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REVIEW 2 major objections 4 minor 63 references

The superconducting gap on the vanadium Mz-even Fermi pockets in CsV3Sb5 is isotropic, which constrains allowed gap symmetries and leaves any anisotropy to other bands.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-07-30 11:20 UTC pith:U75ZE6VY

load-bearing objection Solid sub-Kelvin QPI with a usable k→q map: isotropic gap on the Mz+ pockets is the real result; PDW is a careful null, and the main soft spot is how cleanly the masks isolate band-specific SC QPI. the 2 major comments →

arxiv 2607.27148 v1 pith:U75ZE6VY submitted 2026-07-29 cond-mat.supr-con cond-mat.str-el

Momentum Structure of Superconductivity and Sublattice Effects from Quasiparticle Interference in CsV₃Sb₅

Aaron G. Greenberg , Xinze Yang , Junze Deng , Pranab Kumar Nag , Kirsty Scott , Yi Jiang , Haoyu Hu , Chandra Shekhar
show 6 more authors
Dong Chen Claudia Felser Santiago Blanco-Canosa P\"aivi T\"orm\"a B. Andrei Bernevig Eduardo H. da Silva Neto
This is my paper
classification cond-mat.supr-con cond-mat.str-el
keywords kagome superconductorCsV3Sb5quasiparticle interferencesuperconducting gappair-density wavesublattice interferencecharge density wavescanning tunneling microscopy
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper maps the momentum structure of superconductivity in the kagome metal CsV3Sb5 with sub-Kelvin scanning tunneling spectroscopy. By densely sampling the gap and matching quasiparticle interference patterns to ab initio surface bands, the authors show that the vanadium mirror-even Fermi pockets carry an isotropic gap identical to the spatially averaged density of states. That result rules out several symmetry-allowed anisotropic gaps on those pockets and forces any reported anisotropy onto the remaining vanadium mirror-odd or antimony pz bands. Spectra locked to the charge-density-wave peaks track the average density of states and show no clear subgap enhancement, so they do not support an extra pair-density-wave modulation within the measurement sensitivity. The same data also show that certain scattering vectors are missing precisely where sublattice weight overlap is weak, giving direct spectroscopic access to Fermi-level sublattice character that theory has long invoked for kagome correlations.

Core claim

Quasiparticle interference, interpreted with a first-principles surface Fermi surface and a model of the stripe charge order, shows that the superconducting gap on the vanadium Mz-even (Mz+) kagome-derived pockets is isotropic to within roughly ±6 percent. The arc and line QPI features that map to the corners and flat sides of those pockets all close at the same energy as the real-space average spectrum. Charge-density-wave peak spectra closely follow that average and do not display a distinct subgap enhancement, so they do not support an additional pair-density-wave modulation within the sensitivity of the experiment.

What carries the argument

The k-to-q mapping: ab initio surface Green’s-function quasiparticle interference that assigns the experimental α arcs and λ lines to the rounded corners and flat sides of the Mz+ triangular pockets, while sublattice-resolved wavefunctions explain why other joint-density-of-states vectors are selectively absent.

Load-bearing premise

The claim that the measured arcs and lines come only from the vanadium mirror-even bands rests on surface band calculations plus a model stripe potential; if that band assignment is wrong, the isotropy result does not attach to the stated pockets.

What would settle it

A gap extraction from the same α and λ QPI masks that differed by more than a few percent from the spatially averaged spectrum, or an independent probe showing substantial mirror-odd or antimony weight in those same scattering channels, would overturn the isotropy claim on the Mz+ pockets.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Gap symmetries that would produce different magnitudes on the arcs versus the flat sides of the Mz+ pockets are ruled out.
  • Any reported gap anisotropy in CsV3Sb5 must reside on the Mz-odd or Sb pz bands, not on the Mz+ pockets measured here.
  • Main charge-density-wave Fourier peaks do not carry a clear pair-density-wave signature beyond ordinary density-of-states modulation.
  • Missing QPI vectors can be used as a spectroscopic readout of Fermi-level sublattice character in kagome metals.
  • Realistic theories of intertwined charge order and superconductivity in this family must reproduce an isotropic Mz+ gap.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Pairing mechanisms built on fluctuating chiral charge order should now be checked for whether they naturally leave the Mz+ surface isotropic while allowing anisotropy elsewhere.
  • If a weak pair-density-wave component still exists, the small kink sometimes seen at the Q3/4 peak is the most natural place for higher-sensitivity maps to look next.
  • The same sublattice-sensitive QPI filter could be applied to other kagome or multi-sublattice superconductors where orbital mixing at the Fermi level is poorly known.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. The manuscript reports sub-Kelvin STM/STS spectroscopic mapping of CsV3Sb5 with 50 µeV energy sampling through the superconducting gap, at B=0 and B=3 T. Using surface-projected ab initio Green's-function calculations with a phenomenological 4×1 on-site CDW potential (V0=200 meV) and unfolding, the authors establish a k→q mapping attributing the observed α (arc) and λ (line) QPI features entirely to the V Mz-even kagome-derived pockets. Masked, energy-resolved QPI spectra for α and λ are found to be identical in shape to the spatially averaged DOS, from which the authors conclude the gap on the Mz+ pockets is isotropic with residual anisotropy below ±6%; no Bogoliubov QPI is observed. CDW-peak-selected spectra track the average DOS with no subgap enhancement, which the authors take as non-support for a PDW within their sensitivity, while flagging a small kink at Q3/4 as a possible target for future work. Finally, the absence of JDOS-predicted δ scattering vectors is attributed to sublattice-weight overlap on the Fermi surface, constituting a Fermi-level probe of sublattice character.

Significance. If the central result holds, this is a significant contribution: the first densely energy-sampled (50 µeV steps), sub-Kelvin QPI determination of the momentum structure of the superconducting gap in CsV3Sb5, delivering an explicit falsifiable bound (residual anisotropy < ±6%) on the Mz+ kagome pockets and thereby confining any gap anisotropy reported by bulk probes to the Mz−/Sb pz sectors. The careful scoping of the PDW non-observation — distinguishing trivial DOS-modulation effects from genuine gap modulations, and explicitly identifying the Q3/4 kink as the only candidate anomaly while declining to overclaim — is a model of restraint. The k→q mapping from surface-projected ab initio Green's functions with 4×1 CDW unfolding, and the demonstration that sublattice-weight overlap explains the selective absence of JDOS-predicted δ features, are independently valuable methodological results. Strengths include the field-on/field-off comparison, symmetry-equivalent masks, and reproduction across tips and sample areas.

major comments (2)
  1. [Results, 'Momentum Resolved Gap Structure'; Fig. 4d] The central claim — gap isotropy on the Mz+ pockets with residual anisotropy below ±6% — is inferred from the near-identity of masked α and λ spectra to the real-space-averaged DOS. As the caption to Fig. 4 states, all curves in b–g are 'normalized to their average over the displayed energy ranges'; this self-normalization removes the absolute suppression scale and leaves only shape, so the match is a near-null result whose evidential weight depends entirely on demonstrated band-specific sensitivity. Two specific mechanisms could produce the observed identity without isotropy: (i) the 33×33 nm field of view (Methods, STS Parameters) implies finite Fourier broadening of the sharp Q1/2, Q1/4, and Bragg peaks, and the paper itself shows (Figs. 4e–g) that CDW-peak spectra track the average DOS — so leakage of these peaks into the extended α/λ masks would bias the masked spectra toward the-a-
  2. [Results, 'k→q mapping and sublattice effects'; Methods, 'CDW and unfolding'] The conclusion that the low-energy QPI arises 'entirely from the Mz+ bands' rests on surface-projected DFT plus a phenomenological 4×1 on-site potential on the V kagome layer with V0 = 200 meV and subsequent unfolding (Eq. (3)–(4)). The text asserts that the Mz− sector is 'inconsistent with both the geometry and dispersion' of α/λ and is suppressed by Q1/4 folding, with details deferred to Supplementary Section I D. Since the isotropy claim attaches specifically to the Mz+ pockets, the main text should quantify the robustness of this exclusion: e.g., how the simulated α/λ intensity from the Mz− sector varies with V0 (is 200 meV constrained by experiment?), and an upper limit on residual Mz− or Sb pz spectral weight inside the actual α/λ masks of Fig. 4a. If even weak Mz− weight leaks into the masks, the attribution of any residual anisotropy — and the scope of the ±6% bound — changes.
minor comments (4)
  1. [Competing Interests] The section currently contains the data-availability sentence ('The data that support the findings...') rather than a competing-interests declaration — clearly a copy-paste error.
  2. [Results, 'Momentum Resolved Gap Structure'] The derivation of the ±6% residual-anisotropy bound is entirely in Supplementary Section VI. The main text should at least enumerate the inputs (electronic temperature 520 mK from Dynes calibration, 50 µeV lock-in modulation, segment-by-segment analysis of the arcs/lines) and state how they combine into the bound, so the reader can assess it without the supplement.
  3. [Results, 'STS measurements near the Fermi level'] The statement that there is 'no clear evidence of BQPI' would benefit from a quantitative criterion (e.g., an intensity threshold relative to the normal-state QPI features, or a statement of which new q vectors a nodal or anisotropic gap would have produced in the simulations). As written it is a visual judgment on Fig. 2 and Supplementary Fig. S14.
  4. [General] Several typographical/formatting issues: 'RESUL TS' and 'DA T A A V AILABILITY' headers; inconsistent 'ab initio' spacing throughout; the caption of Fig. 2c notes a distinct color scale only in passing — consider stating the reason (low intensity at 0 meV) more prominently; Ref. [27] is a preprint and should carry an arXiv identifier; the data-availability statement ('upon request') may not meet the journal's data policy.

Circularity Check

0 steps flagged

No significant circularity: gap isotropy is read from measured QPI energy dependence, not forced by fitted inputs or self-citation chains.

full rationale

The central claim—an isotropic superconducting gap on the V Mz+ pockets—comes from experimental energy-dependent intensities of the α and λ QPI masks compared to the real-space-averaged dI/dV (Fig. 4b–d). That comparison is not defined by, nor statistically forced by, any fitted order parameter or gap ansatz. Ab initio surface Green’s functions and a phenomenological 4×1 on-site CDW potential (V0 = 200 meV) plus impurity V0 = 50 meV are used only to assign which Fermi-surface sectors produce α/λ and to motivate the missing δ channels; those modeling choices do not set the measured gap size or the α/λ vs average identity. Methodological citations to the authors’ prior FeSe QPI work and intermediate-band Green’s-function analysis supply technique, not a uniqueness theorem that forbids alternatives. CDW-peak spectra tracking the average DOS is likewise a direct experimental comparison, not a tautology. Weaknesses in sector assignment or mask leakage are correctness/sensitivity issues, not circular reductions of outputs to inputs. Score 0; steps empty.

Axiom & Free-Parameter Ledger

3 free parameters · 5 axioms · 0 invented entities

The load-bearing experimental claim is the measured equality of α/λ gap spectra with the average DOS. Supporting theory assumes standard DFT surface projection, a nonmagnetic constant impurity T-matrix, and a hand-chosen 4×1 on-site CDW potential to mimic stripe folding. No new particles or forces are introduced; Mz± orbital sectors are standard symmetry labels. Free parameters live in the modeling layer used for assignment, not in the gap-size extraction itself.

free parameters (3)
  • CDW on-site amplitude V0 on V kagome = 200 meV
    Phenomenological 4×1 potential strength used to fold the surface FS and QPI; chosen as 200 meV to match observed twofold QPI pattern, not derived from first principles.
  • Impurity on-site potential V0 in T-matrix QPI = 50 meV
    Constant nonmagnetic scatterer strength in Green’s function QPI simulation; set to 50 meV for spectral comparison.
  • Electronic temperature in Dynes calibration = ~520 mK
    STM head thermometer 298 mK; electronic temperature estimated 520 mK from Pb gap fits, entering resolution and anisotropy bound.
axioms (5)
  • domain assumption Surface-projected DFT (PBE) plus Wannier V-d/Sb-p/Cs-s model correctly identifies which FS sheets generate low-energy QPI on the Sb termination.
    Central to excluding Sb pz and Mz− from α/λ and to coloring sublattice weights (Results k→q; Methods first-principles).
  • domain assumption QPI intensity vs energy at normal-state q vectors tracks the superconducting gap magnitude on the connected k-space arcs when BQPI is absent.
    Standard STS/QPI interpretation used to convert α/λ spectra into a momentum-resolved gap (Introduction; Momentum Resolved Gap Structure).
  • domain assumption Nonmagnetic, momentum-independent impurity T-matrix and group-velocity selection rules adequately capture which scattering channels appear.
    Used in QPI simulation and to discard some JDOS vectors (Methods QPI simulation; Fig. 3).
  • ad hoc to paper A 4×1 periodic on-site potential on V is a sufficient model of the surface stripe CDW for unfolding QPI into the primitive BZ.
    Explicit modeling choice in Methods 'CDW and unfolding' with matrix M and Vβ = V0 cos(2π tβ·A1).
  • domain assumption Standard linear-response STM conductance and Fourier analysis represent joint scattering of Bogoliubov/normal quasiparticles without uncontrolled matrix-element inversion.
    Background for all g(q,E) maps; tip-modification risk after Cs sweep is discussed but treated as controlled by junction checks.

pith-pipeline@v1.2.0-grok45-kimik3 · 21502 in / 3607 out tokens · 78265 ms · 2026-07-30T11:20:34.440247+00:00 · methodology

0 comments
read the original abstract

Quantum interference encoded in the sublattice texture of kagome Bloch wavefunctions has been widely invoked as a route to correlated states, including chiral charge order, unconventional superconductivity, and their possible intertwining in pair-density-wave (PDW) states. Using sub-Kelvin scanning tunneling microscopy, we conducted spectroscopic mapping of the kagome material CsV$_3$Sb$_5$ with high energy resolution and dense energy sampling through the superconducting gap. Quasiparticle interference (QPI) analysis, aided by ab initio and symmetry calculations, reveals an isotropic superconducting gap on the Fermi surfaces derived from V $M_z$-even ($M_z^+$) $d$ orbitals, thereby constraining possible gap symmetries and limiting any gap anisotropy to the remaining V $M_z$-odd ($M_z^-$) and Sb $p_z$ bands. Meanwhile, the CDW-peak-selected d$I$/d$V$ spectra closely track the spatially averaged density of states and show no distinct enhancement restricted to subgap energies, which do not support an additional PDW modulation within our sensitivity. Finally, the selective absence of specific QPI scattering vectors points to a spectroscopic sensitivity to sublattice character on the Fermi surface. Together, these results provide a clearer experimental picture of the low-energy electronic structure relevant to kagome superconductivity in CsV$_3$Sb$_5$.

Figures

Figures reproduced from arXiv: 2607.27148 by Aaron G. Greenberg, B. Andrei Bernevig, Chandra Shekhar, Claudia Felser, Dong Chen, Eduardo H. da Silva Neto, Haoyu Hu, Junze Deng, Kirsty Scott, P\"aivi T\"orm\"a, Pranab Kumar Nag, Santiago Blanco-Canosa, Xinze Yang, Yi Jiang.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p021_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p022_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p023_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p024_4.png] view at source ↗

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