{"id":"ab621993-9e3c-4b2e-a696-fa05a2b6bda6","arxiv_id":"2411.10931","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"A DFT-plus-functional-renormalization-group study places FeGe close to competing charge-density-wave, spin-Pomeranchuk, and triplet superconducting instabilities, with superconductivity favored at slightly increased nearest-neighbor interaction.","lead":"Researchers mapped the electronic instabilities of the magnetic kagome metal FeGe using a functional renormalization group calculation built on a realistic band structure. They find the material sits at a multi-phase competition point, and that modestly strengthening nearest-neighbor interactions could favor f-wave superconductivity.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Single-α-band, fixed-kz reduction is the load-bearing assumption; a two-band fRG check would confirm whether the competing-order balance survives.","rationale":"The reader's weakest_assumption identifies exactly the same load-bearing concern: the reduction of the full 3D multi-band problem to a single α band at a fixed kz cut, including the neglect of inter-band K processes and electron-phonon coupling. I agree that this is the most critical step. Every FRG result—the p-CDW, the f-SC phase, the d-Pomeranchuk, and the competition among them—is obtained inside this reduced model. The paper is honest about the limitation, which keeps the verdict CONDITIONAL rather than REJECT, but the material-specific wording of the abstract ('we find FeGe to be in a regime of strong competition...') makes this truncation the hinge of the claim. I did not elevate the strong-coupling issue (U/W ≈ 12) to the main concern because the very small critical temperatures reported in the flow suggest that the effective projected couplings are substantially reduced and the FRG may remain qualitatively controlled; moreover, the authors' a posteriori justification is plausible. The proposed two-band fRG test directly addresses the weakest link and would settle whether the omitted degrees of freedom alter the balance. Because the reader already assigned CONDITIONAL on this basis, the verdict stands unchanged.","tokens_in":29951,"tokens_out":8867,"duration_ms":103346,"concrete_test":"Run the same N-patch fRG on a two-band model containing the α and β bands (the pair with the largest inter-band susceptibility, Fig. S5) at kz,0 = 1.425, with the same cRPA parameters and full momentum-dependent inter-band vertices. If the leading instability at the cRPA point remains the three-Φ condensate (p-CDW/p-SDW) competing with f-SC and the f-SC boundary stays near U1 ≈ 1.5 U1^(0), the single-band truncation is supported; if a K-point order or a different pairing channel becomes leading, the paper's central claim should be revised as a statement about a simplified model, not about FeGe.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim—that FeGe sits near a multi-critical point with f-wave superconductivity emerging for slightly increased nearest-neighbor interaction—depends entirely on the effective model built by projecting the Hubbard-Kanamori interaction onto only the α band at the single kz cut kz,0 ≈ 1.425 (main text and SI Sec. SII). The SI explicitly states that 'competing inter-band processes with wave vector K' are beyond the first approach, and the conclusion concedes that including other bands 'will be crucial' when studying orders competing with the CDW. This is a transparent truncation rather than an internal error, but it is the least secure condition for the material-specific claim: the bare-susceptibility argument that selects the α band as largest (Figs. S4, S7) does not guarantee that the dressed FRG vertex, which couples charge, spin, and pairing channels, remains dominated by this single band at this kz. If the neglected K-point inter-band processes or the other kz Van-Hove cuts host a leading instability, the p-CDW/f-SC/d-Pomeranchuk competition obtained at the cRPA star would not describe FeGe. No code or data is released, so the reader cannot independently assess this reduction from the manuscript alone.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript studies the ordering tendencies of the kagome magnet FeGe using density functional theory plus functional renormalization group. Starting from the ab-initio band structure in the antiferromagnetic phase and cRPA interactions, the authors argue that the α-band at a fixed kz cut (kz,0 ≈ 1.425) captures the dominant intra-band correlations. They project the Hubbard-Kanamori interaction onto this single band and run a 120-patch temperature-flow FRG to map out a phase diagram in the (U, U1) plane. The resulting phase diagram contains ferrimagnetic, d-wave spin-Pomeranchuk, p-wave charge/spin bond density wave, canted magnetic, and f-wave spin-triplet superconducting phases. At the cRPA parameters (white star) the system is in a strongly competing regime, and the authors propose that increasing U1 slightly favors f-wave superconductivity. The paper includes a detailed SI with flow equations, susceptibilities, and Landau analyses.","tokens_in":30141,"tokens_out":8040,"duration_ms":81058,"significance":"The paper provides a first realistic, ab-initio-informed FRG study of a magnetic kagome metal, going beyond simplified single-orbital lattice models. It identifies two universal ingredients—sublattice interference and spin-layer locking from the AFM parent—and shows how they select longitudinal spin orders and equal-spin triplet pairing. The forward nature of the calculation (cRPA inputs, no fitting to the phase diagram) is a strength, as is the explicit documentation of flow equations and the Landau analysis of the multi-Q CDW state. If the single-band reduction is validated, the prediction that FeGe sits near a multi-critical point and that f-wave superconductivity can be induced by tuning U1 is significant and testable by pressure or doping experiments. However, reproducibility is currently limited by the absence of released code or data.","major_comments":[{"comment":"The single-α-band, fixed-kz reduction is load-bearing for the material-specific claims, yet the SI explicitly states that 'competing inter-band processes with wave vector K' are beyond the first approach and the Conclusion concedes that 'it will be crucial to include other bands' when studying orders that compete with a CDW. The bare-susceptibility selection of the α band (Figs. S4, S7) does not by itself guarantee that the dressed FRG vertex, which couples particle-particle and particle-hole channels, remains dominated by this band at this kz. Please provide a two-band check (e.g., including the β band in the susceptibility or a coupled FRG estimate) or a concrete quantitative argument for why inter-band and other-kz processes cannot change the leading instability at the cRPA star.","section":"SI Sec. SI; Conclusion"},{"comment":"The canted antiferromagnetic (FM-xy) phase, which the conclusion says is consistent with experimental observations of the canted phase in FeGe [35–38,57,68], is realized in the phase diagram only for U ≥ 1.75 U^(0) (at U1 = 0.5 U^(0)) and not at the cRPA star (U = U^(0), U1 = U1^(0)). Since the star is the parameter set used to characterize FeGe, the connection to experiment needs clarification: either the cRPA values have uncertainties covering this region, or this phase should be presented as a nearby-parameter prediction rather than a direct finding at the ab-initio parameters.","section":"SI Sec. SV, Fig. S16; Conclusion"},{"comment":"At the cRPA star the SI states that 'we cannot distinguish a clear winner of the competing orders' and describes the regime as one in which p-CDW/p-SDW, f-wave SC, and Pomeranchuk features all grow large, while Fig. 2 assigns this point to p-CDW+p-SDW. Because the abstract's central claim is strong competition rather than a unique order, the criterion used to assign a phase label in this ambiguous region (e.g., eigenvalue gaps or threshold on the leading channel) should be specified explicitly; as written, the main-text phase label overstates the FRG classification at the white star.","section":"Main text Fig. 2; SI Sec. SV"}],"minor_comments":[{"comment":"The Q vectors are defined differently in the main text (Q1=(2π,0), Q2=(-π,-√3π), Q3=(-π,√3π)) and in SI Eq. (S34) (Q1=(0,2π/√3), Q2=(π,-π/√3), Q3=(-π,-π/√3)); please unify the notation so the form factors f_k^(n)=sin(k·Q_n/(4π)) in Eq. (4) are consistent with the eigenvectors shown in Fig. S20.","section":"Main text and SI, Q-vector definitions"},{"comment":"There is a repeated 'where where' in the sentence introducing Eqs. (S27)-(S28), and the main text contains the typo 'ferrimagentism' in the phase-description paragraph.","section":"SI Sec. SIV"},{"comment":"The f-SC region requires U1 ≥ 1.5 U1^(0), a 50% enhancement over the cRPA value; the phrase 'slightly increased nearest-neighbor interaction' in the abstract and conclusion is stronger than the phase diagram supports and should be quantified.","section":"Main text, Fig. 2"},{"comment":"No code or data availability statement is provided, and no repository is referenced. Given that the key single-band reduction cannot be independently assessed from the manuscript alone, releasing the band-projection data and patch-FRG code (or at least the projected dispersion and interaction tables) would substantially strengthen reproducibility.","section":"Data availability"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the scope of a condensed matter theory journal. The dependence on Ref. [56] (a companion preprint) for the DFT band structure and cRPA interactions is acceptable, but the editor may wish to ensure that this companion work is available or published. The lack of released code/data may be a concern for a journal that emphasizes reproducibility; I would encourage the editor to ask for a data/code availability statement. The citation practice appears standard and not self-promotional beyond the necessary companion reference."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's my take. The paper is a solid, honest FRG study. What's new: it's the first FRG calculation on a realistic DFT-derived band structure for FeGe in the AFM phase, and it takes the cRPA interaction parameters without fitting them to the phase diagram. The white star is a forward calculation. The result—FeGe sits near a p-CDW / f-SC / d-Pomeranchuk multiphase boundary, with f-wave triplet SC winning for U1 roughly 1.5 times cRPA—is internally consistent and clearly presented. The SI is unusually transparent: flow equations, loop integrals, patching, and threshold criteria are all there.\n\nWhat the paper does well: it identifies the α band as the dominant susceptibility channel, argues the quasi-2D reduction quantitatively for that band, and shows how sublattice interference and AFM layer polarization suppress transverse spin channels. The connection to the earlier single-orbital kagome Hubbard model is made explicitly without overclaiming.\n\nWhere it gets soft: the single-α-band, fixed-kz cut is load-bearing. The bare susceptibility argument selects the α band, but it doesn't prove that the dressed FRG vertex, which couples charge, spin, and pairing channels, is still dominated by this band at this kz. The authors acknowledge this in the SI—they say inter-band K processes are beyond the first approach, and the conclusion says including other bands will be crucial. That's the right caveat, but it means the material-specific claim is conditional. Electron-phonon coupling is also excluded, which the authors note matters for a 100 K CDW. No code or data is released; independent reproduction is a substantial project. The superconducting suggestion is a phase-diagram statement, not a verified prediction—fine, as long as readers treat it as motivation, and the paper mostly frames it that way.\n\nBottom line: this is a competently done and honest theoretical study. The central competition is plausible for the effective model, and the model reduction is a transparent approximation rather than a hidden error. It deserves a serious referee. For a reader working on kagome magnets or FRG, it is worth citing. I would send it out, with the expectation that referees will push for a clearer statement of what is robust beyond the α-band projection.","headline":"A solid, transparent FRG study of FeGe's AFM phase that finds a plausible multiphase competition, but the fixed-kz single-α-band reduction is the load-bearing approximation and the result is conditional on it.","tokens_in":30762,"tokens_out":2051,"would_cite":true,"duration_ms":23306,"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":"FeGe sits at a three-way competition among p-wave charge order, d-wave magnetic order, and f-wave superconductivity, and a modest increase in nearest-neighbor repulsion tips it toward superconductivity.","keywords":["FeGe","kagome metal","functional renormalization group","f-wave superconductivity","charge density wave","spin Pomeranchuk","sublattice interference","phase competition"],"falsifier":"A three-dimensional multi-band FRG calculation at the cRPA parameters that includes $\\alpha$-$\\beta$ inter-band processes at $K$: if the leading eigenvector of the susceptibility is an inter-band $K$-point order that dominates over the $M$-point $p$-wave CDW, or if raising $U_1$ to 1.5 times its cRPA value no longer produces an $f$-wave pairing divergence, the central scenario fails. Experimentally, if pressure or doping tuned to increase $U_1/U$ does not reveal a superconducting dome next to the CDW, the predicted balance is wrong.","tokens_in":29726,"feed_emoji":"🧲","tokens_out":10834,"duration_ms":103796,"temperature":0.7,"pith_summary":"The paper asks whether the charge density wave in the magnetic kagome metal FeGe can come from electronic correlations alone, and what other orders those correlations would produce. Using a density-functional band structure reduced to the dominant quasi-two-dimensional $\\alpha$ band, the authors run functional renormalization group flows that treat charge, spin, and pairing fluctuations on equal footing. They find that at the interaction values extracted from constrained RPA, FeGe sits in a regime of strong competition among a $p$-wave charge/spin density wave, a $d$-wave spin Pomeranchuk order, and $f$-wave spin-triplet superconductivity. Slightly increasing the nearest-neighbor interaction, to about 1.5 times its ab-initio value, tips the balance toward the superconducting state. If correct, this means FeGe is a promising platform for inducing superconductivity in a magnetic kagome metal by pressure, doping, or strain.","feed_headline":"A nudge to nearest-neighbor repulsion can make FeGe superconducting","feed_subtitle":"Functional renormalization places the magnetic kagome metal on a three-phase border where f-wave triplet pairing wins.","key_machinery":"The machinery is patch functional renormalization group on a quasi-two-dimensional single-band model derived from DFT. The $\\alpha$ band at fixed out-of-plane momentum $k_{z,0} \\approx 1.425$ is patched at 120 Fermi-surface points, and the full multi-orbital Hubbard-Kanamoni interaction is projected onto that band, reducing the vertex to two independent functions $V_{\\uparrow\\uparrow}$ and $V_{\\uparrow\\downarrow}$. The flow with temperature as cutoff tracks all one-loop particle-particle and particle-hole fluctuations simultaneously and signals an instability when the renormalized vertex diverges; the angular structure of the divergent eigenvector identifies the order parameter. Two further ingredients carry the argument: sublattice interference at the Van Hove points, where each $M$ point has weight on only one kagome sublattice, and the Landau free energy for the three $p$-wave CDW order parameters, whose quartic coefficient $\\lambda$ is computed from the band dispersion to be negative, favoring a state with all three order parameters condensed.","core_discovery":"The central claim is that FeGe's interaction-driven Fermi-surface instabilities are dominated by a single band, the $\\alpha$ band, whose low-energy properties are quasi-two-dimensional, with Van Hove points at the projected $M$ points. Starting from the DFT band structure in the antiferromagnetic phase and projecting the extended Hubbard-Kanamoni interaction onto this band, functional renormalization group calculations yield a phase diagram in the on-site ($U$) and nearest-neighbor ($U_1$) interaction plane. At the cRPA values ($U = 5.72$ eV, $U_1 = 2.30$ eV), the system is not deep in any single ordered phase: $p$-wave charge/spin density wave at wave vector $M$, $d$-wave spin Pomeranchuk order, and $f$-wave pairing all grow large, and the authors cannot identify a clear winner. For $U_1$ at or above about 1.5 times the cRPA value, the $f$-wave pairing instability wins for all $U$ studied; this spin-triplet state pairs equal spins on next-nearest-neighbor sites. The paper also argues that the antiferromagnetic layer polarization suppresses unequal-spin scattering, which explains why equal-spin orders dominate, and that the $p$-wave CDW and canted antiferromagnetic phases found are consistent with experiments.","pith_inferences":["If the three-order near-degeneracy is as fragile as computed, then including the omitted $\\beta$ band and inter-band $K$-point processes could shift the phase boundaries, but the qualitative dome of equal-spin triplet pairing next to the CDW region is likely robust because it follows from the layer-polarization suppression of opposite-spin scattering.","The same mechanism suggests a design rule for magnetic kagome metals more broadly: any perturbation that raises the ratio of nearest-neighbor to on-site repulsion, such as chemical pressure, hydrostatic pressure, or ligand substitution, should favor equal-spin triplet superconductivity.","A testable experimental signature of the $d$-wave spin Pomeranchuk phase is a spin-nematic response: anisotropy in the spin susceptibility or in transport that onsets with the density-wave order but without long-range magnetic order.","Since the paper's superconducting $T_c$ is set by electronic scales only, observation of superconductivity in FeGe at a sizable fraction of the CDW temperature would imply that phonons or inter-band processes set the pairing scale."],"forward_implications":["At the cRPA interaction values, FeGe is a near-degenerate multi-phase system: small changes in interaction ratios, strain, or additional couplings can switch the leading instability.","Raising the nearest-neighbor interaction $U_1$ to about 1.5 times its cRPA value, independent of on-site $U$, produces an $f$-wave spin-triplet superconducting instability, so tuning $U_1/U$ is a concrete route toward superconductivity in FeGe.","The $p$-wave CDW with wave vector $M$ and the canted antiferromagnetic order obtained in the quasi-2D model are consistent with the experimentally observed orders, supporting the electronic-interaction scenario for these phases.","Critical temperatures from purely electronic fluctuations are small compared with the bandwidth, so the observed 100 K CDW transition likely requires cooperation with phonons or additional bands; the authors flag this as an open direction."],"supporting_citations":[{"why":"Supplies the DFT band structure and the cRPA interaction parameters that fix the starting point of the phase diagram.","marker":"[56]"},{"why":"Provides the functional renormalization group framework for correlated fermion systems used to compute the interacting vertex.","marker":"[60]"},{"why":"Supplies the N-patch FRG scheme and the projection of instabilities onto Fermi-surface form factors.","marker":"[61]"},{"why":"The kagome Hubbard model FRG study that established the p-wave type density-wave instabilities and competing orders this work generalizes to FeGe.","marker":"[45]"},{"why":"Establishes the sublattice interference mechanism at Van Hove points that the paper identifies in the $\\alpha$ band of FeGe.","marker":"[49]"},{"why":"Reported the discovery of the charge density wave in FeGe and its wave vector connecting van Hove points, the experimental motivation and comparison target.","marker":"[25]"},{"why":"Documents magnetism and charge density wave order in FeGe, providing the experimental canted antiferromagnetic background.","marker":"[26]"},{"why":"Provides experimental evidence for competing itinerant and local spin interactions in FeGe, used as a comparison for the canted order.","marker":"[57]"}],"fun_headline_variants":["Tuning repulsion nudges kagome magnet FeGe toward superconductivity","FeGe: stronger nearest-neighbor repulsion favors f-wave pairing","A repulsion boost tips FeGe from CDW to superconducting","Kagome magnet FeGe: a nudge to superconductivity","FeGe: raising repulsion makes triplet pairing win"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that reducing FeGe to a single quasi-two-dimensional $\\alpha$ band at a fixed out-of-plane momentum $k_{z,0}$, and neglecting inter-band scattering at $K$ and electron-phonon coupling, does not change which instability wins.","fun_headline_variants_meta":{"raw":{"variants":["Tuning repulsion nudges kagome magnet FeGe toward superconductivity","FeGe: stronger nearest-neighbor repulsion favors f-wave pairing","A repulsion boost tips FeGe from CDW to superconducting","Kagome magnet FeGe: a nudge to superconductivity","FeGe: raising repulsion makes triplet pairing win"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000419,"raw_usage":{"total_tokens":2198,"prompt_tokens":1026,"completion_tokens":1172,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":642,"completion_tokens_details":{"reasoning_tokens":1084}},"tokens_in":642,"tokens_out":1172,"duration_ms":9110,"temperature":1.0,"reasoning_tokens":1084,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T19:08:50.404210+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A three-dimensional multi-band FRG calculation at the cRPA parameters that includes $\\alpha$-$\\beta$ inter-band processes at $K$: if the leading eigenvector of the susceptibility is an inter-band $K$-point order that dominates over the $M$-point $p$-wave CDW, or if raising $U_1$ to 1.5 times its cRPA value no longer produces an $f$-wave pairing divergence, the central scenario fails. Experimentally, if pressure or doping tuned to increase $U_1/U$ does not reveal a superconducting dome next to the CDW, the predicted balance is wrong.","supporting_citations":[{"cited_title":"L., Platt, C","cited_arxiv_id":null,"evidence_quote":"The kagome Hubbard model FRG study that established the p-wave type density-wave instabilities and competing orders this work generalizes to FeGe."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes the sublattice interference mechanism at Van Hove points that the paper identifies in the $\\alpha$ band of FeGe."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Reported the discovery of the charge density wave in FeGe and its wave vector connecting van Hove points, the experimental motivation and comparison target."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Documents magnetism and charge density wave order in FeGe, providing the experimental canted antiferromagnetic background."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides experimental evidence for competing itinerant and local spin interactions in FeGe, used as a comparison for the canted order."}],"review_version":1}