{"id":"48303815-a8cf-4d72-ad8c-f48a65646ad3","arxiv_id":"1908.10901","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"In a three-orbital model treated with DMFT, dynamical Hund's-metal correlations boost boson-mediated superconductivity and enhance the orbital selectivity of the gaps, contrary to the quasiparticle picture.","lead":"The paper studies a model of iron-based superconductors where pairing comes from boson exchange and electrons are dressed by strong correlations. It finds that the special 'Hund's metal' correlations make superconductivity more robust, not less, compared with an ordinary correlated metal of similar strength.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central claim depends on the assumption that the pairing vertex is not renormalized by Coulomb repulsion; a vertex-consistent calculation is needed to confirm the Hund's-metal enhancement.","rationale":"The reader's verdict is conditional primarily on the unrenormalized pairing vertex, and this is exactly the point I find most load-bearing. The calculation correctly dresses the single-particle Green's functions with the DMFT self-energy, and the comparison against the quasiparticle approximation is well posed and internally consistent. The weak point is that the irreducible pairing interaction is taken to be the bare g for all values of U and J_H. In the fulleride context this is justified by the local nature of the phonon-mediated attraction and by the freezing of charge fluctuations. For non-local spin/orbital fluctuation mediators in iron-based superconductors, the same argument is not automatic, and the irreducible particle-particle vertex will contain repulsive contributions from U and J_H. Since the central claim is a comparison between two correlated regimes, a U-dependent vertex renormalization could reduce or reverse the predicted enhancement of U_c with J_H. The authors acknowledge this as a limitation, but they do not provide a calculation that protects the main result against it. Therefore the CONDITIONAL verdict is appropriate; the requested self-consistent vertex calculation is the natural next step. I do not see a reason to change the reader's verdict.","tokens_in":10257,"tokens_out":6676,"duration_ms":73208,"concrete_test":"Compute the effective local irreducible vertex in the s-wave singlet particle-particle channel from the same DMFT impurity model, for example by measuring the two-particle Green's function and inverting the Bethe-Salpeter equation. Then solve the linearized Eliashberg equation with the attractive bare g plus the U/J_H-induced vertex, and compare the resulting U_c(J_H) curve with Fig. 2d. A minimal version is to replace g with an effective coupling g_eff = g - Gamma_pp(0,0) using the static local vertex; check whether the sign of dU_c/dJ_H changes. If the enhancement survives, the central claim is robust; if it is suppressed, the unrenormalized-vertex assumption is the reason.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central mechanism assumes that the pairing interaction g is not renormalized by the Coulomb repulsion, so that fully dressed electrons pair with the bare coupling. This is the load-bearing assumption. In the model, the particle-particle propagator is dressed with the Hubbard/Hund self-energy, but the irreducible pairing vertex remains the bare g at all U and J_H. For the fulleride case (Ref. [3]) this is justified because the phonon-mediated attraction is an inverted Hund's coupling local in spin/orbital space, and U only freezes charge fluctuations. For non-local spin/orbital-fluctuation mediators relevant to iron-based superconductors, the same argument does not hold, and the irreducible vertex in the pairing channel will generically contain repulsive components of order U that may counteract the attractive g. Since the central claim is a quantitative comparison between Hund's metal and ordinary correlated metal, a U-dependent vertex renormalization can change the outcome: if the effective pairing interaction is progressively suppressed with U, the predicted enhancement of U_c with J_H (Fig. 2d) may be reduced or reversed. The authors acknowledge this limitation explicitly, but the main result is not protected by an independent calculation.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript studies a three-orbital model motivated by iron-based superconductors, combining DMFT for the correlated normal state with a BCS treatment of an intraorbital attractive pairing interaction of strength g. The authors compare the full frequency-dependent DMFT solution with a quasiparticle approximation matched by the same quasiparticle weights Z_mu, and find that in the Hund's-metal regime (large J_H/U) superconductivity survives up to much larger U than in the quasiparticle picture. They attribute this to the redistribution of spectral weight into an energy window around the Fermi level of order J_H, and they also show that the orbital dependence of the gaps becomes strongly selective in this regime, which they connect to experiments in FeSe.","tokens_in":10463,"tokens_out":18547,"duration_ms":155165,"significance":"If the central mechanism is correct, the paper provides a concrete and testable scenario in which Hund's-metal correlations cooperate with a bosonic pairing glue, going beyond quasiparticle-based descriptions that are common in the iron-based superconductivity literature. The calculation is transparent and free of experimental fitting: the phase diagram is generated from fixed U, J_H, and g, and the DMFT-versus-QP comparison is a controlled diagnostic based on matching Z. The prediction of orbital-selective gap enhancement that is not captured by a quasiparticle approximation is falsifiable. The main limitation is that the irreducible pairing vertex is assumed bare, so the quantitative claim is conditional on that assumption.","major_comments":[{"comment":"The central result rests on the assumption that the pairing vertex is not renormalized by U and J_H, so that fully dressed electrons still feel the bare coupling g. The manuscript explicitly acknowledges this and borrows the justification from alkali-fulleride physics (Ref. [3]), where the bosonic attraction is an inverted Hund's coupling that is local in spin/orbital space and decoupled from charge fluctuations. For the nonlocal spin/orbital-fluctuation mediators relevant to iron-based superconductors, the irreducible vertex in the pairing channel will generically acquire repulsive components of order U that can counteract the attractive g. Because the headline claim is a quantitative comparison between a Hund's metal and an ordinary correlated metal with the same Z, the U_c(J_H) enhancement in Fig. 2d could be reduced or reversed once vertex corrections are included. I therefore ask for either a vertex-consistent calculation (for example, including a repulsive U in the pairing channel or a ladder renormalization) or a controlled estimate that brackets the magnitude of the vertex correction; in the interim, the conclusion should be explicitly qualified as conditional on the bare-vertex assumption.","section":"Assumptions paragraph (main text)"},{"comment":"The abstract's central comparison is with an ordinary correlated metal having the same effective mass renormalization and the same density of states at the Fermi level. The numerical comparison, however, matches only the quasiparticle weights Z_mu between the full DMFT solution and the QP approximation. The full DMFT spectral function contains incoherent spectral weight that has no counterpart in the QP approximation, so the two cases are not guaranteed to have the same A(omega=0). If the Hund's-metal spectral-weight redistribution contributes at the Fermi level, part of the enhanced pairing susceptibility would come from a larger Fermi-level DOS rather than from finite-frequency dynamical correlations alone. The manuscript should report the local DOS at omega=0 for the cases compared in Fig. 3, or explicitly adjust the claim if the DOS differs.","section":"Abstract and Fig. 3"},{"comment":"The main text states that no cutoff is introduced in the pairing interaction, yet the gaps in Fig. 2 vanish at a finite U_c even for parameters where the normal state remains metallic with nonzero Fermi-level DOS and Im Sigma(0)=0. At T=0 with an attractive constant g, the BCS gap equation has a nonzero solution for any positive Fermi-level DOS; hence the plotted U_c must be a numerical closure threshold set by an implicit frequency/energy cutoff or by a convergence criterion. This should be stated explicitly: define the criterion used to declare Delta=0 and specify the frequency grid or cutoff entering the gap equation, so that the U_c(J_H) comparison in Fig. 2d is reproducible.","section":"Fig. 2 and 'BCS solutions' paragraph"}],"minor_comments":[{"comment":"The title and abstract contain the typo 'boson-media ted' (should be 'boson-mediated'); please correct it.","section":"Title and abstract"},{"comment":"The paper repeatedly refers to the supplemental material for the cutoff analysis and model details; if the SM is not included with the arXiv posting, readers cannot verify the robustness claim. Please ensure the SM is publicly available or summarize the key cutoff results in the main text.","section":"Supplemental material reference [48]"},{"comment":"Reference [25] contains a malformed author list ('J. de' Medici, L.and Mravlje') that should be corrected.","section":"Reference [25]"},{"comment":"There are a few typographical errors in the text, including 'stablize' in the final section and 'distintive' near Fig. 4; these should be corrected in the revision.","section":"Conclusions"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is within the journal's scope and the numerical work is solid, but the central quantitative claim is conditional on the bare-vertex assumption. I would not reject, but I would request a substantive response to the vertex-consistency concern before acceptance; the other two major comments are also addressable within the manuscript's scope."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The thing to know about this paper is that it gives a concrete mechanism by which Hund's metal physics boosts boson-mediated superconductivity beyond what a quasiparticle picture predicts, and it makes a good case that this explains why phenomenological fits to FeSe required such large orbital-selective renormalizations. The calculation is internally consistent and the comparison with a quasiparticle approximation is well controlled by matching Z values. This is a real contribution to the iron-based superconductors discussion.\n\nWhat is actually new is the emphasis on finite-frequency spectral weight. The authors show that in a Hund's metal, with JH/U ~ 0.25, the spectral weight piles up in an energy window of order JH around the Fermi level, and that this weight contributes to the Cooper bubble. For the same Z and the same density of states at the Fermi level, the full DMFT gaps are much larger than the QP gaps, and Uc increases with JH in DMFT while it decreases in QP. The orbital-selective gap ratio also grows with U in the Hund's metal regime, which they connect to the extreme Z differentiations that appeared in FeSe analyses. That connection is interpretive, not a fit, but it is suggestive and clearly argued.\n\nThe soft spot is the one the authors themselves flag in the text: they assume the pairing vertex is not renormalized by the Coulomb repulsion, borrowing the argument from alkali fullerides where the phonon-induced attraction is an inverted Hund's coupling. For non-local spin/orbital fluctuation mediators, that argument does not carry over, and the irreducible vertex in the pairing channel will generically contain repulsive components of order U. So the central quantitative claim—the enhancement of Uc with JH—could be reduced or reversed if the vertex renormalization is treated consistently. I agree with the stress-test note on this; it is a genuine load-bearing assumption, not a technicality. A second, minor issue is that g = 2 eV puts the gaps around half the bandwidth, so the BCS gap equation is used in a strong-coupling regime where one would want a cutoff study; the authors cite a supplemental cutoff analysis, which I could not inspect, but the vertex issue is the bigger one.\n\nBottom line: this is a serious paper by people who know the field. The mechanism is plausible, the numerics look careful, and the connection to FeSe is worth discussing. It deserves peer review, but the referees should press for a self-consistent treatment of the pairing vertex or at least an honest assessment of the range of validity of the bare-vertex approximation. I would not desk-reject it. If I worked on iron-based superconductors, I would cite it.","headline":"A credible mechanism paper for Hund's-metal superconductivity, well executed with a controlled quasiparticle comparison, but the central enhancement rests on a bare pairing vertex that needs a self-consistent check.","tokens_in":10990,"tokens_out":3823,"would_cite":true,"duration_ms":35775,"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":"Superconductivity survives in Hund's metals much better than in ordinary correlated metals with the same quasiparticle weight and density of states.","keywords":["Hund's metal","superconductivity","iron-based superconductors","dynamical mean-field theory","orbital-selective pairing","spectral weight redistribution","boson-mediated pairing","strongly correlated electrons"],"falsifier":"Compute the same three-orbital model with the pairing vertex renormalized by the local Coulomb repulsion—for instance by including ladder vertex corrections in the particle-particle channel—and compare the superconducting gap at fixed quasiparticle weight; if the gap collapses to the quasiparticle value at large $J_H/U$, the spectral-weight mechanism is not the operative one.","tokens_in":1681,"feed_emoji":"⚡","tokens_out":3899,"duration_ms":116249,"temperature":0.7,"pith_summary":"The paper argues that a Hund's metal—a multiorbital bad metal whose correlations are shaped strongly by the Hund's coupling rather than solely by the local Coulomb repulsion—is not an obstacle to boson-mediated superconductivity but an asset. It studies a three-orbital model inspired by iron-based superconductors, pairing fully dressed electrons through a constant coupling $g$ while the single-particle propagators carry the full frequency-dependent self-energy from dynamical mean-field theory. The result is that the superconducting gap survives at interaction strengths where a quasiparticle approximation with the same mass renormalization and density of states predicts zero gap. The result matters because it reconciles two pictures usually opposed: strong local correlations and itinerant boson-exchange pairing. The operative mechanism is the spectral weight that Hund's correlations push into an energy window of order $J_H$ around the Fermi level, where it joins the pairing glue.","feed_headline":"Hund's metal correlations boost superconductivity, not kill it","feed_subtitle":"Spectral weight piled near the Fermi energy pairs with the bosonic glue, preserving gaps even at strong repulsion.","key_machinery":"The load-bearing object is the orbital- and frequency-dependent self-energy $\\Sigma_{\\mu\\mu}(i\\omega_n)$ computed by dynamical mean-field theory and inserted into the Cooper bubble of the BCS gap equation, so that Cooper pairs are formed by fully dressed electrons. Its companion is the quasiparticle weight $Z_\\mu = (1 - \\partial \\Im \\Sigma_{\\mu\\mu}/\\partial \\omega_n)^{-1}$, which the paper uses as the benchmark for 'the same degree of correlation.' The comparison that isolates the mechanism is the full DMFT calculation versus a quasiparticle approximation that keeps only the low-frequency limit of the self-energy: the two give nearly identical gaps at small $J_H$, but in the Hund's-metal regime the finite-frequency part of the self-energy—spectral weight redistributed into an energy window of order $J_H$ around the Fermi level—feeds the particle-particle channel and boosts pairing.","core_discovery":"The central discovery is that a Hund's metal renormalizes the Cooper-pair propagator in a way a standard quasiparticle description misses, and that the missing piece actively favors pairing. Concretely, solving the BCS gap equation with DMFT-dressed Green's functions at four electrons in three orbitals, the critical interaction $U_c$ at which the gaps close grows with $J_H/U$, whereas in the quasiparticle approximation $U_c$ shrinks as $J_H$ grows. For comparable quasiparticle weights $Z_\\mu$, the small-$J_H$ regime shows Mott-like bands at an energy scale of order $U$ and gaps that vanish near $U_c\\sim W$, while the Hund's-metal regime concentrates spectral weight within an energy range of order $J_H$ of the Fermi level and preserves sizeable gaps up to much larger $U$. The same dynamical spectral-weight redistribution also amplifies the orbital selectivity of the gaps, $|\\Delta_{xz}|/|\\Delta_{xy}|$, even when the quasiparticle weights themselves are nearly isotropic; the paper reads this as explaining why earlier quasiparticle-based fits to FeSe required extreme orbital-selective $Z$'s.","pith_inferences":["If the mechanism is generic, it suggests a materials-design rule: a moderately correlated metal with a large Hund's coupling and a boson mode in the same energy window should be a better superconductor than an otherwise similar Fermi liquid, so searches for new superconductors should consider Hund's metals even when their resistivity looks bad.","The transfer to iron-based superconductors is non-trivial because the pairing glue there is non-local spin or orbital fluctuations; a natural extension is a cluster or diagrammatic calculation in which the pairing vertex itself is renormalized by $U$, which would test whether the unrenormalized-vertex assumption survives beyond local fullerenes.","A quantitative prediction the paper does not make explicit is that the benefit should be largest when the boson frequency or pairing cutoff is comparable to or larger than $J_H$, and should disappear for very low-energy bosons—an experimentally checkable axis if a material's phonon spectrum and Hund's coupling can be tuned independently."],"forward_implications":["The critical repulsion needed to destroy superconductivity increases with the Hund's coupling in the full dynamical calculation, so Hund's-metal materials can remain superconducting even when they are bad metals with strongly suppressed quasiparticle weights.","Orbital-selective superconducting gaps emerge from dynamical correlations alone, so phenomenological fits to FeSe that require extremely orbital-selective quasiparticle weights can be reinterpreted as single-parameter proxies for this finite-frequency physics.","The mechanism applies to any bosonic pairing channel whose coupling is not renormalized by the local Coulomb repulsion, including phonons and spin or orbital fluctuations of the fulleride type.","In the same Hund's-metal regime, finite-frequency correlations may also enhance particle-hole instabilities such as nematicity, a direction the paper reports as preliminary."],"supporting_citations":[{"why":"Provides the fulleride result that a boson-mediated pairing vertex is not renormalized by $U$ when the coupling involves only local spin and orbital degrees of freedom, the premise imported into the Hund's-metal model.","marker":"[3]"},{"why":"Documents the redistribution of spectral weight into an energy window of order $J_H$ around the Fermi level in Hund's metals, the mechanism the paper invokes.","marker":"[15]"},{"why":"Establishes the orbital-selective Hund's-metal crossover and the quasiparticle-weight behavior used to define the same degree of correlation.","marker":"[17]"},{"why":"Describes the long-tail suppression of quasiparticle weights in Hund's metals, the benchmark against which the gap results are compared.","marker":"[32]"},{"why":"Supplies the experimental FeSe superconducting-gap anisotropies that motivate the orbital-selective-gap analysis.","marker":"[41]"},{"why":"Gives the three-orbital tight-binding model whose Fermi-surface pockets the paper adapts.","marker":"[49]"},{"why":"Provides a complementary random-phase-approximation treatment of spin-mediated pairing on a correlated electronic structure, against which the present approach is framed.","marker":"[53]"}],"fun_headline_variants":["Hund's metal turns repulsion into pairing fuel","Spectral weight shift: Hund's metal saves superconductivity","Hund's metal: gaps survive where quasiparticles fail","Orbital-selective gaps without extreme Z's: Hund's metal","Beyond quasiparticles: Hund's metal enhances pairing"],"cache_read_input_tokens":13184,"weakest_assumption_plain":"The whole claim rests on assuming that the boson-mediated pairing interaction is not weakened by the local Coulomb repulsion, so fully dressed electrons still feel the bare coupling $g$; if $U$ also renormalizes the pairing vertex, the Hund's-metal enhancement could disappear.","fun_headline_variants_meta":{"raw":{"variants":["Hund's metal turns repulsion into pairing fuel","Spectral weight shift: Hund's metal saves superconductivity","Hund's metal: gaps survive where quasiparticles fail","Orbital-selective gaps without extreme Z's: Hund's metal","Beyond quasiparticles: Hund's metal enhances pairing"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000272,"raw_usage":{"total_tokens":1607,"prompt_tokens":893,"completion_tokens":714,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":509,"completion_tokens_details":{"reasoning_tokens":631}},"tokens_in":509,"tokens_out":714,"duration_ms":7157,"temperature":1.0,"reasoning_tokens":631,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T10:30:48.078494+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the same three-orbital model with the pairing vertex renormalized by the local Coulomb repulsion—for instance by including ladder vertex corrections in the particle-particle channel—and compare the superconducting gap at fixed quasiparticle weight; if the gap collapses to the quasiparticle value at large $J_H/U$, the spectral-weight mechanism is not the operative one.","supporting_citations":[{"cited_title":"Hardy, A","cited_arxiv_id":null,"evidence_quote":"Establishes the orbital-selective Hund's-metal crossover and the quasiparticle-weight behavior used to define the same degree of correlation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the three-orbital tight-binding model whose Fermi-surface pockets the paper adapts."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides a complementary random-phase-approximation treatment of spin-mediated pairing on a correlated electronic structure, against which the present approach is framed."}],"review_version":1}