{"id":"e52d39ed-749d-4275-a421-0f6e376e60a0","arxiv_id":"1908.04561","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"Optical spectroscopy and DFT+DMFT show intermediate electron correlations (U≈4 eV) in Co3Sn2S2 and reveal a correlation-flattened band connecting its Weyl cones, supporting the persistence of its Weyl semimetal state.","lead":"Optical measurements show that electrons in the magnetic Weyl semimetal Co3Sn2S2 have about half the kinetic energy predicted by standard calculations, pointing to intermediate-strength electron interactions. Combining the data with many-body simulations puts the Coulomb interaction at about 4 eV and suggests that interactions flatten an electronic band between the material's Weyl points.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Flat-band assignment depends on a static quasiparticle Hamiltonian whose own limitations the authors concede; the 36 meV peak needs a full-DMFT optical or direct ARPES check.","rationale":"I read the paper as claiming, first, intermediate correlations (KE reduction), second, U ≈ 4 eV from high-energy peak ratios, and third, a correlation-flattened band connecting Weyl cones evidenced by the 36 meV peak. The first two are argued as well as optical measurements allow; I do not object to them. The third is the weakest link. Fig. 4b's σ_QP spectrum is computed from a static quasiparticle Hamiltonian, and the authors explicitly concede this misses part of the correlation physics. At renormalization factors of roughly 0.7, frequency-dependent self-energy and vertex corrections can substantially modify low-energy interband conductivity. Therefore the agreement between the four fitted Lorentzians and the QP peaks is suggestive but not yet conclusive. A full-DMFT optical calculation with the existing CTQMC self-energy would be the most direct numerical check; a null result would falsify the flat-band assignment, and a positive one would strengthen it materially. The HSE06/mBJ statement in Methods also indicates functional sensitivity of the single-particle WSM picture, but because the WSM state is supported by prior ARPES and transport work, I treat the QP-Hamiltonian issue as more load-bearing. The reader's weakest_assumption points to the same place, so I agree; no change in the CONDITIONAL verdict is needed.","tokens_in":20019,"tokens_out":7677,"duration_ms":86481,"concrete_test":"Recompute the low-energy σ_1(ω) from the same DFT+DMFT solution retaining the full frequency-dependent self-energy, and include the DMFT current vertex (or at least evaluate the bubble with Σ(ω+iδ) rather than freezing the QP Hamiltonian of Eq. 5). Compare the resulting peak positions and line shapes with the H_QP-based peaks T1–T4 in Fig. 4b. If the ~38 meV peak vanishes or shifts by more than ~10 meV, the assignment of the experimental 36 meV peak to the flat band B1 is not robust; if it survives with comparable position and relative intensity, the concern is retired.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing step is not the kinetic-energy reduction (KE^E/KE^T ≈ 0.47, which is well supported), but the assignment of the ~36 meV optical peak to transitions involving a correlation-flattened band B1. The only calculated bridge from the measured spectrum to B1 is the DFT+DMFT quasiparticle Hamiltonian H_QP = H0 − μ + Re Σ̃(0) (Eq. 5). The authors state that a band structure from this Hamiltonian 'cannot totally capture the effect of electronic correlations—the reduction of its Drude spectral weight.' More precisely, H_QP retains only the static real part of the self-energy; it discards Im Σ(ω) and the frequency dependence of Re Σ(ω), and the Kubo-Greenwood conductivity computed from QP bands omits vertex corrections. For a system whose kinetic energy is halved by correlations, these omitted contributions are not small: they can shift interband thresholds, broaden sharp joint-DOS peaks, and move spectral weight into incoherent sidebands. If the experimental 36 meV feature arises from such incoherent or vertex contributions rather than from a coherent QP transition between B1 and the top of B2, then the paper's central claim 'spectroscopic evidence for the flat band B1' is unsupported. The four-Lorentzian decomposition at 36/70/113/131 meV is consistent but not unique; the same envelope could be reproduced with a different background plus one or two broad oscillators. A direct check is therefore required before the flat-band interpretation is accepted.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":20299,"tokens_out":9706,"duration_ms":91813,"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":[{"comment":"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.","section":"Methods, many-body calculations (Eq. 5)"},{"comment":"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.","section":"Methods, single-particle ab initio calculations"},{"comment":"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.","section":"Flat band connecting the two Weyl cones (Fig. 4b)"},{"comment":"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.","section":"Flat band connecting the two Weyl cones"},{"comment":"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).","section":"Narrowness of the electronic bandwidth (Fig. 2h)"}],"minor_comments":[{"comment":"The caption appears to read 'around the Weyl points W1 (d) and W1 (e)'; the second label should presumably be W2.","section":"Fig. 3d/e caption"},{"comment":"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.","section":"Section 'Narrowness of the electronic bandwidth'"},{"comment":"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.","section":"Table 2"},{"comment":"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.","section":"Abstract and main text"},{"comment":"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.","section":"Methods, single-particle ab initio calculations"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is a strong candidate for a high-profile venue if the flat-band evidence is strengthened. The most important points are the functional sensitivity of the WSM state (HSE06/mBJ show no band inversion) and the reliance on a static QP Hamiltonian for the central peak assignment; both are fixable by additional calculations and/or softened claims. I would not reject, but I would not accept without these points being addressed."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nYou should know two things about arXiv:1908.04561. First, the optical kinetic-energy reduction in Co3Sn2S2 is real and well supported: two independent estimates (Drude weight integration and plasma frequency) give KE^E/KE^T ≈ 0.47 ± 0.04, and the authors carefully rule out Fermi-level shifts and argue against phonon and spin-ordering explanations. That is a solid experimental result. Second, the more exciting claim—that a band connecting the two Weyl cones is flattened by correlations and produces the 36 meV optical peak—is plausible but not yet demonstrated. It rests on a DFT+DMFT quasiparticle Hamiltonian (Eq. 5) that keeps only the static real part of the self-energy. The authors concede this Hamiltonian cannot capture the Drude weight reduction. The Kubo-Greenwood calculation from QP bands also omits vertex corrections and the frequency dependence of the self-energy. For a system with kinetic energy halved by correlations, those omitted pieces are not small; they can shift thresholds, broaden joint-DOS peaks, and move weight into incoherent sidebands. So the 36 meV peak could in principle have an alternative origin—phonon, magnon, or incoherent—and the four-Lorentzian decomposition that isolates it is consistent but not unique.\n\nWhat is genuinely new: the optical conductivity measurements, the U ≈ 4 eV estimate from interband peak ratios plus DMFT renormalization factors, and the prediction that the WSM state survives with a correlation-flattened band. The U estimate is a fit, not a parameter-free derivation, but it is a reasonable way to go given the data. The paper also does good housekeeping: the Fermi-level dependence of the theoretical Drude weight is checked, the double-exchange explanation for the 36 meV peak is tested via Δω²_scr vs χ², and the temperature dependence of the peak is shown.\n\nThe weak link is exactly where the stress-test puts it. The flat band is the load-bearing novelty, and the only bridge from the measured spectrum to it is a static QP Hamiltonian whose own limitations the authors state. That doesn't make the claim wrong, but it means the paper's title-level finding is conditional. Direct ARPES imaging of B1, a full DMFT optical calculation including vertex corrections, or a constrained-RPA U for this compound would settle it.\n\nI would send this to peer review—the kinetic-energy result alone deserves referee time—and I would push the authors hard on the flat-band assignment. The paper is honest, clearly written, and the calculations are serious. For my own work, I'd cite the kinetic-energy reduction and the U estimate, but I'd hold off on the flat band until it is confirmed.\n\nRecommendation: peer review with major revision.","headline":"Solid kinetic-energy evidence for intermediate correlations; the flat-band claim is plausible but needs stronger evidence than a static QP Hamiltonian.","tokens_in":20943,"tokens_out":2422,"would_cite":true,"duration_ms":24625,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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…","keywords":["Weyl semimetal","electronic correlations","flat band","optical conductivity","DFT+DMFT","kagome lattice","Co3Sn2S2","ferromagnetic metal"],"falsifier":"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.","tokens_in":19795,"feed_emoji":"🔬","tokens_out":8261,"duration_ms":81685,"temperature":0.7,"pith_summary":"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.","feed_headline":"36 meV peak ties Weyl semimetal to a flattened band","feed_subtitle":"Optical data plus many-body calculations show medium-strength correlations create the flat band while the Weyl cones survive.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Single-particle ab initio calculations that predict Weyl cones and Fermi arcs in Co3Sn2S2 and place the Weyl points about 60 meV above EF; these form the non-interacting baseline the paper tests against correlations.","marker":"[50–52]"},{"why":"Angle-resolved photoemission measurement giving the measured bandwidth ratio (about 0.70) and Fermi-level position used to calibrate $U \\approx 4$ eV.","marker":"[63]"},{"why":"Introduces the kinetic-energy spectral-weight formula used in Eq. (1) and the experimental-versus-theoretical kinetic-energy comparison as a correlation diagnostic.","marker":"[67]"},{"why":"Optical-spectroscopy study of LaFeAsO that supplies the Drude-Lorentz analysis and kinetic-energy reduction methodology employed here.","marker":"[69]"},{"why":"DFT+DMFT formalism and the quasiparticle Hamiltonian of Eq. (5) used to compute renormalized bands, Weyl cones, Fermi arcs, and the flat band B1.","marker":"[80, 81]"},{"why":"Provides the Wannier-based tight-binding model and Kubo-Greenwood formula used to compute the quasiparticle optical conductivity peaks T1–T4.","marker":"[91]"},{"why":"Iterative Green's-function method used to calculate the (001) surface Fermi arcs confirming the Weyl state survives.","marker":"[99]"}],"fun_headline_variants":["Correlations flatten band in Weyl semimetal Co3Sn2S2","Optical peak shows flat band in correlated Weyl semimetal","Weyl cones survive, band flattens under correlations","36 meV peak ties flat band to Weyl cones"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Correlations flatten band in Weyl semimetal Co3Sn2S2","Optical peak shows flat band in correlated Weyl semimetal","Weyl cones survive, band flattens under correlations","36 meV peak ties flat band to Weyl cones"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000683,"raw_usage":{"total_tokens":3196,"prompt_tokens":1140,"completion_tokens":2056,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":756,"completion_tokens_details":{"reasoning_tokens":1981}},"tokens_in":756,"tokens_out":2056,"duration_ms":15212,"temperature":1.0,"reasoning_tokens":1981,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T13:39:42.834295+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Angle-resolved photoemission measurement giving the measured bandwidth ratio (about 0.70) and Fermi-level position used to calibrate $U \\approx 4$ eV."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduces the kinetic-energy spectral-weight formula used in Eq. (1) and the experimental-versus-theoretical kinetic-energy comparison as a correlation diagnostic."},{"cited_title":"G., Yuan, R","cited_arxiv_id":null,"evidence_quote":"Optical-spectroscopy study of LaFeAsO that supplies the Drude-Lorentz analysis and kinetic-energy reduction methodology employed here."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the Wannier-based tight-binding model and Kubo-Greenwood formula used to compute the quasiparticle optical conductivity peaks T1–T4."},{"cited_title":"S., Zhang, S","cited_arxiv_id":null,"evidence_quote":"Iterative Green's-function method used to calculate the (001) surface Fermi arcs confirming the Weyl state survives."}],"review_version":1}