{"id":"a649b433-4aab-42da-880c-0198cf5703fd","arxiv_id":"2411.16625","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":8,"one_line_summary":"The upward curvature of Hc2(T) in CsV3Sb5 is attributed to Fermi velocity anisotropy from van Hove singularities, not to multiple superconducting gaps.","lead":"This paper reports measurements of the upper critical field of the kagome superconductor CsV3Sb5 and shows that its anomalous upward-bending temperature dependence can be explained by anisotropic Fermi velocity arising from nearby van Hove singularities. Proton irradiation that smears those singularities restores conventional behavior, supporting the explanation.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Irradiation control does not uniquely implicate van Hove smearing: the same disorder that suppresses Hc2 curvature also drives any anisotropic or multiband state toward the dirty isotropic limit, so the corroborating experiment is degenerate.","rationale":"The reader's weakest_assumption is correct and is the most load-bearing issue. The paper's positive contribution—new data and two clean-limit models that both require large Fermi-velocity anisotropy—is credible and worth publishing in conditional form. However, the central causal attribution ('originating from vHs') goes beyond what the data constrain. The two-band fit already requires r_v = 57.6; the single-band vHs model achieves a similar fit with κ_c ≈ 10; gap anisotropy changes the predictions only modestly. Without independent Fermi-velocity measurements or a quantitative disorder model, the conclusion is underdetermined. The irradiation experiment would be decisive if it distinguished vHs smearing from generic dirtying, but it does not: the measured residual resistivity increases by roughly a factor of 30, which would drive any clean anisotropic or multiband superconductor toward the dirty isotropic limit. The paper does not rule out this alternative, and the Supplementary's own discussion of Tc suppression invokes anisotropic-gap averaging rather than vHs smearing, creating an internal tension. This concern does not warrant rejection: the phenomenology is reproducible across two crystals and multiple techniques, and the emphasis on large vF anisotropy is likely robust. Conditional acceptance with a request for a dirty-limit counter-analysis and explicit parameter uncertainties remains appropriate.","tokens_in":29365,"tokens_out":4384,"duration_ms":46607,"concrete_test":"","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that the upward curvature of Hc2(T) in pristine CsV3Sb5 is caused by Fermi-velocity anisotropy originating from nearby van Hove singularities. The decisive corroboration is the proton-irradiation experiment (End Matter, Fig. 3(d)): after 6e16 p/cm2, rho0 rises from ~1.9 to ~58 μΩ cm and Tc falls from 3.5 to 2.0 K, and Hc2(T) reverts to a conventional Maki-de Gennes dirty-limit shape. The paper interprets this as smearing of the vHs, but this is not the only—nor the simplest—explanation. At this disorder level, any mechanism producing upward curvature in the clean limit—two-band effects (Eq. 1 with r_v = 57.6) or gap anisotropy—will be driven toward the dirty isotropic limit; the same data would look exactly like Fig. 2(c) even if vHs played no role. No quantitative model connects the irradiation dose to a smearing width of the vHs or to the reduction of Fermi-velocity anisotropy; the dirty-limit fit is applied post hoc. The test is therefore degenerate: it confirms that disorder destroys the clean-limit anisotropy, but not that the anisotropy has a vHs origin. The vHs attribution rests on fitted κ_c, t_z/E_vH, and r_m with no independent determination of these parameters from DFT or ARPES, and the Supplementary itself ascribes the Tc suppression to anisotropic-gap averaging rather than to vHs smearing, weakening the internal consistency of the irradiation story.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports measurements of the upper critical field H_c2(T) of single-crystal CsV3Sb5 for H||c and H||ab, in pristine and proton-irradiated samples. The pristine data show pronounced upward curvature for both orientations, with zero-temperature values of ~6.0 T (ab) and ~1.2 T (c), and a temperature-dependent anisotropy that falls from ~8.5 near Tc to ~5.5 at low temperatures. The authors fit the data with two theoretical models: a two-band Eilenberger model (Eq. 1) and a single-band model in which the Fermi level is close to van Hove singularities, with optional gap anisotropy (Eq. 2). Both fits reproduce the data only if a large in-plane Fermi-velocity anisotropy is assumed: the two-band fit gives r_v = 57.6, and the vHs fit requires a large cutoff parameter kappa_c with the Fermi level crossing the van Hove energy. After irradiation to 6x10^16 p/cm2, the upward curvature is suppressed and H_c2(T) reverts to a conventional dirty-limit shape. The authors interpret this as smearing of the vHs and conclude that Fermi-velocity anisotropy originating from vHs, rather than multi-band or gap-anisotropy effects, drives the anomalous H_c2(T).","tokens_in":29787,"tokens_out":6442,"duration_ms":61904,"significance":"If the conclusion were established, the paper would provide a valuable resolution of a debated point in kagome superconductors and would tie an observable superconducting property to the proximity of van Hove singularities. The experimental data are of high quality: two crystals give reproducible results, the irradiation dose series is a useful control, and the Supplement contains explicit analytical formulas for H_c2 in both models, including the H_c2(0)/H_GL ratio that is checked against the measured enhancement. However, the central attribution to vHs is currently underdetermined. The models are fitted to the same data they explain, and the irradiation experiment cannot distinguish vHs smearing from the generic dirty-limit suppression of any clean-limit anisotropy. The paper's own central statement that both approaches require a large Fermi-velocity anisotropy is well supported, but the further step from 'large anisotropy is needed' to 'the anisotropy originates from vHs' requires additional evidence. The manuscript would be more convincing if that step were either demonstrated quantitatively or presented as a plausible interpretation rather than the definite conclusion.","major_comments":[{"comment":"The irradiation experiment is presented as the decisive corroboration of vHs smearing, but it is degenerate as a test. At the dose of 6x10^16 p/cm2 the residual resistivity rises from ~1.9 to ~58 micro-ohm cm and Tc falls from 3.5 to 2.0 K; at this disorder level any clean-limit mechanism that produces upward curvature, including the two-band model of Eq. (1) with r_v = 57.6, will be driven toward the dirty isotropic Maki-de Gennes limit. Since the two-band fit to the pristine data is acknowledged to be successful, the recovery of a conventional H_c2(T) shape is expected even if vHs play no role. No quantitative relation is provided between the irradiation dose (or Delta-rho_0) and either a vHs smearing width or a reduction of the Fermi-velocity anisotropy. The experiment therefore confirms that disorder destroys the clean-limit anisotropy, but it does not uniquely implicate vHs as the origin of that anisotropy.","section":"End Matter, Fig. 3(d); main text Fig. 2(c)"},{"comment":"The vHs model is fitted to the same H_c2(T) data that it is used to explain. The upward curvature in the model is controlled by kappa_c = K_c/p_u0 and t_z/E_vH, with the fit requiring kappa_c >> 1 and a Fermi level that crosses the van Hove energy; the mass ratio r_m and the gap-anisotropy constants c_u and c_v add further freedom. The paper does not provide independent determinations of kappa_c, r_m, and t_z/E_vH from DFT, ARPES, or quantum oscillations, and it explicitly leaves the physical realization of the two-band model's 'first' band unspecified. The fits demonstrate consistency with a vHs scenario rather than establishing that vHs are the cause. An independent constraint on these parameters, or a comparison of the fitted Fermi-surface parameters with those measured by quantum oscillations or ARPES, is needed before the title-level claim is load-bearing.","section":"Fig. 1(d) and Supplement Eqs. (B8), (B16)"},{"comment":"The irradiation interpretation contains an internal tension. The Supplement attributes the dose-dependent suppression of Tc to averaging of an anisotropic gap by impurity scattering, stating that in an anisotropic s-wave superconductor impurity scattering can average out the anisotropic gap, while the main text attributes the recovery of the conventional H_c2(T) shape to smearing of the vHs. These mechanisms are not mutually exclusive, but as written the paper invokes one disorder effect (gap averaging) to explain Tc suppression and a different disorder effect (vHs smearing) to explain the change in H_c2(T), without a model showing that the same disorder produces both at the relevant dose. The authors should either reconcile these explanations quantitatively or soften the vHs-smearing claim.","section":"Supplement, 'Estimation of dimensionless scattering parameter'"}],"minor_comments":[{"comment":"The Supplement contains numerous typographical errors, including 'FGG.' for 'FIG.', 'Gn' for 'In', and 'Grradiation' for 'Irradiation', which should be corrected before publication.","section":"Supplement, throughout"},{"comment":"The normalization of the phase diagram uses H_c2,c^GL = 0.6 T and H_c2,ab^GL = 4.8 T, but the corresponding slopes dH_c2/dT at Tc for the pristine sample are not given in the main text; stating them would make the normalization and the quoted anisotropy values easier to reproduce.","section":"Fig. 1(c) caption and main text"},{"comment":"References [37] and [38] are arXiv preprints; if published versions now exist, the published references should be cited, since the text relies on [37] for the ARPES gap-anisotropy values used in the discussion.","section":"References [37], [38]"}],"recommendation":"major_revision","confidential_remarks":"This is a solid experimental paper with a useful comparative modeling exercise, but the conclusion as stated in the title and abstract overreaches the evidence. The irradiation control cannot discriminate vHs smearing from the generic dirty-limit suppression of any clean-limit anisotropy, and the vHs parameters are not independently constrained. I recommend major revision with either a quantitative disorder model connecting the irradiation dose to vHs smearing or a more modest conclusion that explicitly presents the vHs attribution as one consistent interpretation rather than the established origin."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a useful paper. It reports new Hc2(T) measurements on pristine and proton-irradiated CsV3Sb5, including a dose series, and a single-band quasi-2D van Hove model that captures the upward curvature in both field orientations. The two-band fit and the vHs fit both require large Fermi-velocity anisotropy, and the authors are honest that the detailed gap structure is secondary. That is a real insight and it aligns with ARPES and with their earlier magnetotransport work.\n\nWhat is genuinely new: the irradiation experiment showing progressive loss of upward curvature with dose, and the extension of prior 2D vHs Hc2 calculations to include c-axis dispersion and gap anisotropy. The closed-form expressions for Hc2(0)/HGL are nice, and the consistency check against Hc2(0)/HGL and against the DFT-derived tz/EF for the Sb sheet gives the model some anchor.\n\nThe soft spots are real but not fatal. First, the irradiation result is degenerate as a test. At 6e16 p/cm2 the residual resistivity jumps from 1.9 to 58 micro-ohm cm and Tc drops to 2 K; any mechanism that produces upward curvature in the clean limit—two-band effects, gap anisotropy, or vHs—will be driven toward the dirty isotropic limit. The paper interprets this as smearing of the vHs, but no quantitative model connects dose to a vHs smearing width or to the reduction of anisotropy. Second, the vHs attribution rests on fits with several free parameters (kappa_c, tz/EvH, rm, cu, cv) to the very data they explain; there are no error bars and no independent determination of these parameters from DFT or ARPES. Third, the supplementary itself attributes the Tc suppression to anisotropic-gap averaging rather than to vHs smearing, which sits a little uneasily with the main-text story.\n\nNone of this sinks the paper. The central claim that large Fermi-velocity anisotropy is required is robust and is the take-home message. The vHs origin is plausible and probably right for this material, but it is not uniquely established. I would send it to a serious referee; the referee should push for uncertainty quantification and a more quantitative irradiation model, but the paper deserves the time. I'd cite it.","headline":"Solid new data and a plausible vHs-based mechanism for Hc2(T) in CsV3Sb5, but the irradiation \"test\" is degenerate and the vHs attribution rests on fitted parameters.","tokens_in":30387,"tokens_out":2046,"would_cite":true,"duration_ms":19772,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The upward curvature of the upper critical field in the kagome superconductor CsV3Sb5 traces to Fermi-velocity anisotropy produced by van Hove singularities, not to multiple superconducting bands.","keywords":["kagome superconductor","CsV3Sb5","upper critical field","van Hove singularity","Fermi velocity anisotropy","multiband superconductivity","proton irradiation","dirty limit"],"falsifier":"Measure $H_{c2}(T)$ on a series of CsV3Sb5 crystals irradiated to increasing doses while tracking both the residual resistivity and the persistence of the CDW/van Hove signatures (for example with angle-resolved photoemission or quantum oscillations): if the upward curvature survives at doses where sharp saddle-point dispersion is still present, the van Hove mechanism is supported, whereas if the curvature disappears as soon as the sample becomes dirty even while the van Hove signatures remain, the alternative explanation wins.","tokens_in":29181,"feed_emoji":"🧲","tokens_out":15292,"duration_ms":117203,"temperature":0.7,"pith_summary":"CsV3Sb5, a kagome superconductor with van Hove singularities close to the Fermi level, shows an upper critical field $H_{c2}(T)$ that curves upward for both in-plane and c-axis fields, reaching about 6.0 T and 1.2 T at low temperature. The paper argues that this shape is not a fingerprint of multiband or multigap superconductivity. Instead, it shows that both a two-band model and a single-band model with van Hove singularities fit the data only if the Fermi velocity is strongly anisotropic, and that the detailed gap structure plays a secondary role. Proton irradiation, which adds scattering and smears the van Hove singularities, progressively removes the upward curvature and restores the conventional dirty-limit behavior, supporting the same conclusion. If right, the result redirects attention from pairing symmetries to Fermi-surface geometry when interpreting critical-field data in this material family.","feed_headline":"Kagome superconductor's critical field curve points to van Hove anisotropy","feed_subtitle":"Proton irradiation flattens the curve by smearing van Hove singularities; gap structure barely matters.","key_machinery":"The central object is a quasi-classical, Eilenberger-based equation for the upper critical field written for a single band whose Fermi surface has nearly hyperbolic sections near van Hove saddle points, Eq. (2) of the paper. The Fermi-surface averaging in that equation is governed by the effective-mass ratio $r_m$, the cutoff $\\kappa_c$ relative to the distance from the van Hove point, and the c-axis hopping $t_z$; an anisotropic gap factor $\\Omega(\\mathbf{k}_F)$ tests the role of gap structure. A companion two-band model with warped cylindrical Fermi surfaces reproduces the same data only with a Fermi-velocity ratio $r_v \\simeq 57.6$, showing that large velocity anisotropy, not gap multiplicity, is the common ingredient. The same quasiparticle averaging explains why the c-axis $H_{c2}$ curvature is the more pronounced one: in the van Hove model the c-axis ratio $H_{c2}(0)/H_{\\mathrm{GL}}$ grows with a logarithmic large factor, while the in-plane ratio stays of order one.","core_discovery":"The central claim is that the anomalous upward curvature of $H_{c2}(T)$ in CsV3Sb5 is caused by the strong anisotropy of the Fermi velocity that arises because the Fermi level sits close to van Hove singularities. The paper states that both a multi-band/multi-gap description and a single-band van Hove description require a large Fermi-velocity anisotropy to account for the data, while the detailed gap structure is of secondary importance. In the van Hove model the c-axis curvature is naturally stronger than the in-plane curvature, and the zero-temperature value can exceed the linear Ginzburg-Landau extrapolation by a factor of about 2.3. Irradiation with 5-MeV protons at $6\\times 10^{16}$ p/cm$^2$ increases the residual resistivity from about 1.9 to 58 $\\mu\\Omega$ cm, lowers $T_c$ from 3.5 K to 2.0 K, and converts $H_{c2}(T)$ to a conventional Maki-de Gennes dirty-limit shape, which the paper interprets as the smearing of the van Hove singularities by disorder.","pith_inferences":["A sharper test of the van Hove-smearing interpretation would be irradiation at intermediate doses where residual resistivity rises and $T_c$ drops but the CDW anomaly is still visible; upward curvature persisting there, and disappearing only as the van Hove signatures vanish, would confirm the mechanism.","If Fermi-velocity anisotropy from van Hove singularities is the cause, uniaxial strain or pressure that tunes the separation between the Fermi level and the van Hove energy should continuously modulate the strength of the upward curvature; this is a testable prediction beyond the paper.","The clean-limit models leave open how much of the irradiation effect is purely pair-breaking scattering; a model interpolating between clean and dirty limits on a fixed Fermi surface could separate that contribution from true van Hove smearing.","Because the two-band fit also needs a Fermi-velocity ratio near 57.6, the two-band and single-band van Hove descriptions are not cleanly distinguished by $H_{c2}$ alone; independent probes of velocity anisotropy, such as quantum oscillations or band-resolved photoemission, would make the attribution sharper."],"forward_implications":["Upward curvature of $H_{c2}$ in the AV3Sb5 family should not be read as evidence for multiband superconductivity; the same shape can arise from a single band with the Fermi level near van Hove singularities.","Gap anisotropy as large as a factor of 5 in $\\Delta_{\\max}/\\Delta_{\\min}$ changes the $H_{c2}$ curves only modestly, so confirming the role of gap structure requires thermodynamic probes such as specific heat or penetration depth.","Substitutions such as Ta or Nb doping, which leave van Hove singularities near the Fermi level, should continue to show upward curvature even when photoemission shows nearly isotropic gaps, as the paper notes has been observed.","Disorder that smears van Hove singularities should flatten $H_{c2}(T)$ toward the conventional dirty-limit form while also suppressing the CDW transition, linking the critical-field shape to the fate of the singularities."],"supporting_citations":[{"why":"Supplies the anisotropic Fermi-surface model for kagome AV3Sb5 that the single-band van Hove Hc2 calculation builds on.","marker":"[31]"},{"why":"Gives the quasi-classical formalism relating Fermi-velocity anisotropy to temperature-dependent Hc2 and its anisotropy.","marker":"[32]"},{"why":"Provides the DFT Fermi-surface geometry, including the warped-cylinder Sb sheet with tz/EF about 0.12, used to assign two-band fit parameters.","marker":"[20]"},{"why":"Reports photoemission showing isotropic gaps in Ta/Nb-doped CsV3Sb5 while upward curvature persists, supporting the vHs rather than gap-anisotropy explanation.","marker":"[36]"},{"why":"Provides the ARPES gap-anisotropy values used to test whether gap structure changes the Hc2 fits.","marker":"[37]"},{"why":"Defines the conventional dirty-limit Hc2 shape (WHH/Maki-de Gennes) that pristine data deviate from and irradiated data recover.","marker":"[44-46]"},{"why":"Earlier theoretical demonstrations that van Hove singularities near the Fermi level produce upward curvature of Hc2 in two-dimensional systems.","marker":"[74-76]"},{"why":"Supplemental derivation of the two-band and single-band van Hove Hc2 equations, the fits, and the irradiation-dose data.","marker":"[47]"}],"fun_headline_variants":["Van Hove anisotropy dictates kagome superconductor's critical field","Proton irradiation smears van Hove, normalizes CsV3Sb5's Hc2","Why CsV3Sb5's upper critical field bends: van Hove, not bands","Kagome Hc2 curvature explained by van Hove Fermi-velocity anisotropy","Single-band van Hove model beats multi-band for CsV3Sb5 Hc2"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing assumption is that proton irradiation removes the upward curvature by smearing the van Hove singularities, rather than simply by making the system so dirty—residual resistivity jumps from about 1.9 to 58 $\\mu\\Omega$ cm and $T_c$ drops to 2.0 K—that any anisotropic or multiband superconductor would be driven toward the isotropic dirty limit.","fun_headline_variants_meta":{"raw":{"variants":["Van Hove anisotropy dictates kagome superconductor's critical field","Proton irradiation smears van Hove, normalizes CsV3Sb5's Hc2","Why CsV3Sb5's upper critical field bends: van Hove, not bands","Kagome Hc2 curvature explained by van Hove Fermi-velocity anisotropy","Single-band van Hove model beats multi-band for CsV3Sb5 Hc2"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000277,"raw_usage":{"total_tokens":1663,"prompt_tokens":974,"completion_tokens":689,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":590,"completion_tokens_details":{"reasoning_tokens":578}},"tokens_in":590,"tokens_out":689,"duration_ms":5857,"temperature":1.0,"reasoning_tokens":578,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T12:53:46.179176+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure $H_{c2}(T)$ on a series of CsV3Sb5 crystals irradiated to increasing doses while tracking both the residual resistivity and the persistence of the CDW/van Hove signatures (for example with angle-resolved photoemission or quantum oscillations): if the upward curvature survives at doses where sharp saddle-point dispersion is still present, the van Hove mechanism is supported, whereas if the curvature disappears as soon as the sample becomes dirty even while the van Hove signatures remain, the alternative explanation wins.","supporting_citations":[{"cited_title":"Plumb, A","cited_arxiv_id":null,"evidence_quote":"Provides the DFT Fermi-surface geometry, including the warped-cylinder Sb sheet with tz/EF about 0.12, used to assign two-band fit parameters."}],"review_version":1}