarks and does not reduce by construction. Electron doping is obtained from fresh DFT band structures, orbital occupations (Table I), DOS, Bader/Mulliken analysis, and multi-orbital DMFT on the proposed heterostructures; these are parameter-free first-principles results for the new structures, not tautologies. Superconductivity is then estimated by projecting onto a single-band Hubbard model whose hoppings come from a new Wannier fit (t'/t = -0.20, t''/t = 0.10), whose filling is taken from the multi-orbital DMFT occupation n = 0.87, and whose U is set by hand to 6t (motivated by prior cRPA experience that frequency dependence is omitted). The resulting λ_SC(T) curves from DΓA, FLEX and DCA are genuine numerical outputs of those solvers, not algebraic identities of the inputs. Self-citations are to established methods (DΓA, FLEX, DCA, cRPA, SCPH) and to earlier nickelate/cuprate studies that supply context or parameter ranges; none of those citations is a uniqueness theorem that forces the present Tc, nor is any fitted parameter renamed as a prediction. The weakest modeling choices (single-band reduction, hand-chosen U, neglect of residual multi-orbital and interface effects) are assumptions that affect correctness risk, not circularity. Score 2 reflects only the minor, non-load-bearing self-citation of prior parameter regimes; the central claims remain independent.

Axiom & Free-Parameter Ledger

3 free parameters · 4 axioms · 0 invented entities

Central claim rests on standard DFT/DMFT approximations plus a few hand-chosen interaction and filling parameters that map the multi-orbital problem onto a single-band Hubbard model whose Tc is then computed. No new particles or forces are invented; the heterostructure itself is a proposed material, not an abstract entity.

free parameters (3)
  • single-band U = 6t = 2.58 eV
    Set by hand to 6t = 2.58 eV (after noting cRPA-like 5.25t underestimates); used for all DΓA/FLEX/DCA Tc estimates.
  • dx2-y2 filling n = 0.87 (primary)
    Taken from multi-orbital DMFT (0.87) and used as fixed density in the one-band model; also scanned at 0.80/0.90/0.95.
  • hopping ratios t′/t, t″/t = t′/t = −0.20, t″/t = 0.10
    Extracted from Wannier projection of the DFT band; small variations would shift the Fermi-surface shape and Tc.
axioms (4)
  • domain assumption GGA-PBE + PAW/LAPW accurately describes charge transfer and lattice parameters of the La2NiO4:La2XO4 heterostructures.
    Invoked throughout Secs. Structure and DFT bands and SM Secs. I, IX–XIII for occupations, Bader charges, and phonon stability.
  • domain assumption Local DMFT self-energy plus double-counting (FLL) captures the essential correlation-induced mass renormalization and pocket suppression.
    Used to obtain the spectral functions in Fig. 2(c,d) and the filling n = 0.87 fed to the one-band model.
  • ad hoc to paper A single-band Hubbard model on the square lattice with the extracted hoppings and U = 6t is sufficient to estimate the d-wave superconducting eigenvalue.
    Explicitly constructed in SM Sec. IV and solved by DΓA/FLEX/DCA; multi-orbital residual effects and La-5d pockets are assumed to act only as a passive reservoir.
  • domain assumption The heterostructure remains free of inversion-symmetry-breaking reconstructions or chemical disorder that would introduce extra bands near EF.
    Stated as a caveat in the superconductivity section; phonon/AIMD stability is shown but growth-induced disorder is not simulated.

pith-pipeline@v1.1.0-grok45 · 25653 in / 3045 out tokens · 38022 ms · 2026-07-10T05:28:45.301368+00:00 · methodology

0 comments
read the original abstract

Despite enormous expenditures in the research field, the electron-doped side of nickelate superconductors remains uncharted territory. Substituting the trivalent rare-earth cations by a tetravalent one hitherto failed. Here, we demonstrate by first-principles calculations a disorder-free route to electron dope Ruddlesden-Popper nickelates. When intercalating wide-band-gap insulating layers such as La$X$O$_3$ ($X$=Al, Ga, Sc) into La$_2$NiO$_4$, the extra (LaO)$^+$ layers act as electron donors, releasing carriers into the Ni-3$d$ orbitals. This electron doping puts La$_2$NiO$_4$:La$_2$AlO$_4$ naturally in the optimal region for $d_{x^2-y^2}$-wave superconductivity with T$_c$ exceeding 50 K. The same concept also allows us to electron dope La$_3$Ni$_2$O$_7$, the superconductor in the limelight.

Figures

Figures reproduced from arXiv: 2607.08553 by Ao Zhang, Chao Deng, Guiwen Jiang, Karsten Held, Liang Si, Mi Jiang, Motoharu Kitatani, Niklas Witt, Siqi Guo, Wenfeng Wu.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Structural schematic of La [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Paramagnetic DFT band structure and orbital characters of (a) La [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Paramagnetic DFT band structure and orbital characters of (a) La [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Leading [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

discussion (0)

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Reference graph

Works this paper leans on

101 extracted references · 101 canonical work pages

  1. [1]

    To- 6 cotronics

    and the recently reported La 2NiO4/La3Ni2O7 heterostructure (x=1+2) [78, 79]. Following this reasoning, replacing every other unit block of La 2NiO4 by La2XO4 yields structural analogs where La2XO4 (La3X2O7) can be viewed as one (or two) unit cells of LaXO 3 plus an extra (LaO) + layer. Here, La and O ions are expected to retain their 3+ and 2−va- lence s...

  2. [2]

    The (simplified) tight-binding Hamiltonian is constructed witht=-431 meV,t ′=87 meV andt ′′=-46 meV, leading to t′/t=-0.20 andt ′′/t=0.10

    for projecting onto a maximally localized Ni-3d x2−y2 Wannier orbital [39]. The (simplified) tight-binding Hamiltonian is constructed witht=-431 meV,t ′=87 meV andt ′′=-46 meV, leading to t′/t=-0.20 andt ′′/t=0.10. The single-band interaction CoulombUis determined asU=5.25t=2.25 eV. Nevertheless, as discussed in our earlier work [89], the omission of the ...

  3. [3]

    J. G. Bednorz and K. A. M¨ uller, Possible high-Tc superconductivity in the Ba−La−Cu−O system, Z. Phys. B64, 189 (1986)

  4. [4]

    P. W. Anderson,The theory of superconductivity in the high-Tc cuprate superconductors(1997)

  5. [5]

    C. C. Tsuei and J. R. Kirtley, Pairing symmetry in cuprate superconductors, Rev. Mod. Phys.72, 969 (2000). 14 TABLE S.III. DFT calculated Ni-O bond length, lattice parameters (aandc, in unit of ˚A) for relevant bulk materials and the proposed heterostructures. System Type Material In-plane Ni-O (˚A) Out-of-plane Ni-O (˚A) Latticea( ˚A) Latticec( ˚A) Bulk ...

  6. [6]

    Damascelli, Z

    A. Damascelli, Z. Hussain, and Z.-X. Shen, Angle-resolved photoemission studies of the cuprate superconductors, Rev. Mod. Phys.75, 473 (2003)

  7. [7]

    D. Li, K. Lee, B. Y. Wang, M. Osada, S. Crossley, H. R. Lee, Y. Cui, Y. Hikita, and H. Y. Hwang, Superconductivity in an infinite-layer nickelate, Nature572, 624 (2019)

  8. [8]

    S. W. Zeng, C. J. Li, L. E. Chow, Y. Cao, Z. T. Zhang, C. S. Tang, X. M. Yin, Z. S. Lim, J. X. Hu, P. Yang,et al., Superconductivity in infinite-layer nickelate La 1−xCaxNiO2 thin films, Sci. Adv.8, eabl9927 (2022)

  9. [9]

    H. Sun, M. Huo, X. Hu, J. Li, Z. Liu, Y. Han, L. Tang, Z. Mao, P. Yang, B. Wang,et al., Signatures of superconductivity near 80 k in a nickelate under high pressure, Nature621, 493 (2023)

  10. [10]

    D. Zhao, Y. Zhou, M. Huo, Y. Wang, L. Nie, Y. Yang, J. Ying, M. Wang, T. Wu, and X. Chen, Pressure-enhanced spin-density-wave transition in double-layer nickelate La 3Ni2O7−δ, Sci. Bull. , 1239 (2025)

  11. [11]

    G. Wang, N. N. Wang, X. L. Shen, J. Hou, L. Ma, L. F. Shi, Z. A. Ren, Y. D. Gu, H. M. Ma, P. T. Yang, Z. Y. Liu, H. Z. Guo, J. P. Sun, G. M. Zhang, S. Calder, J.-Q. Yan, B. S. Wang, Y. Uwatoko, and J.-G. Cheng, Pressure-induced superconductivity in polycrystalline La 3Ni2O7−δ, Phys. Rev. X14, 011040 (2024)

  12. [12]

    P. W. Anderson, The resonating valence bond state in La 2CuO4 and superconductivity, Science235, 1196 (1987)

  13. [13]

    F. C. Zhang and T. M. Rice, Effective hamiltonian for the superconducting Cu oxides, Phys. Rev. B37, 3759 (1988)

  14. [14]

    Takagi, S

    H. Takagi, S. Uchida, and Y. Tokura, Superconductivity produced by electron doping in CuO 2-layered compounds, Phys. Rev. Lett.62, 1197 (1989)

  15. [15]

    N. P. Armitage, P. Fournier, and R. L. Greene, Progress and perspectives on electron-doped cuprates, Rev. Mod. Phys. 82, 2421 (2010)

  16. [16]

    R. J. Birgeneau, C. Stock, J. M. Tranquada, and K. Yamada, Magnetic neutron scattering in hole-doped cuprate super- conductors, J. Phys. Soc. Jpn.75, 111003 (2006)

  17. [17]

    W. S. Lee, J. J. Lee, E. A. Nowadnick, S. Gerber, W. Tabis, S. W. Huang, V. N. Strocov, E. M. Motoyama, G. Yu, B. Moritz,et al., Asymmetry of collective excitations in electron-and hole-doped cuprate superconductors, Nat. Phys.10, 883 (2014)

  18. [18]

    Abbamonte, L

    P. Abbamonte, L. Venema, A. Rusydi, G. A. Sawatzky, G. Logvenov, and I. Bozovic, A structural probe of the doped holes in cuprate superconductors, Science297, 581 (2002)

  19. [19]

    E. K. Ko, Y. J. Yu, Y. D. Liu, L. Bhatt, J. R. Li, V. Thampy, C.-T. Kuo, B. Y. Wang, Y. H. Lee, K. H. Lee,et al., Signatures of ambient pressure superconductivity in thin film La 3Ni2O7, Nature(London)638, 935 (2025)

  20. [20]

    G. D. Zhou, W. Lv, H. Wang, Z. H. Nie, Y. Q. Chen, Y. Y. Li, H. L. Huang, W.-Q. Chen, Y.-J. Sun, Q.-K. Xue,et al., Ambient-pressure superconductivity onset above 40 K in (La,Pr) 3Ni2O7 films, Nature640, 641 (2025)

  21. [21]

    D. F. Li, B. Y. Wang, K. H. Lee, S. P. Harvey, M. Osada, B. H. Goodge, L. F. Kourkoutis, and H. Y. Hwang, Supercon- ducting dome in Nd 1−xSrxNiO2 infinite layer films, Phys. Rev. Lett.125, 027001 (2020)

  22. [22]

    Osada, B

    M. Osada, B. Y. Wang, B. H. Goodge, S. P. Harvey, K. H. Lee, D. F. Li, L. F. Kourkoutis, and H. Y. Hwang, Nickelate superconductivity without rare-earth magnetism:(La,Sr)NiO 2, Adv. Mater.33, 2104083 (2021)

  23. [23]

    Y. X. Wang, K. Jiang, J. J. Ying, T. Wu, J. G. Cheng, J. P. Hu, and X. H. Chen, Recent progress in nickelate supercon- ductors, Natl. Sci. Rev.12, nwaf373 (2025)

  24. [24]

    Puphal, V

    P. Puphal, V. Sundaramurthy, V. Zimmermann, K. K¨ uster, U. Starke, M. Isobe, B. Keimer, and M. Hepting, Phase formation in hole-and electron-doped rare-earth nickelate single crystals, APL Mater.11, 081107 (2023)

  25. [25]

    Rizwan, S

    M. Rizwan, S. Gul, T. Iqbal, U. Mushtaq, M. H. Farooq, M. Farman, R. Bibi, and M. Ijaz, A review on perovskite lanthanum aluminate (LaAlO 3), its properties and applications, Mater. Res. Express6, 112001 (2019)

  26. [26]

    Lybye, F

    D. Lybye, F. W. Poulsen, and M. Mogensen, Conductivity of A-site and B-site doped LaAlO 3, LaGaO 3, LaScO 3 and LaInO3 perovskites, Solid State Ion.128, 91 (2000). 15

  27. [27]

    Hohenberg and W

    P. Hohenberg and W. Kohn, Inhomogeneous electron gas, Phys. Rev.136, B864 (1964)

  28. [28]

    Kohn and L

    W. Kohn and L. J. Sham, Self-consistent equations including exchange and correlation effects, Phys. Rev.140, A1133 (1965)

  29. [29]

    Metzner and D

    W. Metzner and D. Vollhardt, Correlated lattice fermions ind=∞dimensions, Phys. Rev. Lett.62, 324 (1989)

  30. [30]

    Georges, G

    A. Georges, G. Kotliar, W. Krauth, and M. J. Rozenberg, Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions, Rev. Mod. Phys.68, 13 (1996)

  31. [31]

    P. E. Bl¨ ochl, Projector augmented-wave method, Phys. Rev. B50, 17953 (1994)

  32. [32]

    Kresse and J

    G. Kresse and J. Furthm¨ uller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mater. Sci.6, 15 (1996)

  33. [33]

    Kresse and J

    G. Kresse and J. Furthm¨ uller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B54, 11169 (1996)

  34. [34]

    Blaha, K

    P. Blaha, K. Schwarz, G. K. H. Madsen, D. Kvasnicka, and J. Luitz, wien2k, an augmented plane wave+ local orbitals program for calculating crystal properties, Wien2k, An augmented plane wave+ local orbitals program for calculating crystal properties (2001)

  35. [35]

    Schwarz, P

    K. Schwarz, P. Blaha, and G. K. H. Madsen, Electronic structure calculations of solids using the wien2k package for material sciences, Comput. Phys. Commun.147, 71 (2002)

  36. [36]

    J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett.77, 3865 (1996)

  37. [37]

    Miyake and F

    T. Miyake and F. Aryasetiawan, Screened coulomb interaction in the maximally localized wannier basis, Phys. Rev. B77, 085122 (2008)

  38. [38]

    L. Si, P. T. Liu, and C. Franchini, Evolution of the coulomb interactions in correlated transition-metal perovskite oxides from the constrained random phase approximation, Phys. Rev. Mater.9, 015001 (2025)

  39. [39]

    L. Si, W. Xiao, J. Kaufmann, J. M. Tomczak, Y. Lu, Z. C. Zhong, and K. Held, Topotactic hydrogen in nickelate superconductors and akin infinite-layer oxidesABO 2, Phys. Rev. Lett.124, 166402 (2020)

  40. [40]

    G. H. Wannier, The structure of electronic excitation levels in insulating crystals, Phys. Rev.52, 191 (1937)

  41. [41]

    Marzari, A

    N. Marzari, A. A. Mostofi, J. R. Yates, I. Souza, and D. Vanderbilt, Maximally localized wannier functions: Theory and applications, Rev. Mod. Phys.84, 1419 (2012)

  42. [42]

    A. A. Mostofi, J. R. Yates, Y.-S. Lee, I. Souza, D. Vanderbilt, and N. Marzari, wannier90: A tool for obtaining maximally- localised wannier functions, Comput. Phys. Commun.178, 685 (2008)

  43. [43]

    Kuneˇ s, R

    J. Kuneˇ s, R. Arita, P. Wissgott, A. Toschi, H. Ikeda, and K. Held, Wien2wannier: From linearized augmented plane waves to maximally localized wannier functions, Comput. Phys. Commun.181, 1888 (2010)

  44. [44]

    A. I. Liechtenstein, V. I. Anisimov, and J. Zaanen, Density-functional theory and strong interactions: Orbital ordering in Mott-Hubbard insulators, Phys. Rev. B52, R5467 (1995)

  45. [45]

    V. I. Anisimov, I. V. Solovyev, M. A. Korotin, M. T. Czy˙ zyk, and G. A. Sawatzky, Density-functional theory and NiO photoemission spectra, Phys. Rev. B48, 16929 (1993)

  46. [46]

    E. Gull, A. J. Millis, A. I. Lichtenstein, A. N. Rubtsov, M. Troyer, and P. Werner, Continuous-time monte carlo methods for quantum impurity models, Rev. Mod. Phys.83, 349 (2011)

  47. [47]

    Parragh, A

    N. Parragh, A. Toschi, K. Held, and G. Sangiovanni, Conserved quantities ofSU(2)-invariant interactions for correlated fermions and the advantages for quantum monte carlo simulations, Phys. Rev. B86, 155158 (2012)

  48. [48]

    Wallerberger, A

    M. Wallerberger, A. Hausoel, P. Gunacker, A. Kowalski, N. Parragh, F. Goth, K. Held, and G. Sangiovanni, w2dynamics: Local one-and two-particle quantities from dynamical mean field theory, Comput. Phys. Commun.235, 388 (2019)

  49. [49]

    J. E. Gubernatis, M. Jarrell, R. N. Silver, and D. S. Sivia, Quantum monte carlo simulations and maximum entropy: Dynamics from imaginary-time data, Phys. Rev. B44, 6011 (1991)

  50. [50]

    A. W. Sandvik, Stochastic method for analytic continuation of quantum monte carlo data, Phys. Rev. B57, 10287 (1998)

  51. [51]

    Kaufmann and K

    J. Kaufmann and K. Held, ana cont: Python package for analytic continuation, Comput. Phys. Commun.282, 108519 (2023)

  52. [52]

    Galler, P

    A. Galler, P. Thunstr¨ om, J. Kaufmann, M. Pickem, J. M. Tomczak, and K. Held, The AbinitioDΓA project v1. 0: Non- local correlations beyond and susceptibilities within dynamical mean-field theory, Comput. Phys. Commun.245, 106847 (2019)

  53. [53]

    K. Held, A. A. Katanin, and A. Toschi, Dynamical vertex approximation: An introduction, Prog. Theor. Phys. Suppl. 176, 117 (2008)

  54. [54]

    Rohringer, H

    G. Rohringer, H. Hafermann, A. Toschi, A. A. Katanin, A. E. Antipov, M. I. Katsnelson, A. I. Lichtenstein, A. N. Rubtsov, and K. Held, Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory, Rev. Mod. Phys.90, 025003 (2018)

  55. [55]

    Kitatani, T

    M. Kitatani, T. Sch¨ afer, H. Aoki, and K. Held, Why the critical temperature of high-Tc cuprate superconductors is so low: The importance of the dynamical vertex structure, Phys. Rev. B99, 041115(R) (2019)

  56. [56]

    Toschi, A

    A. Toschi, A. A. Katanin, and K. Held, Dynamical vertex approximation: A step beyond dynamical mean-field theory, Phys. Rev. B75, 045118 (2007)

  57. [57]

    Kitatani, R

    M. Kitatani, R. Arita, T. Sch¨ afer, and K. Held, Strongly correlated superconductivity with long-range spatial fluctuations, J. Phys.5, 034005 (2022)

  58. [58]

    N. E. Bickers, D. J. Scalapino, and S. R. White, Conserving approximations for strongly correlated electron systems: Bethe-salpeter equation and dynamics for the Two−Dimensional Hubbard model, Phys. Rev. Lett.62, 961 (1989)

  59. [59]

    N. E. Bickers and S. R. White, Conserving approximations for strongly fluctuating electron systems. ii. numerical results and parquet extension, Phys. Rev. B43, 8044 (1991). 16

  60. [60]

    N. Witt, E. G. C. P. van Loon, T. Nomoto, R. Arita, and T. O. Wehling, Efficient fluctuation-exchange approach to low-temperature spin fluctuations and superconductivity: From the hubbard model to Na xCoO2 ·yH 2O, Phys. Rev. B 103, 205148 (2021)

  61. [61]

    N. Witt, L. Si, J. M. Tomczak, K. Held, and T. O. Wehling, No superconductivity in Pb 9Cu1(PO4)6O found in orbital and spin fluctuation exchange calculations, SciPost Phys.15, 197 (2023)

  62. [62]

    J. Li, M. Wallerberger, N. Chikano, C.-N. Yeh, E. Gull, and H. Shinaoka, Sparse sampling approach to efficient ab initio calculations at finite temperature, Phys. Rev. B101, 035144 (2020)

  63. [63]

    Shinaoka, J

    H. Shinaoka, J. Otsuki, M. Ohzeki, and K. Yoshimi, Compressing green’s function using intermediate representation between imaginary-time and real-frequency domains, Phys. Rev. B96, 035147 (2017)

  64. [64]

    Wallerberger, S

    M. Wallerberger, S. Badr, S. Hoshino, S. Huber, F. Kakizawa, T. Koretsune, Y. Nagai, K. Nogaki, T. Nomoto, H. Mori, et al., sparse-ir: Optimal compression and sparse sampling of many-body propagators, SoftwareX21, 101266 (2023)

  65. [65]

    M. H. Hettler, A. N. Tahvildar-Zadeh, M. Jarrell, T. Pruschke, and H. R. Krishnamurthy, Nonlocal dynamical correlations of strongly interacting electron systems, Phys. Rev. B58, R7475 (1998)

  66. [66]

    E. Gull, P. Werner, O. Parcollet, and M. Troyer, Continuous-time auxiliary-field monte carlo for quantum impurity models, Europhys. Lett.82, 57003 (2008)

  67. [67]

    T. A. Maier, M. S. Jarrell, and D. J. Scalapino, Structure of the pairing interaction in the Two−Dimensional Hubbard model, Phys. Rev. Lett.96, 047005 (2006)

  68. [68]

    T. A. Maier, M. Jarrell, and D. J. Scalapino, Pairing interaction in the two-dimensional Hubbard model studied with a dynamic cluster quantum monte carlo approximation, Phys. Rev. B74, 094513 (2006)

  69. [69]

    Maier, M

    T. Maier, M. Jarrell, T. Pruschke, and M. H. Hettler, Quantum cluster theories, Rev. Mod. Phys.77, 1027 (2005)

  70. [70]

    Togo and I

    A. Togo and I. Tanaka, First principles phonon calculations in materials science, Scr. Mater.108, 1 (2015)

  71. [71]

    Tadano, Y

    T. Tadano, Y. Gohda, and S. Tsuneyuki, Impact of rattlers on thermal conductivity of a thermoelectric clathrate: A first-principles study, Phys. Rev. Lett.114, 095501 (2015)

  72. [72]

    Tadano and S

    T. Tadano and S. Tsuneyuki, Self-consistent phonon calculations of lattice dynamical properties in cubic SrTiO 3 with first-principles anharmonic force constants, Phys. Rev. B92, 054301 (2015)

  73. [73]

    Kresse and J

    G. Kresse and J. Hafner, Ab initio molecular dynamics for open-shell transition metals, Phys. Rev. B48, 13115 (1993)

  74. [74]

    Jinnouchi, J

    R. Jinnouchi, J. Lahnsteiner, F. Karsai, G. Kresse, and M. Bokdam, Phase transitions of hybrid perovskites simulated by machine-learning force fields trained on the fly with bayesian inference, Phys. Rev. Lett.122, 225701 (2019)

  75. [75]

    Jinnouchi, F

    R. Jinnouchi, F. Karsai, and G. Kresse, On-the-fly machine learning force field generation: Application to melting points, Phys. Rev. B100, 014105 (2019)

  76. [76]

    See Supplemental Material at http://link.aps.org/supplemental/10.1103/qp4p-x6g3 for additional results and computa- tional details of DFT, DMFT, cRPA, DΓA, FLEX, DCA and AIMD calculations

  77. [77]

    G. M. l. Luke, Y. Fudamoto, K. M. Kojima, M. I. Larkin, J. Merrin, B. Nachumi, Y. J. Uemura, Y. Maeno, Z. Q. Mao, Y. Mori,et al., Time-reversal symmetry-breaking superconductivity in Sr 2RuO4, Nature394, 558 (1998)

  78. [78]

    K. T. Jacob and G. Rajitha, Thermodynamic properties of strontium titanates: Sr 2TiO4, Sr 3Ti2O7, Sr 4Ti3O10, and SrTiO3, J. Chem. Thermodyn.43, 51 (2011)

  79. [79]

    Li, X.-G

    J. Li, X.-G. Tang, Q.-X. Liu, Y.-P. Jiang, W.-H. Li, and Z.-X. Tang, Interfacial resistive switching properties of Sr2TiO4/SrTiO3 heterojunction thin films prepared via sol-gel process, Ceram. Int.47, 18808 (2021)

  80. [80]

    M. Z. Shi, D. Peng, K. B. Fan, Z. F. Xing, S. H. Yang, Y. Z. Wang, H. P. Li, R. Q. Wu, M. Du, B. H. Ge,et al., Pressure induced superconductivity in hybrid ruddlesden–popper La 5Ni3O11 single crystals, Nat. Phys.21, 1780 (2025)

Showing first 80 references.