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arxiv: 2508.13845 · v2 · submitted 2025-08-19 · ❄️ cond-mat.mtrl-sci · cond-mat.supr-con· physics.comp-ph

Extraction of the self energy and Eliashberg function from angle resolved photoemission spectroscopy using the xARPES code

Thomas P. van Waas , Christophe Berthod , Jan Berges , Nicola Marzari , J. Hugo Dil , Samuel Ponc\'e This is my paper

Pith reviewed 2026-05-18 22:33 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci cond-mat.supr-conphysics.comp-ph
keywords self-energyEliashberg functionARPESmaximum entropy methodBayesian inferenceelectron-phonon couplingspectral function decomposition
0
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The pith

Self-energies and Eliashberg functions can be extracted from ARPES data even when electron bands are curved rather than linear.

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

The paper shows how to extract self-energies consistently from angle-resolved photoemission spectroscopy spectra without assuming linear band dispersions. It extends the maximum-entropy method to also extract the Eliashberg function by using Bayesian inference to optimize both the dispersion parameters and the magnitudes of electron-electron and electron-impurity interactions. This matters for studying anisotropic many-body interactions in materials because it allows more accurate decomposition of the spectral function into non-interacting parts and interaction contributions. The method is validated on model data and applied to experimental sets from strontium titanate and graphene, where it identifies phonon modes and shows consistent results across dispersions.

Core claim

The authors establish that self-energies can be extracted consistently for curved dispersions by extending the maximum-entropy method to Eliashberg-function extraction with Bayesian inference. This procedure optimizes the parameters describing the dispersions and the magnitudes of electron-electron and electron-impurity interactions, as shown through comparisons on model data and demonstrations on two experimental data sets from a two-dimensional electron liquid on TiO2-terminated SrTiO3 and Li-doped graphene.

What carries the argument

An extension of the maximum-entropy method that incorporates Bayesian inference to jointly optimize dispersion shapes and self-energy magnitudes in the decomposition of the spectral function.

If this is right

  • Self-energies become extractable for materials whose bands curve significantly, removing a previous limitation.
  • The Eliashberg function extraction gains automation through parameter optimization instead of manual choices.
  • Phonon modes can be identified in two-dimensional electron liquids using ARPES data.
  • Separate dispersions in doped graphene yield matching Eliashberg functions with higher consistency.

Where Pith is reading between the lines

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

  • This approach may allow researchers to reanalyze existing ARPES data sets for better interaction parameters in other materials.
  • Combining the extracted functions with theoretical models could help predict properties like superconductivity more accurately.
  • The Bayesian optimization might be adaptable to other spectroscopic data analysis problems involving similar decompositions.

Load-bearing premise

The spectral function decomposes into a non-interacting dispersion plus additive self-energy contributions that can be fit independently while varying the dispersion shape.

What would settle it

Observing that the extracted self-energies or Eliashberg functions disagree substantially with values obtained from independent calculations or other experimental probes on the same material would indicate the method's limitations.

Figures

Figures reproduced from arXiv: 2508.13845 by Christophe Berthod, Jan Berges, J. Hugo Dil, Nicola Marzari, Samuel Ponc\'e, Thomas P. van Waas.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p018_7.png] view at source ↗
read the original abstract

Angle-resolved photoemission spectroscopy is a powerful experimental technique for studying anisotropic many-body interactions through the electron spectral function. Existing attempts to decompose the spectral function into non-interacting dispersions and electron-phonon, electron-electron, and electron-impurity self-energies rely on linearization of the bands and manual assignment of self-energy magnitudes. Here, we show how self-energies can be extracted consistently for curved dispersions. We extend the maximum-entropy method to Eliashberg-function extraction with Bayesian inference, optimizing the parameters describing the dispersions and the magnitudes of electron-electron and electron-impurity interactions. We compare these novel methodologies with state-of-the-art approaches on model data, then demonstrate their applicability with two high-quality experimental data sets. With the first set, we identify the phonon modes of a two-dimensional electron liquid on TiO$_2$-terminated SrTiO$_3$. With the second set, we obtain unprecedented agreement between two Eliashberg functions of Li-doped graphene extracted from separate dispersions. We release these functionalities in the novel Python code xARPES.

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 paper presents the xARPES Python code and a Bayesian extension of the maximum-entropy method for extracting self-energies and Eliashberg functions from ARPES data on curved dispersions. It simultaneously optimizes parameters describing the non-interacting dispersion together with the magnitudes of electron-electron and electron-impurity interactions, validates the approach on model spectra, and applies it to two experimental datasets (TiO2-terminated SrTiO3 and Li-doped graphene), claiming improved consistency in the extracted Eliashberg functions compared with prior linear-band methods.

Significance. If the decomposition can be shown to be unique and robust, the method would offer a practical advance for quantitative analysis of many-body interactions in ARPES spectra of systems with non-linear bands, such as 2D electron liquids and doped graphene. The public release of the code and the direct comparison of Eliashberg functions extracted from independent dispersions on the graphene dataset are concrete strengths that support reproducibility and falsifiability.

major comments (2)
  1. The central procedure optimizes dispersion parameters and the scalar magnitudes of electron-electron and electron-impurity self-energies against the same spectral function (abstract). Because Re Σ(ω) directly renormalizes band velocity and curvature, adjustments to the assumed bare dispersion can be absorbed into changes in the fitted self-energy magnitude. The manuscript does not report posterior widths, multiple-initialization stability, or a controlled test with deliberately misspecified dispersion; without these, the claim of consistent extraction for curved dispersions rests on an unverified uniqueness assumption.
  2. The abstract states that comparisons on model data and two experimental sets show agreement on graphene Eliashberg functions, yet no quantitative error bars, uncertainty estimates, or explicit statement of post-hoc parameter choices are provided. This omission makes it difficult to judge whether the reported agreement is robust or sensitive to modeling decisions.
minor comments (2)
  1. Notation for the decomposed spectral function and the precise definition of the Bayesian regularization term should be clarified in the methods section to allow independent implementation.
  2. Figure captions should explicitly state the fitting ranges and any constraints applied to the dispersion parameters for each dataset.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting issues of uniqueness and uncertainty quantification. We address each major comment below and will revise the manuscript to incorporate additional robustness checks and uncertainty estimates.

read point-by-point responses

  1. Referee: The central procedure optimizes dispersion parameters and the scalar magnitudes of electron-electron and electron-impurity self-energies against the same spectral function (abstract). Because Re Σ(ω) directly renormalizes band velocity and curvature, adjustments to the assumed bare dispersion can be absorbed into changes in the fitted self-energy magnitude. The manuscript does not report posterior widths, multiple-initialization stability, or a controlled test with deliberately misspecified dispersion; without these, the claim of consistent extraction for curved dispersions rests on an unverified uniqueness assumption.

    Authors: We agree that potential trade-offs between bare dispersion parameters and the real part of the self-energy represent a legitimate concern for uniqueness. Our joint Bayesian optimization is designed to mitigate this by simultaneously varying dispersion parameters and self-energy magnitudes while enforcing causality and positivity constraints through the maximum-entropy procedure. Validation on synthetic spectra with known ground-truth self-energies and curved dispersions shows accurate recovery, and the graphene dataset provides an internal consistency check via independent extractions from two distinct dispersions. Nevertheless, the manuscript does not include explicit posterior widths, multiple-initialization tests, or deliberate misspecification experiments. We will add these analyses, including posterior distributions from the Bayesian optimizer and stability results under varied initial conditions, in the revised manuscript. revision: yes

  2. Referee: The abstract states that comparisons on model data and two experimental sets show agreement on graphene Eliashberg functions, yet no quantitative error bars, uncertainty estimates, or explicit statement of post-hoc parameter choices are provided. This omission makes it difficult to judge whether the reported agreement is robust or sensitive to modeling decisions.

    Authors: We acknowledge that the presented results lack quantitative error bars and explicit discussion of parameter sensitivity. Although the Bayesian optimization framework produces posterior distributions that could supply uncertainty estimates, these were not computed or displayed for the extracted Eliashberg functions in the current version. We will revise the manuscript to include posterior-derived error bars on the Eliashberg functions for both model and experimental cases, add a discussion of sensitivity to modeling choices, and clarify the specific parameter settings used for the SrTiO3 and graphene datasets. revision: yes

Circularity Check

0 steps flagged

No significant circularity: method is a regularized fit validated on model data

full rationale

The paper describes an inverse-problem method that simultaneously optimizes bare-dispersion parameters and scalar self-energy magnitudes to reproduce measured ARPES spectra, using an extended maximum-entropy procedure with Bayesian regularization. This optimization is tested on synthetic model spectra whose ground-truth dispersions and interactions are known independently, then applied to two experimental datasets. No load-bearing step reduces by construction to its own inputs: the extracted quantities are outputs of the fit under explicit modeling assumptions, not tautological re-statements of those assumptions. No self-citation chain, imported uniqueness theorem, or ansatz smuggling is invoked to justify the central claim. The procedure is therefore self-contained against external benchmarks and receives a score of zero.

Axiom & Free-Parameter Ledger

3 free parameters · 1 axioms · 0 invented entities

The method rests on the standard ARPES spectral-function decomposition into dispersion plus self-energies; the only free parameters introduced are the dispersion-shape parameters and the magnitudes of electron-electron and electron-impurity interactions that are optimized together with the Eliashberg function.

free parameters (3)
  • dispersion parameters
    Shape parameters of the non-interacting bands that are varied during the fit.
  • electron-electron interaction magnitude
    Scalar magnitude of the electron-electron self-energy component that is optimized jointly.
  • electron-impurity interaction magnitude
    Scalar magnitude of the electron-impurity self-energy component that is optimized jointly.
axioms (1)
  • domain assumption The measured spectral function can be written as the convolution of a non-interacting dispersion with additive self-energy contributions from phonons, electrons, and impurities.
    Invoked in the abstract as the basis for the extraction procedure.

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