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REVIEW 3 major objections 3 minor 27 references

Origin of the Unusual Temperature Dependence of the Upper Critical Field of Kagome Superconductor CsV3Sb5: Multiple Bands or van Hove Singularities?

T0 review · 3 major / 3 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read 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.

desk verdict 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. read the letter →

arxiv 2411.16625 v2 pith:4RIZ3DPC submitted 2024-11-25 cond-mat.supr-con cond-mat.str-el

Ramakanta Chapai , Alexei E. Koshelev , Matthew P. Smylie , Duck Young Chung , Asghar Kayani , Khushi Bhatt , Gaurab Rimal , Mercouri G. Kanatzidis
show 3 more authors
Wai-Kwong Kwok John Mitchell Ulrich Welp
This is my paper · ORCID
classification cond-mat.supr-concond-mat.str-el
keywords kagomesuperconductorCsV3Sb5uppercriticalfieldvanHovesingularityFermivelocityanisotropymultibandsuperconductivityprotonirradiationdirtylimit
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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.

What would settle it

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.

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Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

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

  • 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.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 3 minor

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).

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 (3)
  1. [End Matter, Fig. 3(d); main text Fig. 2(c)] 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.
  2. [Fig. 1(d) and Supplement Eqs. (B8), (B16)] 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.
  3. [Supplement, 'Estimation of dimensionless scattering parameter'] 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.
minor comments (3)
  1. [Supplement, throughout] The Supplement contains numerous typographical errors, including 'FGG.' for 'FIG.', 'Gn' for 'In', and 'Grradiation' for 'Irradiation', which should be corrected before publication.
  2. [Fig. 1(c) caption and main text] 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.
  3. [References [37], [38]] 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.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the models are explicitly fitted to the Hc2 data, the closed-form ratios are internal consistency checks rather than out-of-sample predictions, and the irradiation control is an external though degenerate test; minor self-citation is not load-bearing.

full rationale

The paper is largely self-consistent and does not disguise its fitting procedure. The two-band model (Eq. 1) and the single-band van Hove model (Eq. 2) are both used to fit the measured Hc2(T) curves, and the quoted large Fermi-velocity anisotropy rv=57.6 and vHs parameters (κc, tz/EvH) are fit outputs, not independent predictions. The closed-form ratios Hc2(0)/Hc2_GL are derived within each model and then evaluated with those same fit parameters; they therefore serve as internal consistency checks, not as out-of-sample predictions. The central statement that 'both approaches require a large Fermi velocity anisotropy to account for the Hc2-data' is a summary of the fits, not a claim that the data were predicted from first principles. The irradiation experiment is an external, qualitative corroboration, but it is degenerate: at 6×10^16 p/cm2 the residual resistivity rises from ~1.9 to ~58 μΩ cm and Tc falls from 3.5 to 2.0 K, so any clean-limit anisotropy mechanism (two-band, gap-anisotropic, or vHs-induced) would be driven toward the dirty isotropic limit; the data therefore do not uniquely identify vHs smearing. This is a scientific under-determination concern, not a circularity. The paper also imports its vHs Fermi-surface model from the authors' prior work [30,31], and that model is an ansatz; however, it is cited transparently as a model source rather than as a uniqueness theorem, and the proximity of vHs to the Fermi level is independently supported by external DFT and ARPES references. Accordingly, no circular reduction of the central claim to its own inputs is exhibited; the minor self-citation and the fitted-parameter consistency checks do not rise to load-bearing circularity.

Assumptions & free parameters 8 free parameters · 5 assumptions · 0 invented entities

The central claim depends on a simplified single-band model with several fitted parameters and on the interpretation of the irradiation experiment. No new physical entities are introduced. The main free parameters are the two-band velocity ratio (rv=57.6) and single-band parameters kc and tz/EvH; these are fitted to the Hc2 data rather than predicted from band structure.

free parameters (8)
  • two-band band weight w1 = 0.46
    Fitted to Hc2(T) data in Fig. 1(c); controls the relative weight of the two Fermi surface sheets.
  • two-band Fermi velocity ratio rv = vF2^2/vF1^2 = 57.6
    Fitted; the large value is required to reproduce the upward curvature and is the key parameter for the conclusion.
  • two-band c-axis hopping tz1/EF1 = 0.057
    Fitted to c-axis Hc2(T) in the two-band model.
  • two-band c-axis hopping tz2/EF2 = 0.133
    Fitted; close to the DFT-derived value for the Sb-derived warped cylinder sheet.
  • single-band mass ratio rm = mv/mu = not stated explicitly for the fit; representative figures use rm constrained by gap anisotropy
    Controls the hyperbolic Fermi surface shape in the vHs model; the fitted value is not listed in the text.
  • single-band cutoff ratio kappa_c = Kc/pu0 = 10 (isotropic gap) or 11.3 (with gap anisotropy)
    Fitted; larger kappa_c brings the Fermi surface closer to the vHs and increases velocity anisotropy.
  • single-band tz/EvH = 0.6 (case of Fermi level crossing vHs)
    Fitted; determines whether the Fermi level crosses the van Hove energy along the c-axis.
  • gap anisotropy constants cu, cv = constrained by Delta_min/Delta_max ~ 0.2 in Fig. S9
    Phenomenological parameters for gap anisotropy; shown to have a secondary effect on Hc2.
assumptions (5)
  • standard math Quasiclassical Eilenberger equations with lowest-Landau-level projection describe Hc2 in clean layered superconductors.
    Used as the starting point for Eq. (1) and Eq. (2) in the main text; standard in superconductivity theory (Refs. 32, 69).
  • domain assumption The Fermi surface of CsV3Sb5 can be represented near the van Hove points by hyperbolic sections with a single cutoff Kc.
    Supplemental Eq. (B2) and Fig. S7; this is a simplified model, not derived from the full DFT band structure.
  • domain assumption The Fermi level crosses the van Hove energy at some c-axis momenta (2|tz| > EvH).
    Supplemental section on c-axis upper critical field; the upward curvature amplification relies on this crossing.
  • ad hoc to paper Proton irradiation smears the van Hove singularities and reduces Fermi velocity anisotropy without other substantial changes.
    End Matter and Fig. 3(d); used to explain the recovery of conventional Hc2, but irradiation also introduces strong disorder and reduces Tc.
  • domain assumption The 'first band' in the two-band model that carries the small Fermi velocity can be identified with the hexagonal vHs sheet.
    Main text: 'it is tempting to relate the first band to the large hexagonal Fermi surface sheet in close proximity to the vHS'; this identification is not directly verified.

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Cite this review

Pith. "Pith review of Origin of the Unusual Temperature Dependence of the Upper Critical Field of Kagome Superconductor CsV3Sb5: Multiple Bands or van Hove Singularities?." pith.science (2026). https://pith.science/paper/4RIZ3DPC

@misc{pith2026241116625,
  author       = {Pith},
  title        = {Pith review of: Origin of the Unusual Temperature Dependence of the Upper Critical Field of Kagome Superconductor CsV3Sb5: Multiple Bands or van Hove Singularities?},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4RIZ3DPC}},
  note         = {Machine review of arXiv:2411.16625}
}
read the original abstract

Van Hove singularities (vHs) located close to the Fermi level in Kagome superconductors AV3Sb5 (A = K, Rb, Cs) have profound influence on their electronic and transport characteristics. Specifically, magneto-transport and susceptibility measurements on CsV3Sb5 reveal an anomalous temperature dependence of the upper critical field H_c2 (T), characterized by a pronounced upward curvature for both in-plane and c-axis magnetic fields, with zero-temperature H_c2 values of ~6.0 T and ~1.2 T, respectively. Our theoretical analysis, using a newly developed single-band model incorporating vHs and gap anisotropy, suggests that the observed upper critical field behavior is predominantly driven by the anisotropy of the Fermi velocity originating from vHs, instead of multi-band effects or gap anisotropy. Increased electron scattering introduced by proton irradiation defects smears out the vHs, reduces anisotropy, and recovers the conventional H_c2 (T) behavior, corroborating our proposed model.

Figures

Figures reproduced from arXiv: 2411.16625 by the authors.

Figure 1
Figure 1. FIG. 1. Temperature dependence of the [PITH_FULL_IMAGE:figures/full_fig_p015_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The [PITH_FULL_IMAGE:figures/full_fig_p016_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a) The superconducting transition of sample S2 as seen in the temperature dependence of the [PITH_FULL_IMAGE:figures/full_fig_p018_3.png] view at source ↗

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