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Unconventional gapping behavior in a kagome superconductor

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Pith's one-line read A kagome superconductor hosts two nearly independent superconducting gaps.

desk verdict A careful experimental study with a novel two-regime phenomenology in CsV3Sb5, but the band-selective pairing interpretation rests on a heat-capacity anomaly whose background subtraction may be compromised. read the letter →

arxiv 2411.15333 v1 pith:MA7HJ4VP submitted 2024-11-22 cond-mat.str-el cond-mat.mes-hallcond-mat.mtrl-scicond-mat.supr-con

Md Shafayat Hossain , Qi Zhang , Eun Sang Choi , Danilo Ratkovski , Bernhard Lüscher , Yongkai Li , Yu-Xiao Jiang , Maksim Litskevich
show 14 more authors
Zi-Jia Cheng Jia-Xin Yin Tyler A. Cochran Brian Casas Byunghoon Kim Xian Yang Jinjin Liu Yugui Yao Ali Bangura Zhiwei Wang Mark H. Fischer Titus Neupert Luis Balicas M. Zahid Hasan
This is my paper · ORCID
classification cond-mat.str-elcond-mat.mes-hallcond-mat.mtrl-scicond-mat.supr-con
keywords kagomesuperconductorCsV3Sb5two-gapsuperconductivityband-selectivepairinguppercriticalfieldthermalconductivityheatcapacitynodalgap
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

The paper studies the kagome-lattice superconductor CsV$_3$Sb$_5$ and argues that its superconducting state consists of two nearly independent superconducting regimes, each tied to a different band of the Fermi surface. The evidence includes a pronounced upturn of the upper critical field below about 1 K, a second small heat-capacity anomaly near 0.6 K, a slope change in the thermal conductivity near 0.8 K, and a 90-degree rotation of the thermal-conductivity anisotropy between the two regimes. The authors interpret these observations as the sequential opening of two nearly decoupled gaps, with the lower-temperature gap possibly nodal. If correct, this band-selective pairing would replace the usual multiband picture in which one dominant gap induces pairing in other bands, and it would reconcile conflicting reports of nodal and nodeless superconductivity in this family.

What carries the argument

The argument is carried by the split Fermi surface of CsV$_3$Sb$_5$, specifically the circular pocket around the $\Gamma$ point derived mostly from Sb $p$ orbitals and the hexagonal pocket derived mostly from V $d$ orbitals. The paper assigns a primary gap to the Sb-derived band and a secondary, nearly decoupled gap to the V-derived band, reproducing the measured heat capacity and thermal conductivity with a minimal two-gap model. The experimental load is carried by four observations: the low-temperature upturn of the upper critical field $\mu_0H_{c2}$ for both in-plane and out-of-plane fields, the second heat-capacity anomaly near 0.6 K, the change in slope of $\kappa_{xx}/T$ near 0.8 K, and the 90-degree rotation of the in-plane thermal-conductivity anisotropy while the $\mu_0H_{c2}$ anisotropy direction remains fixed, which rules out ordinary field-anisotropy explanations and points to a strongly anisotropic or nodal gap on one band.

What would settle it

Measure the heat capacity of a high-quality single crystal down to about 50 mK at several fixed fields: the two-gap scenario predicts that the 0.6 K anomaly tracks the upturn in $H_{c2}$ and disappears once the field exceeds $H_{c2}$, whereas a separate phase transition or an inhomogeneity artifact would leave the anomaly position or shape essentially unchanged with field.

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Extended reading notes

Core claim

CsV$_3$Sb$_5$ displays two distinct superconducting regimes separated near 1 K, with no evidence of a phase transition between them. In the higher-temperature regime, a first gap opens on the Sb-derived Fermi surface pocket while substantial quasiparticle weight remains visible in thermodynamics and thermal transport. Below roughly 1 K, a second, nearly decoupled gap opens on a V-derived band with a much higher upper critical field, removing that residual weight. The band that acquires the second gap continues to host low-energy quasiparticles, possibly because that gap has nodes. The authors conclude that superconductivity here is band-selective: pairing develops essentially independently on separate bands rather than being induced from a dominant primary gap.

Load-bearing premise

The conclusion rests on the assumption that the second heat-capacity bump near 0.6 K and the sharp rise in the magnetic field needed to destroy superconductivity below about 1 K are two signatures of the same event — a second superconducting gap opening on a separate band — and not a different phase transition, sample variation, or an artifact of the background subtraction.

Editorial extensions

If this is right

  • The standard multiband scenario, in which one dominant gap induces pairing in the other bands, fails for CsV$_3$Sb$_5$; the two gaps behave as nearly decoupled.
  • The lower-temperature gap is likely strongly anisotropic or nodal, which would explain the residual density of states reported by tunneling experiments.
  • The second gap carries a much higher upper critical field, possibly because that band is in the dirty limit or has a shorter coherence length, analogous to MgB$_2$.
  • The 90-degree switch of the thermal-conductivity anisotropy, without a corresponding rotation of the $H_{c2}$ anisotropy, offers a new way to detect gap anisotropy in multi-gap superconductors.
  • The two-fold symmetric, nematic character of the normal state is inherited by the superconducting state, visible in both $H_{c2}$ and thermal transport.

Reading between the lines

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

  • If the second gap is nodal, thermal-conductivity measurements below roughly 0.1 K should reveal a residual linear-in-$T$ term whose magnitude reflects the nodal quasiparticle density; this cleanly distinguishes nodal from fully gapped scenarios.
  • Because the gaps are nearly decoupled, perturbations that act on one band only — disorder, strain, or doping — should alter one gap's $T_c$ and $H_{c2}$ while leaving the other nearly unchanged, a direct test of band selectivity.
  • The 90-degree rotation of the thermal-conductivity pattern may track the orientation of the nematic charge order; applying uniaxial strain to reorient the nematic domains should rotate the low-temperature thermal-conductivity anisotropy by the same amount.
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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 / 6 minor

Summary. The manuscript reports combined electrical transport, thermal transport, and specific heat measurements on the kagome superconductor CsV3Sb5, claiming the discovery of two distinct superconducting regimes with a boundary near 1 K. In the proposed scenario, a primary superconducting gap opens near Tc ≈ 3.5 K on one Fermi surface, while a second, nearly decoupled gap opens near 0.8–0.6 K on a different band, producing a sharp upturn in Hc2 at low temperatures, a second anomaly in C/T, a slope change in κxx/T, and a 90° rotation of the in-plane thermal conductivity anisotropy. The authors argue against a phase transition separating the two regimes and propose band-selective pairing with possible nodal structure in the second gap.

Significance. If the central claim holds, this would be an important contribution to the physics of multiband superconductors, suggesting that orbital-selective or band-selective pairing with nearly decoupled gaps can occur in a kagome lattice and that the conventional proximity-induced multigap scenario fails in CsV3Sb5. The experimental work is substantial: the Hc2 phase diagrams are cross-validated on two separate exfoliated samples and with three different resistive criteria (50%, 10%, and 90% of the normal-state resistivity), and the thermal conductivity angular data are carefully checked against accidental sample canting. The paper is also appropriately cautious in some places, noting that more complete thermal conductivity and modeling work is needed to establish the pairing symmetry. However, the central interpretation rests on thermodynamic evidence whose reliability is undermined by the normal-state reference field choice, and the paper's own assertion that no phase transition separates the two regimes is in tension with the observed heat capacity peak. These issues affect the load-bearing claim and require additional measurements or modeling.

major comments (3)
  1. [Methods Section X, Extended Fig. 8, Fig. 2c] The 9 T ab-plane field used as the normal-state reference for the heat capacity subtraction is not above Hc2 in the temperature range where the second anomaly appears. The manuscript states that 9 T is 'above and very close to μ0Hc2,||', but Fig. 2c shows μ0Hc2,|| exceeding 9 T below roughly 1 K and extrapolating to nearly 10 T at zero temperature. Therefore, at T ≲ 1 K the 9 T trace is itself in the superconducting state, and subtracting it from the zero-field trace does not cleanly remove the lattice/phonon background. The second specific-heat anomaly near 0.6 K could be an artifact of this incomplete subtraction. A safe reference field (clearly above Hc2 at all measured temperatures, e.g., 14 T or 16 T) is needed to confirm the thermodynamic signature. Because this second anomaly is the strongest thermodynamic support for the nearly decoupled two-gap scenario, this issue is load-bearing for the central claim.
  2. [Abstract, Fig. 3c] The abstract states that the two superconducting regimes are separated 'while finding no evidence for a phase transition', yet Fig. 3c shows a peak in the electronic contribution to C/T near 0.6 K. A genuine thermodynamic peak in C/T at a characteristic temperature is the standard signature of a phase transition, so the default interpretation of a real peak is a phase transition unless the two-gap crossover model quantitatively explains the peak shape and why it does not constitute a thermodynamic transition. The current manuscript does not provide such a quantitative analysis; it only shows a model calculation in Fig. 3d with a qualitative caption. The authors should either demonstrate that a nearly decoupled two-gap model (without an intervening phase transition) quantitatively reproduces the observed C/T peak of the correct shape and height, or soften the claim that there is no phase-transition-like feature.
  3. [Sec. 'Two-gap model', Fig. 3b and 3d] The two-gap model is presented as a consistency check but the connection between the model and the experimentally observed Hc2 upturn is not established. The model calculations in Fig. 3b and 3d are described only qualitatively (see SI), and the Hc2(T) curves in Fig. 2c and 2f are not reproduced from the same model. To support the claim that band-selective pairing with nearly decoupled gaps explains the full set of observations, the authors need to show that a single set of model parameters produces (i) the approximate temperature scale of the second gap opening, (ii) the sharp Hc2 upturn with its near-isotropy across field orientations, and (iii) the thermal conductivity slope change. Without this quantitative link, the scenario remains one of several possible interpretations of the transport data.
minor comments (6)
  1. [Fig. 3c caption] The caption states that the 9 T field is 'close to μ0Hc2^{ab}', but does not mention that Hc2,|| exceeds 9 T at low temperatures; this should be clarified to warn the reader about the subtraction issue.
  2. [Methods Section X] The phrase 'with both values being above and very close to μ0Hc2,⊥ and μ0Hc2,|| respectively' is imprecise for the ab-plane case; consider specifying the temperature range over which 9 T is above Hc2.
  3. [Main text, paragraph on heat capacity] The sentence 'The extrapolation of the heat capacity to T = 0 K suggests the near absence of residual electronic contribution' is presented without an error estimate or the extrapolation procedure; adding these would strengthen the claim.
  4. [Methods Section XI] The three listed sources of thermal conductivity anisotropy are stated to be exhaustive, but this claim should be justified or softened, as other mechanisms (e.g., multiband quasiparticle scattering, vortex-channel contributions) could also affect κxx/T anisotropy.
  5. [Fig. 4c] The values '450' and '1350' in the figure caption appear to be typos for 45° and 135°; please correct them.
  6. [Methods Section XIII] The fit function cos 2φ + cos 2(φ + φ0) is declared but the amplitudes of the two components are not stated; the fit would be more meaningful if the relative amplitude were reported.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the two-regime claim rests on independent raw measurements; the two-gap model is an explicit post-hoc consistency check, and one self-citation is not load-bearing.

full rationale

The central claim of two nearly decoupled superconducting gaps is built from directly measured quantities: Hc2(T) from resistivity (Fig. 2c,f), kappa_xx/T from thermal transport (Fig. 3a), C/T anomalies after field-background subtraction (Fig. 3c), and the in-plane thermal-conductivity anisotropy rotation (Fig. 4). None of these observations is defined in terms of the two-gap model. The model in Fig. 3b,d is introduced only 'to corroborate the two-gap scenario' by assuming 'two weakly coupled superconducting gaps on different Fermi surfaces' and 'a primary gap on the Sb-derived band with a secondary gap on the V-derived band' (main text around Fig. 3); it is therefore a consistency check whose output is built into its input, but the paper does not present it as an independent first-principles prediction, so this does not constitute the derivation of the central claim. The citation to Ritz et al. (ref. 23) supporting orbital-selective pairing is likely from overlapping authors (M. H. Fischer and T. Neupert are coauthors of both works), but it is used only to motivate the assumption, not as a uniqueness theorem or as the evidence for the experimental regimes. Two genuine scientific concerns are not circularity: the normal-state reference for the heat-capacity subtraction, mu0H = 9 T along the ab-plane (Methods X; Extended Fig. 8a), may lie below Hc2,|| at the lowest temperatures according to the paper's own phase diagram (Fig. 2c), which could affect the 0.6 K anomaly; and the abstract's statement of 'no evidence for a phase transition' is in tension with the observed 'very modest peak' in C/T near 0.6 K. These are correctness/artifact risks that should be probed with a higher reference field, but they do not make the argument circular. Overall, the load-bearing evidence is self-contained external measurement, so the circularity score is low.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The ledger shows that the paper's experimental identification of two regimes is relatively assumption-light, but the interpretive step to band-selective pairing relies on a model whose parameters are not shown and on an assumed band assignment from prior DFT. No new physical entities are introduced.

free parameters (3)
  • GL coherence length xi_GL(0) = ~17 nm (in-plane), ~13.6 nm from Hc2,perp(T=0)
    Fitted from the temperature dependence of Hc2 in regime I using the 2D Ginzburg-Landau formula. Characterizes the 2D superconducting state but is not central to the two-gap claim.
  • Superconducting thickness d_SC = ~8 nm (from Hc2,par(T=0) fit)
    Fitted from the same GL analysis. The extracted thickness is much smaller than the sample thickness, which the paper treats as an upper bound due to Pauli-limit violation.
  • Two-gap model parameters (primary gap on Sb-derived band, secondary gap on V-derived band, interband coupling) = not specified in main text
    Used in the minimal model to reproduce C/T and kappa/T in Fig. 3b,d. The parameter values and fitting procedure are deferred to the SI, so the model comparison is qualitative in the preprint.
assumptions (5)
  • domain assumption The Fermi surface consists of a circular pocket around the Gamma point (Sb p orbitals) and a hexagonal pocket (V d orbitals).
    Invoked in the two-gap model section ('we consider the circular pocket around the Gamma-point... and the hexagonal pocket...'). Taken from band structure calculations (ref 7).
  • domain assumption The charge density wave reduces the six-fold lattice symmetry to two-fold and produces a nematic normal state.
    Used to interpret the two-fold symmetric Hc2 and normal-state magnetoresistivity. Based on prior reports (refs 15, 16).
  • ad hoc to paper The three listed sources of thermal conductivity anisotropy are exhaustive.
    In Methods Section XI, the paper enumerates three possible sources and concludes sources (1) and (2) cannot explain the 90-degree rotation, leaving source (3). This completeness assumption is load-bearing for the nodal gap inference.
  • ad hoc to paper The second heat-capacity anomaly at ~0.6 K and the Hc2 upturn are both manifestations of a second nearly decoupled superconducting gap, not of a distinct phase transition or other order.
    This is the central interpretation: the paper argues against field-induced phases or dimensional crossovers but does not rule out other thermodynamic transitions. The observed 'very modest peak' in C/T is itself a possible transition signature.
  • domain assumption The direction of maximum in-plane Hc2 is the same in both superconducting regimes and does not rotate.
    This is verified by the authors in Extended Fig. 7 for T=1.8 K vs 0.3 K, so it is supported, but the assumption enters the argument that the thermal conductivity rotation cannot be explained by an Hc2 rotation.

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Pith. "Pith review of Unconventional gapping behavior in a kagome superconductor." pith.science (2026). https://pith.science/paper/MA7HJ4VP

@misc{pith2026241115333,
  author       = {Pith},
  title        = {Pith review of: Unconventional gapping behavior in a kagome superconductor},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MA7HJ4VP}},
  note         = {Machine review of arXiv:2411.15333}
}
read the original abstract

Determining the types of superconducting order in quantum materials is a challenge, especially when multiple degrees of freedom, such as bands or orbitals, contribute to the fermiology and when superconductivity competes, intertwines, or coexists with other symmetry-breaking orders. Here, we study the Kagome-lattice superconductor CsV3Sb5, in which multiband superconductivity coexists with a charge order that substantially reduces the compound's space group symmetries. Through a combination of thermodynamic as well as electrical and thermal transport measurements, we uncover two superconducting regimes with distinct transport and thermodynamic characteristics, while finding no evidence for a phase transition separating them. Thermodynamic measurements reveal substantial quasiparticle weight in a high-temperature regime. At lower temperatures, this weight is removed via the formation of a second gap. The two regimes are sharply distinguished by a pronounced enhancement of the upper critical field at low temperatures and by a switch in the anisotropy of the longitudinal thermal conductivity as a function of in-plane magnetic field orientation. We argue that the band with a gap opening at lower temperatures continues to host low-energy quasiparticles, possibly due to a nodal structure of the gap. Taken together, our results present evidence for band-selective superconductivity with remarkable decoupling of the (two) superconducting gaps. The commonly employed multiband scenario, whereby superconductivity emerges in a primary band and is then induced in other bands appears to fail in this unconventional kagome superconductor. Instead, band-selective superconducting pairing is a paradigm that seems to unify seemingly contradicting results in this intensely studied family of materials and beyond.

Figures

Figures reproduced from arXiv: 2411.15333 by the authors.

Figure 1
Figure 1. Observation of two-dimensional and two-fold symmetric superconductivity in CsV3Sb5 visualized through its upper critical field. a, Crystal structure of CsV3Sb5, featuring a layered, quasi two-dimensional crystal structure along the c-axis and forming a six-fold symmetric V kagome lattice within the V-Sb slab. b, Four-probe resistivity of a mechanically exfoliated ∼90 nm thick CsV3Sb5 crystal, exhibiting metallic beh… view at source ↗
Figure 4
Figure 4. Angular dependence of the in-plane thermal conductivity within the I and II regimes. a, Polar plot of the in-plane thermal conductivity under fixed magnetic fields of 𝜇0𝐻 = 1, 4, 6, and 12 T, as the field is rotated within the ab-plane as a function of the planar angle 𝜙 at 𝑇 ≃ 0.7 K (regime II). The angle 𝜙 represents the orientation between the in-plane magnetic field and the direction of the applied heat current … view at source ↗
Figure 3
Figure 3. In line with the convention in Figs. 1e and 1f, φ represents the angle between the in-plane magnetic field along the ab plane (𝜇0𝐻c2,|| ) and the axis with the largest 𝐻c2,|| .As depicted in Extended Figs. 3a and 3b, we observe a consistent two-fold modulation in the magnetoresistivity across all the magnetic fields shown. The modulation is particularly prominent within the field range encompassing the onset and off… view at source ↗

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Interplay of superconductivity and charge-density-wave order in kagome materials

    cond-mat.supr-con 2024-11 accept novelty 6.0 of 10

    A symmetry-based Ginzburg-Landau analysis shows that a 2x2 charge-density wave in kagome metals induces superconducting pair-density waves that inherit the broken symmetries of the CDW.

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