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REVIEW 5 major objections 5 minor 99 references

Electronic correlations and flattened band in magnetic Weyl semimetal candidate Co3Sn2S2

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Pith's one-line read In ferromagnetic Co3Sn2S2, the band connecting the two Weyl cones is flattened by electronic correlations with U ≈ 4 eV, and the resulting interband transitions explain a sharp 36 meV peak in the optical conductivity that single-particle…

desk verdict Solid kinetic-energy evidence for intermediate correlations; the flat-band claim is plausible but needs stronger evidence than a static QP Hamiltonian. read the letter →

arxiv 1908.04561 v2 pith:4YPUPAQT submitted 2019-08-13 cond-mat.mtrl-sci cond-mat.str-elcond-mat.supr-con

Yueshan Xu , Jianzhou Zhao , Changjiang Yi , Qi Wang , Qiangwei Yin , Yilin Wang , Xiaolei Hu , Luyang Wang
show 8 more authors
Enke Liu Gang Xu Ling Lu Alexey A. Soluyanov Hechang Lei Youguo Shi Jianlin Luo Zhi-Guo Chen
This is my paper · ORCID
classification cond-mat.mtrl-scicond-mat.str-elcond-mat.supr-con
keywords WeylsemimetalelectroniccorrelationsflatbandopticalconductivityDFT+DMFTkagomelatticeCo3Sn2S2ferromagneticmetal
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

This paper argues that Co3Sn2S2, a ferromagnetic kagome metal already identified as a magnetic Weyl semimetal candidate, is an intermediately correlated metal in which Coulomb repulsion does not destroy the Weyl state but reshapes it. Comparing optical conductivity with single-particle ab initio calculations, the authors find that the measured electronic kinetic energy is about half the calculated value and that the interband-transition peaks are red-shifted and sharpened, from which they estimate a Hubbard $U$ of about 4 eV. With that interaction strength, density functional theory plus dynamical mean-field theory produces Weyl cones and Fermi arcs, and it turns the band connecting the two Weyl cones into a nearly flat band near the Fermi energy. The sharp asymmetric optical peak near 36 meV—absent in single-particle spectra and vanishing above the ferromagnetic transition—is presented as spectroscopic evidence for this correlation-flattened band. If correct, this puts flat-band physics and Weyl topology in the same material, a combination that has been predicted but rarely observed.

What carries the argument

The argument is carried by three linked tools. Equation (1) converts the integrated Drude spectral weight into an electronic kinetic energy, making the measured-versus-calculated kinetic-energy ratio a direct correlation diagnostic. A Drude-Lorentz fit decomposes the asymmetric 36 meV feature into four Lorentzian peaks whose energies are compared with four DFT+DMFT interband transitions (T1–T4); this decomposition is the bridge from theory to the measured spectrum. The quasiparticle Hamiltonian of Eq. (5), built from density functional theory plus dynamical mean-field theory, provides the renormalization factors used to estimate $U \approx 4$ eV and the momentum-resolved bands showing the flattened B1: it is the object in which the Weyl cones survive while the connecting band loses its dispersion. The same many-body calculation produces the Fermi arcs and Berry-curvature texture that certify the Weyl state.

What would settle it

Look for the flattened band directly: angle-resolved photoemission along the W1–W2 direction in the ferromagnetic state should show a nearly dispersionless B1 band near the Fermi energy, not the steep linearly dispersing band of the single-particle calculation. As an optical test, a clean sample measured across the ferromagnetic transition should show the 36 meV peak only in the magnetic Weyl state; if the peak persists above the transition temperature, or if a differently constrained fit needs no four-Lorentzian decomposition, the flat-band assignment is falsified.

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Extended reading notes

Core claim

The paper's central claim is that intermediate-strength electronic correlations flatten a band that connects the two bulk Weyl cones of ferromagnetic Co3Sn2S2, and that this flat band can be seen in optics. The kinetic energy obtained by integrating the measured Drude spectral weight is $K^E_{8K}/K^T \approx 0.47 \pm 0.04$, and the square-ratio of plasma frequencies gives $0.46 \pm 0.02$; the experimental $\alpha$ and $\beta$ interband peaks sit at about 217 and 708 meV versus about 320 and 932 meV in theory. Matching these ratios to DFT+DMFT band-narrowing factors yields $U \approx 4$ eV. At this $U$, the quasiparticle band structure retains bulk Weyl cones and surface Fermi arcs, while band B1 along the W1–W2 direction flattens near the Fermi energy. Four interband transitions involving B1 and the dispersionless parts of bands B2 and B3 produce calculated peaks near 39, 70, 113, and 131 meV, and the experimental low-energy feature around 36 meV decomposes into Lorentzians at those positions, whereas the single-particle spectrum has no peak there. The paper concludes that the 36 meV peak is spectroscopic evidence for the correlation-flattened band B1 connecting the Weyl cones.

Load-bearing premise

The paper's conclusion rests on treating the measured 36 meV asymmetric peak as four interband transitions whose energies are predicted by a quasiparticle Hamiltonian that the authors say cannot fully capture correlation effects (it misses part of the Drude spectral weight); if the Lorentzian decomposition or that Hamiltonian is inaccurate, the 36 meV peak could have a different origin and the flat-band claim would not follow.

Editorial extensions

If this is right

  • Co3Sn2S2 becomes a concrete example where a Weyl semimetal state and a correlation-flattened band coexist, so flat-band-enhanced correlation effects can be studied in a topological semimetal.
  • The measured $U \approx 4$ eV and kinetic-energy ratio $K^E/K^T \approx 0.47$ give quantitative benchmarks for modeling correlated kagome magnets.
  • The 36 meV peak and its four-Lorentzian decomposition become a spectroscopic fingerprint that can be looked for in other magnetic Weyl candidates.
  • Because the flat band connects Weyl points of opposite chirality, it sits near energies where anomalous Hall and transport effects have been observed, implying those effects can be reexamined with correlation-renormalized bands.

Reading between the lines

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

  • If the flat band B1 is as close to the Fermi energy as claimed, its divergent density of states should enhance the tendency toward magnetic instabilities or pairing near the Weyl points; measuring the 36 meV peak under magnetic field and doping would probe this directly.
  • The same kinetic-energy-ratio and interband-peak-ratio analysis could be applied to other shandite and kagome magnets to see whether correlation-flattened Weyl bands are common across the family.
  • A useful independent test would be high-resolution photoemission along the W1–W2 direction: a clear dispersionless B1 band would confirm the optical assignment, while its absence would force a different explanation for the 36 meV feature.
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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

5 major / 5 minor

Summary. This paper combines optical reflectance spectroscopy (8-6000 meV) on single-crystal Co3Sn2S2 with single-particle DFT and DFT+DMFT calculations. The authors report that the Drude spectral weight (and hence kinetic energy) at 8 K is about 47% of the single-particle value, with a consistent estimate from the plasma frequency, indicating intermediate-strength electronic correlations. They further compare the energies and side slopes of high-energy interband peaks with DMFT bandwidth-renormalization factors to estimate U ≈ 4 eV. With this U, their DFT+DMFT calculations yield bulk Weyl cones, surface Fermi arcs, and a quasiparticle band B1 that is flattened along the direction connecting the Weyl points; four calculated optical transitions involving B1 and the dispersionless parts of B2/B3 produce peaks near 38, 70, 113, and 131 meV. Since an asymmetric experimental peak near 36 meV can be fit by four Lorentzians at these positions and is absent in single-particle spectra, the paper claims this feature provides spectroscopic evidence for the correlation-flattened band.

Significance. The strength of the paper is the combined experimental-theoretical approach. The kinetic-energy reduction is supported by two independent estimates, and the discussion carefully rules out several mundane origins (Fermi-level shifts, ordered spin correlations, polarons, electron-phonon coupling). The paper also presents explicit DFT+DMFT calculations of the WSM state and ties the low-energy optical feature to a specific band-structure effect. If the flat-band assignment survives scrutiny, this is an important observation of correlation-induced flattening in a magnetic WSM. The main caveats are that the flat-band assignment is made through a static quasiparticle Hamiltonian whose own limitations the authors concede, that the WSM starting point appears sensitive to the DFT functional, and that the four-Lorentzian decomposition is not uniquely constrained. The result is therefore promising but needs stronger validation before 'spectroscopic evidence' is warranted.

major comments (5)
  1. [Methods, many-body calculations (Eq. 5)] The identification of the ~36 meV peak with transitions involving flat band B1 is built on H_QP = H0 - mu + Re Sigma~(0). The authors state that this Hamiltonian 'cannot totally capture the effect of electronic correlations--the reduction of its Drude spectral weight.' Because sigma_QP(omega) is computed by Kubo-Greenwood from the QP bands, it omits Im Sigma(omega), the frequency dependence of Re Sigma(omega), and vertex corrections. With the kinetic energy reduced by roughly a factor of 0.47, those omitted terms cannot be assumed small; they can shift interband thresholds, broaden or suppress sharp joint-DOS peaks, and move weight into incoherent sidebands. The 36/70/113/131 meV agreement is thus a postdiction of an approximation whose own limitation is conceded, not an independent confirmation. A full-frequency DMFT optical conductivity (or an ARPES map of the flat band) is needed to validate the assignment; alternatively, the 'spectroscopic evidence' claim should be weakened.
  2. [Methods, single-particle ab initio calculations] The Methods state that HSE06 and mBJ band structures 'do not exhibit band inversions near the Fermi energy' (Supplementary Note 3). The Weyl points underlying the paper's central narrative come from the single-particle calculations used throughout. This functional sensitivity suggests that the WSM state may depend on the chosen approximation, and it undermines the premise that band B0 connects two Weyl cones. The main text should reconcile this discrepancy: for example, by showing that DFT+DMFT with U ≈ 4 eV yields Weyl points even when starting from a non-inverted HSE/mBJ band structure, or by explaining why the HSE/mBJ results are not reliable for this material. Without this, the 'persistence of a WSM state' claim is conditional on the starting functional.
  3. [Flat band connecting the two Weyl cones (Fig. 4b)] The experimental asymmetric peak is decomposed into four Lorentzians at 36, 70, 113, and 131 meV, with widths of 37, 98, 108, and 108 meV. The fit is consistent with the DMFT peak positions, but it is not unique: the envelope could also be described by fewer broad oscillators plus a different background or Tauc-Lorentzian contribution. Please provide fit residuals, confidence bounds on the oscillator parameters, and a quantitative comparison against a simpler model (e.g., two Lorentzians plus a smooth background) to support the four-component decomposition.
  4. [Flat band connecting the two Weyl cones] The disappearance of the 36 meV feature above TC is used as evidence tying it to the WSM/flat-band state. However, magnetic excitations (magnons or spin fluctuations), which also vanish above TC, can appear at similar energies and are not excluded by the double-exchange scaling test, which only rules out one exchange-splitting mechanism via the Delta(omega_scr^2) vs chi^2 linearity. A magnon calculation, magnetic-field dependence of the peak, or a comparison with the full DMFT optical response is needed to rule out this alternative origin.
  5. [Narrowness of the electronic bandwidth (Fig. 2h)] The value U ≈ 4 eV is obtained by matching experimental peak-energy and slope ratios to band-width renormalization factors computed within the same DFT+DMFT framework, with J/U fixed to 0.2 and U varied. The subsequent DMFT spectra and the flat band are therefore generated with a parameter fitted to the same data set. This is a reasonable calibration strategy, but it means the low-energy peak agreement is a postdiction; the paper should state this explicitly and, if possible, support U with an independent probe (e.g., photoemission satellite structure or constrained RPA).
minor comments (5)
  1. [Fig. 3d/e caption] The caption appears to read 'around the Weyl points W1 (d) and W1 (e)'; the second label should presumably be W2.
  2. [Section 'Narrowness of the electronic bandwidth'] The text uses S both for the spectral weight in Eq. (1) and for the slope ratio S(beta_T)/S(beta_E); rename the slope variable to avoid confusion.
  3. [Table 2] The four Lorentzian terms have very large widths (Gamma_2 = 98, Gamma_3 = 108, Gamma_4 = 108 meV) with nearest-neighbor separations of only 18-43 meV; a separate figure showing the components and the fit residual would make the decomposition more transparent.
  4. [Abstract and main text] The abstract uses 'side-slope ratios' while the main text defines the relevant slope only later; the terminology should be unified and defined at first use.
  5. [Methods, single-particle ab initio calculations] The HSE06/mBJ statement is important enough to warrant a one-sentence main-text summary rather than being deferred to Supplementary Note 3, since it appears to contradict the central WSM assumption.

Circularity Check

0 steps flagged · score 0.0 of 10

U~4 eV is calibrated to the high-energy α/β interband peaks; the 36 meV flat-band peak is an independent, out-of-sample check, so no circularity is present.

full rationale

The derivation chain is non-circular. The kinetic-energy reduction K_E/K_T ≈ 0.47 is an independent comparison of Drude spectral weights/plasma frequencies with DFT, and the paper checks that Fermi-level shifts cannot explain it. The Coulomb U is then estimated by matching the high-energy interband peaks (E(αE)/E(αT) ≈ 0.68, E(βE)/E(βT) ≈ 0.76, slope ratio ≈ 0.74) to DFT+DMFT bandwidth renormalization factors; none of these calibration inputs is the low-energy 36 meV feature. The DFT+DMFT run with U≈4 eV then produces the quasiparticle bands, including the flat band B1, and optical-conductivity peaks T1–T4 at ~38/70/113/131 meV. The experimental asymmetric 36 meV peak is decomposed into four Lorentzians at 36/70/113/131 meV, so the agreement is an out-of-sample consistency check rather than a fitted-input prediction. The authors' concession that the quasiparticle Hamiltonian 'cannot totally capture the effect of electronic correlations—the reduction of its Drude spectral weight' is a stated model limitation and a correctness risk, not a circular step. Citations to prior work on Co3Sn2S2 as a WSM candidate are background; the correlated WSM state and the flat band are computed in this paper and do not reduce to those citations by construction. The non-uniqueness of the four-Lorentzian decomposition is a fitting ambiguity, not circularity.

Assumptions & free parameters 2 free parameters · 4 assumptions · 1 invented entities

The central claims rest on a fitted Hubbard U, a chosen double-counting scheme, and the validity of the low-energy QP Hamiltonian for topology and flat-band structure. No new physical entities beyond the predicted flat band are introduced.

free parameters (2)
  • U (Hubbard Coulomb interaction) = ~4 eV
    Chosen to match measured interband peak energy and slope ratios (0.68, 0.74, 0.76) to DFT+DMFT renormalization factors; not computed from first principles for Co3Sn2S2.
  • J (Hund's coupling) = ~0.8 eV (J/U = 0.2)
    Fixed by the ratio J/U = 0.2 following d7 cobalt compounds; not independently determined for Co3Sn2S2.
assumptions (4)
  • domain assumption DFT+DMFT with the fully localized double-counting scheme and density-density interactions describes the correlated electronic structure of Co3Sn2S2.
    Invoked in Methods for many-body calculations; the double-counting choice affects renormalization factors and band positions.
  • domain assumption The low-energy quasiparticle Hamiltonian H_QP = H0 - mu + Re Sigma(0) (Eq. 5), which omits the Drude spectral weight reduction, is sufficient to determine Fermi arcs, Weyl cones, and the flat band.
    Stated in Methods as a limitation; central to the flat band and WSM persistence claims.
  • domain assumption The experimental 36 meV optical peak originates from interband transitions involving the flat band rather than from phonons or magnons.
    The paper argues indirectly against phonons and double exchange, but does not measure a nonmagnetic analog or explicitly rule out magnetic excitations.
  • standard math Kramers-Kronig transformation and Kubo-Greenwood formula are valid for extracting sigma1(omega) and sigma_QP(omega).
    Used to obtain the optical conductivity from reflectance and to compute the quasiparticle optical conductivity.
invented entities (1)
  • Correlation-flattened band B1 connecting the two Weyl cones independent evidence
    purpose: Explains the low-energy optical peak at ~36 meV and demonstrates that electronic correlations flatten a band between Weyl points.
    This is a predicted quasiparticle feature that can be directly tested by ARPES; flat bands in Co3Sn2S2 have been reported in ARPES (ref 63), providing an independent handle, though the specific connection to Weyl cones is new.

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Pith. "Pith review of Electronic correlations and flattened band in magnetic Weyl semimetal candidate Co3Sn2S2." pith.science (2026). https://pith.science/paper/4YPUPAQT

@misc{pith2026190804561,
  author       = {Pith},
  title        = {Pith review of: Electronic correlations and flattened band in magnetic Weyl semimetal candidate Co3Sn2S2},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4YPUPAQT}},
  note         = {Machine review of arXiv:1908.04561}
}
read the original abstract

The interplay between electronic correlations and topological protection may offer a rich avenue for discovering emergent quantum phenomena in condensed matter. However, electronic correlations have so far been little investigated in Weyl semimetals (WSMs) by experiments. Here, we report a combined optical spectroscopy and theoretical calculation study on the strength of electronic correlations in a kagome magnet Co3Sn2S2 and the influence of electronic correlations on its WSM state expected within a single-particle picture. The electronic kinetic energy estimated from our optical data is about half of that obtained from single-particle ab initio calculations, which indicates intermediate-strength electronic correlations in this system. Furthermore, comparing the energy ratios between the interband-transition peaks at high energies in the experimental and single-particle-ab-initio-calculation derived optical conductivity spectra with the electronic bandwidth renormalization factors obtained by many-body calculations enables us to estimate the Coulomb-interaction strength (U ~ 4 eV) of electronic correlations in Co3Sn2S2. Our many-body calculations with U ~ 4 eV show that a WSM state, which is characterized by bulk Weyl cones and surface Fermi arcs, survives in this correlated electron system. Besides, a sharp experimental optical conductivity peak at low energy, which is absent in the single-particle-ab-initio-calculation-derived optical conductivity spectrum but is consistent with the optical conductivity peaks obtained by many-body calculations, indicates that an electronic band connecting the two Weyl cones is flattened by electronic correlations and emerges near the Fermi energy in Co3Sn2S2. Our work paves the way for exploring flat-band-generated quantum phenomena in WSMs.

Figures

Figures reproduced from arXiv: 1908.04561 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
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Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
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Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

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Pith tools

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