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arxiv: 2605.20985 · v1 · pith:RW435DHUnew · submitted 2026-05-20 · ❄️ cond-mat.str-el · cond-mat.mtrl-sci· cond-mat.supr-con

Hubbard-U-corrected electron-phonon interactions in strongly correlated materials via the finite-displacement method

Jiale Chen , Youyou Tu , Chengliang Xia , Jin Zhao , Hanghui Chen This is my paper

Pith reviewed 2026-05-21 02:25 UTC · model grok-4.3

classification ❄️ cond-mat.str-el cond-mat.mtrl-scicond-mat.supr-con
keywords electron-phonon couplingHubbard UDFT+ULaNiO2RuO2phonon modessuperconductivityfinite-displacement method
0
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The pith

Hubbard U corrections applied to electron-phonon g-matrices keep coupling weak in hole-doped LaNiO2 while stabilizing phonons in RuO2.

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

The paper develops an algorithm that folds Hubbard U corrections into the finite-displacement calculation of phonons and electron-phonon g matrices. It tests the approach on 20% hole-doped LaNiO2 and on strained RuO2. In the nickelate the corrections raise the coupling only modestly, leaving the total strength too low to produce the observed superconducting transition temperatures. In the ruthenate the same corrections remove imaginary phonon modes and cut the coupling value, narrowing the gap with experiment.

Core claim

By extending the finite-displacement method so that Hubbard U acts on the electron-phonon g matrices as well as on the electronic and phonon structures, the work finds that the electron-phonon coupling in 20% hole-doped LaNiO2 stays small and cannot account for superconductivity, while the corrections remove imaginary modes and substantially lower the coupling in RuO2 on a TiO2 substrate.

What carries the argument

The algorithm that integrates the DFT+U correction with the finite-displacement method and applies the U term directly to the electron-phonon g matrices.

If this is right

  • Electron-phonon coupling is unlikely to explain superconductivity in hole-doped infinite-layer nickelates.
  • Hubbard U corrections are required to obtain real phonon frequencies in strained RuO2 films.
  • Fermi-surface shape controls the size of the electron-phonon coupling more strongly than a simple additive U correction.

Where Pith is reading between the lines

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

  • The same finite-displacement plus U procedure can be used to reassess electron-phonon roles in other correlated oxides.
  • Self-consistent adjustment of U or inclusion of higher-order correlation terms could further modify the reported g-matrix values.

Load-bearing premise

The chosen Hubbard U values on the nickel and ruthenium orbitals capture the correlation strength, and Fermi-surface topology differences between DFT+U and GW fully explain the contrast in computed coupling strengths.

What would settle it

A measurement or independent calculation that finds an electron-phonon coupling strength in 20% hole-doped LaNiO2 large enough to produce a 10-30 K transition temperature would falsify the insufficiency claim.

Figures

Figures reproduced from arXiv: 2605.20985 by Chengliang Xia, Hanghui Chen, Jiale Chen, Jin Zhao, Youyou Tu.

Figure 1
Figure 1. Figure 1: Electronic properties of 20% hole-doped LaNiO [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Phonon properties of 20% hole-doped LaNiO [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Electron-phonon properties of 20% hole-doped LaNiO [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Electronic self-energy of 20% hole-doped LaNiO [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Electronic properties of strained RuO2: (a-c) Band structure calculated at URu = 1, 3, 5 eV, respectively. (d-f) Density of states calculated at URu = 1, 3, 5 eV, respectively. The blue and green lines denote the projections onto Ru-d and O-p orbitals, respectively. (g-i) Fermi surface calculated at URu = 1, 3, 5 eV, respectively. Left sub-panel is for kz = 0 plane and right sub-panel is for kz = π plane, … view at source ↗
Figure 6
Figure 6. Figure 6: Phonon properties of strained RuO2. (a-c) Phonon spectrum calculated at URu = 1, 3, 5 eV, respectively. The color scale represents the magnitude of the mode-resolved electron–phonon matrix element gqν, averaged over the Fermi surface for each phonon mode ν and wavevector q; red indicates the largest values and blue the smallest. (d-f) Phonon density of states calculated at URu = 1, 3, 5 eV, respectively. T… view at source ↗
Figure 7
Figure 7. Figure 7: Electron-phonon properties of strained RuO [PITH_FULL_IMAGE:figures/full_fig_p017_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Electronic self-energy of strained RuO2 that arises from the electron-phonon inter￾actions, calculated at URu = 3 eV. (a) Comparison between quasiparticle energy (red solid line) and bare energy (blue dashed line). The right inset shows the high symmetry k path. kf is the Fermi wave vector and k1 is the wave vector corresponding to ε = εF − 0.1 eV. The left inset shows the real part of the electronic self-… view at source ↗
read the original abstract

Although the density functional theory plus Hubbard $U$ correction method (DFT+U) is broadly used to study electronic structure of strongly correlated materials, the extension of this method to electron-phonon $g$ matrices has received limited attention. Here, we implement an algorithm that integrates DFT+U method with the finite-displacement method for the calculations of phonons and electron-phonon $g$ matrices. The Hubbard $U$ corrections are applied not only to electronic and phonon structures, but, more importantly, also to electron-phonon $g$ matrices. We demonstrate our algorithm in two prototypical correlated materials: infinite-layer nickelates LaNiO$_2$ and ruthenium dioxide RuO$_2$. We find that: i) While the Hubbard $U$ corrections weakly increase the electron-phonon interaction of 20% hole-doped LaNiO$_2$, its total electron-phonon coupling remains small and is insufficient to account for the observed superconducting transition temperature of about 10-30 K. Our results contrast with the recent work showing that the full GW corrections yield an elevated electron-phonon coupling of 20% hole-doped LaNiO$_2$ five times larger than its DFT value. We attribute this discrepancy to the differences in the Fermi surface topology between DFT+$U$ and GW methods. ii) The inclusion of Hubbard $U$ corrections eliminates the imaginary phonon modes of RuO$_2$ under strain on the TiO$_2$ substrate and substantially reduces the electron-phonon coupling. Our results alleviate the discrepancy between the reported large theoretical electron-phonon coupling and the low superconducting transition temperature observed experimentally. Our work provides an algorithm that fully includes the Hubbard $U$ corrections on electron-phonon properties of correlated materials, and highlights the importance of Fermi surface shape and correlation effects on phonon spectrum and electron-phonon $g$ matrices.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript implements an algorithm integrating the DFT+U method with the finite-displacement approach to compute phonons and electron-phonon g-matrices, applying Hubbard U corrections directly to the g-matrices. For 20% hole-doped LaNiO2, it reports that U weakly increases the total electron-phonon coupling λ but the value remains small and insufficient to explain the observed Tc of 10-30 K, attributing the contrast with prior GW results (which yield ~5× larger λ) to differences in Fermi-surface topology. For strained RuO2 on TiO2, U eliminates imaginary phonon modes and substantially lowers λ, helping reconcile theory with low experimental Tc. The work emphasizes the importance of correlation effects on phonon spectra and g-matrices.

Significance. If the central results hold after verification, the algorithm provides a practical route to include strong-correlation corrections in electron-phonon calculations for materials such as infinite-layer nickelates and ruthenates. This is relevant for assessing whether electron-phonon coupling can account for superconductivity in these systems. The direct application of U to g-matrices and the demonstration of its effects on phonon stability represent useful methodological progress, particularly given the experimental context for both compounds.

major comments (2)
  1. [§4] §4 (LaNiO2 results): The attribution of the large discrepancy in λ between DFT+U and the referenced GW calculation entirely to Fermi-surface topology differences is not supported by quantitative evidence in the manuscript, such as explicit comparison of FS contours or DOS on the same k-grid. This attribution is load-bearing for the claim that DFT+U λ is too small to explain Tc ~10-30 K.
  2. [Method and results sections] Method and results sections: The specific Hubbard U values chosen for Ni 3d and Ru 4d orbitals lack reported sensitivity tests (e.g., variation of U by ±2 eV and its effect on λ). If λ changes by more than ~30% under such variation, the quantitative conclusions on insufficiency for superconductivity in LaNiO2 and reduction in RuO2 would require revision.
minor comments (2)
  1. [Abstract and §1] Abstract and §1: The experimental Tc range of 'about 10-30 K' for LaNiO2 should include a specific citation to the relevant experimental work for clarity.
  2. [Figure captions and text] Figure captions and text: Ensure all convergence parameters (k-grid, displacement amplitude, U convergence) are stated explicitly in the main text rather than only in supplementary material, to allow reproducibility assessment.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their positive assessment of our manuscript and for the constructive comments. We address each major comment below.

read point-by-point responses

  1. Referee: §4 (LaNiO2 results): The attribution of the large discrepancy in λ between DFT+U and the referenced GW calculation entirely to Fermi-surface topology differences is not supported by quantitative evidence in the manuscript, such as explicit comparison of FS contours or DOS on the same k-grid. This attribution is load-bearing for the claim that DFT+U λ is too small to explain Tc ~10-30 K.

    Authors: We agree that an explicit side-by-side comparison of Fermi-surface contours and DOS on the same k-grid would provide stronger quantitative support for attributing the λ discrepancy to differences in Fermi-surface topology. In the revised manuscript we will add such a comparison, drawing on the band structures already computed in our DFT+U calculations and contrasting them with the topology reported in the referenced GW study. This addition will reinforce our conclusion that the DFT+U value of λ remains insufficient to explain the observed Tc. revision: yes

  2. Referee: Method and results sections: The specific Hubbard U values chosen for Ni 3d and Ru 4d orbitals lack reported sensitivity tests (e.g., variation of U by ±2 eV and its effect on λ). If λ changes by more than ~30% under such variation, the quantitative conclusions on insufficiency for superconductivity in LaNiO2 and reduction in RuO2 would require revision.

    Authors: We acknowledge the value of sensitivity tests for the Hubbard U parameters. In the revised manuscript we will report additional calculations in which U for the Ni 3d and Ru 4d orbitals is varied by ±2 eV, showing the resulting changes in λ and the phonon spectra. These tests will either confirm the robustness of our quantitative conclusions or prompt appropriate adjustments to the discussion of superconductivity in LaNiO2 and the stabilization in RuO2. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected; results are direct computational outputs.

full rationale

The paper implements and applies an extension of the finite-displacement method to incorporate Hubbard U corrections into electronic structure, phonons, and electron-phonon g matrices. Reported quantities (weak U-induced increase in λ for hole-doped LaNiO2 remaining too small for observed Tc; elimination of imaginary modes and reduction of λ in strained RuO2) are obtained from explicit calculations with chosen U values on Ni 3d and Ru 4d orbitals. No equation reduces these outputs to the inputs by construction, no parameter is fitted to the target e-ph coupling and then relabeled as a prediction, and no load-bearing premise rests solely on a self-citation chain. The contrast with prior GW results and the attribution to Fermi-surface topology differences are interpretive comparisons against external calculations rather than internal reductions. The derivation chain consists of independent, verifiable computational steps that remain self-contained against experimental Tc values and prior literature.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claims rest on the standard DFT+U framework for treating local correlations and on the finite-displacement approximation for extracting phonons and coupling; U values function as adjustable parameters chosen to reproduce electronic structure.

free parameters (1)
  • Hubbard U for Ni and Ru d orbitals
    U is introduced as a correction parameter whose specific numerical value is chosen to improve the description of electronic structure and then applied to phonons and g matrices.
axioms (1)
  • domain assumption DFT+U provides a sufficient description of strongly correlated electrons for extending corrections to lattice and electron-phonon properties
    Invoked when stating that U corrections are applied consistently to electronic structure, phonons, and g matrices.

pith-pipeline@v0.9.0 · 5898 in / 1478 out tokens · 58545 ms · 2026-05-21T02:25:45.824439+00:00 · methodology

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Reference graph

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