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arxiv: 2605.11401 · v1 · submitted 2026-05-12 · ❄️ cond-mat.supr-con

Recognition: 2 theorem links

· Lean Theorem

Superconductivity Reinforces Charge-Density-Wave Phase Coherence across Cuprates

H. Lee , C.-T. Kuo , M. Fujita , C.-C. Kao , J.-S. Lee
Authors on Pith no claims yet

Pith reviewed 2026-05-13 01:20 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con
keywords cupratescharge-density-wavesuperconductivityphase coherenceresonant x-ray scatteringhigh-TcCDW orderwave-vector locking
0
0 comments X

The pith

Superconductivity enhances charge-density-wave phase coherence across cuprate families while suppressing amplitude.

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

The paper challenges the long-held view that superconductivity in cuprates competes with and suppresses charge-density-wave (CDW) order. Instead, it demonstrates that superconductivity systematically improves the phase coherence of CDW across several cuprate families. Using resonant soft x-ray scattering, the study reveals a BCS-like increase in coherence below the superconducting transition temperature Tc. This coherence enhancement appears as no broadening of CDW peaks and precise locking of the wave vector. The effect persists even in aged, disordered crystals and aligns with data from various cuprate types.

Core claim

The central discovery is that superconductivity reshapes CDW order by suppressing its amplitude but strengthening its phase coherence, as evidenced by the lack of CDW peak broadening and near-perfect wave-vector locking below Tc in multiple cuprate families.

What carries the argument

Resonant soft x-ray scattering combined with coherence-sensitive momentum-profile analysis that isolates phase coherence from disorder scattering, inhomogeneity, and resolution effects.

If this is right

  • CDW order shows a dual response to superconductivity: amplitude suppression paired with phase coherence strengthening.
  • The coherence growth follows a BCS-like trend below Tc and remains consistent across Bi-, Hg-, Y-, and Nd-based cuprates.
  • Near-perfect wave-vector locking and absence of peak broadening occur even in disorder-dominated samples from long-term crystal aging.
  • An additional phase-level interplay with lattice coupling is revealed beyond simple amplitude competition.

Where Pith is reading between the lines

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

  • This dual reshaping could influence models of how superconductivity coexists with or stabilizes other ordered phases in cuprates.
  • Similar coherence enhancements might be testable in non-cuprate systems with competing density-wave orders.
  • The emphasis on phase coherence over amplitude suggests new experimental probes focused on locking and correlation length below Tc.

Load-bearing premise

The momentum-profile analysis accurately isolates genuine CDW phase coherence without being dominated by disorder scattering, sample inhomogeneity, or instrumental resolution.

What would settle it

Observation of CDW peak broadening or loss of wave-vector locking below Tc in high-quality samples across cuprate families would falsify the enhancement of phase coherence.

Figures

Figures reproduced from arXiv: 2605.11401 by C.-C. Kao, C.-T. Kuo, H. Lee, J.-S. Lee, M. Fujita.

Figure 1
Figure 1. Figure 1: FIG. 1. Momentum profiles of CDW order across supercon [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Promotion of CDW phase coherence below [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. CDW phase coherence under the disorder. (a) [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

For decades, superconductivity in high-Tc cuprates has been viewed as a competitor that suppresses charge-density-wave (CDW) order by reducing its amplitude and spatial extent. Here, we show that this picture is incomplete, as superconductivity is accompanied by a systematic enhancement of CDW phase coherence across multiple cuprate families. Using resonant soft x-ray scattering combined with a coherence-sensitive momentum-profile analysis, we uncover a BCS-like growth of phase coherence below Tc, which phenomenologically manifests as the absence of CDW peak broadening and near-perfect wave-vector locking. This enhancement remains visible even in a disorder-dominated regime created by long-term crystal aging and follows a common trend when compared with published data on Bi-, Hg-, Y-, and Nd-based cuprates. These results indicate that superconductivity reshapes CDW order in two distinct ways, suppressing its amplitude while strengthening its phase coherence, and reveal an additional phase-level interplay with lattice coupling in high-Tc cuprates.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript reports resonant soft x-ray scattering measurements across multiple cuprate families (Bi-, Hg-, Y-, and Nd-based) showing that superconductivity below Tc enhances CDW phase coherence. This is inferred from coherence-sensitive momentum-profile analysis revealing absence of CDW peak broadening and near-perfect wave-vector locking, even in long-term aged, disorder-dominated crystals. The effect is contrasted with amplitude suppression and compared to prior published data, indicating a dual role for superconductivity in reshaping CDW order with additional lattice-coupling implications.

Significance. If the momentum-profile analysis robustly isolates phase coherence, the result would revise the standard picture of CDW-SC competition in high-Tc cuprates by demonstrating a cooperative phase-level reinforcement. The cross-family consistency and persistence in aged samples add generality; the experimental approach using resonant soft x-ray scattering with profile fitting offers a useful probe for coherence effects.

major comments (2)
  1. [§4] §4 (momentum-profile analysis and fitting procedure): The claim that the coherence-sensitive fitting isolates true phase coherence (manifested as no broadening and wave-vector locking) from resolution, inhomogeneity, and static disorder is central to interpreting the BCS-like growth below Tc. However, the manuscript provides no explicit resolution deconvolution tests, Monte Carlo lineshape simulations, or comparison to a known phase-coherent reference sample, leaving the separation vulnerable to the alternative that broadening is masked by instrumental limits or aging-induced static effects.
  2. [§5] §5 (cross-family comparison and aged-crystal data): The systematic enhancement trend is presented as following a common pattern when overlaid on published Bi-, Hg-, Y-, and Nd-based results, but the manuscript does not detail whether the same fitting protocol and resolution corrections were applied uniformly to the external datasets; this weakens the generality claim.
minor comments (2)
  1. [Figure 3] Figure 3 caption and axis labels: the momentum profiles lack explicit indication of the fitted resolution function or error bars on the extracted coherence length, reducing clarity for readers attempting to assess the no-broadening claim.
  2. [Abstract and §3] The abstract states the enhancement 'remains visible even in a disorder-dominated regime' but the main text does not quantify the aging-induced disorder level (e.g., via rocking-curve widths or resistivity) relative to the instrumental resolution.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments and for recognizing the potential significance of our findings on superconductivity-enhanced CDW phase coherence. We address each major comment below and will incorporate revisions to strengthen the manuscript.

read point-by-point responses

  1. Referee: §4 (momentum-profile analysis and fitting procedure): The claim that the coherence-sensitive fitting isolates true phase coherence (manifested as no broadening and wave-vector locking) from resolution, inhomogeneity, and static disorder is central to interpreting the BCS-like growth below Tc. However, the manuscript provides no explicit resolution deconvolution tests, Monte Carlo lineshape simulations, or comparison to a known phase-coherent reference sample, leaving the separation vulnerable to the alternative that broadening is masked by instrumental limits or aging-induced static effects.

    Authors: We agree that explicit validation of the fitting procedure would strengthen the separation of phase coherence from resolution and disorder effects. In the revised manuscript we will add resolution deconvolution tests using the measured instrumental resolution function, Monte Carlo simulations of Lorentzian and Gaussian lineshapes under controlled coherence lengths, and a direct comparison to a reference sample (e.g., a low-disorder YBCO crystal) where phase coherence is independently established by other probes. These additions will be placed in the methods section and supplementary information. revision: yes

  2. Referee: §5 (cross-family comparison and aged-crystal data): The systematic enhancement trend is presented as following a common pattern when overlaid on published Bi-, Hg-, Y-, and Nd-based results, but the manuscript does not detail whether the same fitting protocol and resolution corrections were applied uniformly to the external datasets; this weakens the generality claim.

    Authors: We acknowledge that the manuscript does not explicitly document the uniform application of the fitting protocol and resolution corrections to the external published datasets. In the revision we will add a dedicated paragraph in the methods section (and a supplementary table) that specifies the exact fitting function, background subtraction, and resolution correction procedure applied to each family, together with the source references and any re-analysis steps performed on the published data. This will make the cross-family comparison fully reproducible. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental observations and cross-family comparison are independent of self-referential fitting or derivation

full rationale

The paper reports resonant soft x-ray scattering measurements on cuprate crystals and interprets the absence of CDW peak broadening plus wave-vector locking below Tc as enhanced phase coherence. This is compared to previously published data on Bi-, Hg-, Y-, and Nd-based cuprates. No equations, ansatz, or fitting procedure is shown that defines the coherence metric from the same dataset in a self-referential loop; the momentum-profile analysis is presented as a measurement tool rather than a tautological re-expression of the input data. The central claim therefore rests on direct experimental contrast and external literature benchmarks rather than reducing to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper is purely experimental and relies on established condensed-matter techniques rather than new theoretical postulates.

axioms (1)
  • domain assumption Resonant soft x-ray scattering intensity at the CDW wave-vector directly reflects the CDW order parameter amplitude and phase coherence.
    Invoked when interpreting momentum profiles as measures of phase coherence.

pith-pipeline@v0.9.0 · 5481 in / 1255 out tokens · 39130 ms · 2026-05-13T01:20:25.559445+00:00 · methodology

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Reference graph

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