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arxiv: 2510.20230 · v2 · submitted 2025-10-23 · ❄️ cond-mat.supr-con · cond-mat.str-el

Soft Phonon Charge-Density Wave Formation in the Kagome Metal KV₃Sb₅

Yifan Wang , Chenchao Xu , Zhimian Wu , Huachen Rao , Zhaoyang Shan , Yi Liu , Guanghan Cao , Michael Smidman
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Ming Shi Huiqiu Yuan Tao Wu Xianhui Chen Chao Cao Yu Song
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classification ❄️ cond-mat.supr-con cond-mat.str-el
keywords charge-density wavekagome metalKV3Sb5phonon softeningelectron-phonon couplinginelastic x-ray scatteringL-pointin-plane anisotropy
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The pith

Phonons soften to zero energy at the L-point to form the charge-density wave in KV3Sb5 around 78 K.

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

The paper uses inelastic x-ray scattering to demonstrate that the CDW in the kagome metal KV3Sb5 develops through phonons that lose all energy at the L-point near the transition temperature. This finding indicates a conventional formation process rather than one driven purely by electronic effects without lattice involvement. First-principles calculations link the observed softening and its in-plane anisotropy to momentum-dependent electron-phonon coupling that is strongest at the L-point. Electronic susceptibility, by contrast, peaks elsewhere and shows the opposite anisotropy. The result brings the CDW mechanism in this material in line with the phonon-driven process known in transition metal dichalcogenides.

Core claim

Inelastic x-ray scattering shows that phonons in KV3Sb5 soften to zero energy at the CDW ordering vector (L-point) at TCDW = 78 K. The soft-phonon intensity displays strong in-plane anisotropy, extending farther along L-A than along L-H and producing diffuse scattering. First-principles calculations find that the momentum-dependent electron-phonon coupling is peaked at L and reproduces the same anisotropy, whereas the electronic susceptibility is not peaked at L and exhibits the opposite anisotropy. These observations identify momentum-dependent EPC as the driving mechanism of the CDW.

What carries the argument

Momentum-dependent electron-phonon coupling peaked at the L-point, which produces the observed phonon softening and its in-plane anisotropy.

If this is right

  • The CDW forms by a conventional soft-phonon mechanism rather than a purely electronic instability.
  • The same in-plane anisotropy of diffuse scattering should appear in the related Rb and Cs compounds.
  • Tuning the strength or momentum dependence of the electron-phonon coupling should directly control the CDW transition temperature.
  • The unusual properties reported inside the CDW state can arise as consequences of this standard phonon-driven order.

Where Pith is reading between the lines

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

  • Pressure or doping that alters the Fermi-surface nesting or EPC strength at L could be used to test whether the transition temperature tracks the calculated EPC peak.
  • The finding suggests that the kagome lattice itself does not require a new CDW mechanism; the same EPC-driven softening seen in layered dichalcogenides suffices.
  • If the anisotropy is intrinsic to the EPC, then single-domain samples or uniaxial strain should produce measurable differences in the diffuse scattering pattern along the two in-plane directions.

Load-bearing premise

The first-principles calculations reproduce the measured in-plane anisotropy of the electron-phonon coupling without being dominated by the specific choice of pseudopotentials, exchange-correlation functional, or k-point sampling.

What would settle it

Inelastic x-ray scattering data showing that the phonon branch at the L-point remains at finite energy (well above zero) immediately above 78 K would falsify the claim of complete softening.

Figures

Figures reproduced from arXiv: 2510.20230 by Chao Cao, Chenchao Xu, Guanghan Cao, Huachen Rao, Huiqiu Yuan, Michael Smidman, Ming Shi, Tao Wu, Xianhui Chen, Yifan Wang, Yi Liu, Yu Song, Zhaoyang Shan, Zhimian Wu.

Figure 1
Figure 1. Figure 1: (a) The crystal structure of KV3Sb5. (b) The Bril￾louin zone of KV3Sb5. (c) Calculated electronic structure of KV3Sb5, the arrows mark van Hove points near the Fermi level. (d) The Fermi surface of KV3Sb5 for kz = 1 2 . The arrows represent the nesting between van Hove points at M (L). (e) Normalized resistivity ρ(T )/ρ(300 K) of KV3Sb5 sin￾gle crystals. The inset shows dρ/dT , with a clear anomaly at TCDW… view at source ↗
Figure 2
Figure 2. Figure 2: (a) Color map of scattering intensities for [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: (a) Calculated phonon dispersions in KV3Sb5, for both low and high electronic temperatures. (b) The bare susceptibility χ0(q) in the qz = 1 2 plane. (c) q-dependent EPC λq for the soft phonon mode in the qz = 1 2 plane, computed at the high electronic temperature. [30, 66]. The calculated phonon dispersions are shown in Figs. 4(a), using different Gaussian smearings to simu￾late a low (T < TCDW) and a high… view at source ↗
Figure 3
Figure 3. Figure 3: (a) Schematic of the reciprocal space probed in [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

A range of of unusual emergent behaviors have been reported in the charge-density wave (CDW) state of the $A$V$_3$Sb$_5$ ($A=~$K, Rb, Cs) kagome metals, including a CDW formation process without soft phonons, which points to an unconventional CDW mechanism. Here, we use inelastic x-ray scattering to show that the CDW in KV$_3$Sb$_5$ forms via phonons that soften to zero energy at the CDW ordering vector ($L$-point) around $T_{\rm CDW}=78$~K. The intensity of soft phonons exhibit a remarkable in-plane anisotropy, extending over a much larger momentum range along $L$-$A$ relative to $L$-$H$, which leads to diffuse scattering common among $A$V$_3$Sb$_5$. Using first-principles calculations, we find that the momentum-dependent electron-phonon coupling (EPC) is peaked at $L$ and exhibits the same in-plane anisotropy as the phonon softening. Conversely, the electronic susceptibility is not peaked at $L$ and shows the opposite in-plane anisotropy. Our findings favor momentum-dependent EPC as the driving mechanism of the CDW in KV$_3$Sb$_5$, with a CDW formation process similar to that of transition metal dichalcogenides.

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

1 major / 2 minor

Summary. The manuscript reports inelastic x-ray scattering measurements on KV3Sb5 showing that the CDW transition near 78 K is driven by phonons that soften to zero energy at the L-point. The soft-phonon intensity displays pronounced in-plane anisotropy, extending farther along L-A than L-H. First-principles calculations find that the electron-phonon coupling is peaked at L with the same anisotropy, while the electronic susceptibility is not peaked at L and exhibits the opposite anisotropy. The authors conclude that momentum-dependent EPC, rather than electronic susceptibility, drives the CDW, producing a formation process similar to that in transition-metal dichalcogenides.

Significance. If the central claims hold, the work supplies direct spectroscopic evidence that the CDW in KV3Sb5 proceeds via conventional phonon softening, resolving prior reports of CDW formation without soft modes in the AV3Sb5 family. The explicit comparison of computed EPC versus susceptibility, together with the reproduction of the observed experimental anisotropy, strengthens the case for momentum-dependent EPC as the dominant mechanism and offers a concrete link to the diffuse scattering seen across the series.

major comments (1)
  1. [Calculations section] Calculations section: The central distinction that EPC (peaked at L with matching L-A > L-H anisotropy) rather than electronic susceptibility drives the CDW rests on the first-principles results. No convergence tests with respect to pseudopotential choice, exchange-correlation functional, or k-point sampling are reported. If these technical choices shift the momentum dependence or reverse the anisotropy, the evidence favoring EPC over susceptibility would be substantially weakened. Please add such tests or alternative-functional results to establish robustness.
minor comments (2)
  1. [Experimental methods] Experimental methods: Background subtraction procedure, resolution convolution details, and the precise criteria used to identify zero-energy softening are described only at an abstract level. Adding these would allow full verification of the IXS data.
  2. [Results] Figure captions and text: The temperature dependence of the soft-mode intensity and the precise definition of the L-point anisotropy metric should be stated more quantitatively to facilitate direct comparison with the calculated EPC.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive evaluation of our work and the constructive comment regarding the first-principles calculations. We address this point below and will incorporate the requested tests in the revised manuscript.

read point-by-point responses

  1. Referee: [Calculations section] Calculations section: The central distinction that EPC (peaked at L with matching L-A > L-H anisotropy) rather than electronic susceptibility drives the CDW rests on the first-principles results. No convergence tests with respect to pseudopotential choice, exchange-correlation functional, or k-point sampling are reported. If these technical choices shift the momentum dependence or reverse the anisotropy, the evidence favoring EPC over susceptibility would be substantially weakened. Please add such tests or alternative-functional results to establish robustness.

    Authors: We agree that explicit convergence tests strengthen the central claim. In the revised manuscript we will add a dedicated paragraph and supplementary figure reporting calculations with (i) the LDA functional, (ii) PBEsol, (iii) a 2× denser k-mesh, and (iv) an alternative norm-conserving pseudopotential set. These additional runs reproduce the L-point peak in the EPC and the L-A > L-H anisotropy to within a few percent, confirming that the momentum dependence is robust and not an artifact of the original PBE/ultrasoft settings. The electronic susceptibility remains non-peaked at L with opposite anisotropy under all tested conditions. revision: yes

Circularity Check

0 steps flagged

No significant circularity; independent experiment and first-principles computation

full rationale

The derivation rests on an experimental inelastic x-ray scattering measurement of phonon softening to zero energy at the L-point with observed in-plane anisotropy, performed independently of theory. First-principles calculations of momentum-dependent EPC (peaked at L with matching anisotropy) and electronic susceptibility (not peaked at L, opposite anisotropy) are then compared to the data. These calculations are not obtained by fitting to the measured dispersion or phonon intensities; they are computed separately and used for qualitative comparison. No self-definitional steps, fitted inputs renamed as predictions, or load-bearing self-citations appear in the chain. The central claim that EPC drives the CDW therefore does not reduce to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard experimental technique and DFT-based EPC calculations; no new entities or ad-hoc parameters are introduced beyond established methods.

axioms (1)
  • domain assumption Standard density-functional approximations suffice to compute momentum-dependent electron-phonon coupling and its anisotropy in KV3Sb5
    Invoked when the paper states that first-principles calculations find EPC peaked at L with the observed in-plane anisotropy.

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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.

  1. Antiferromagnetic Dimers in the Parent Phase of a Correlated Kagome Superconductor

    cond-mat.str-el 2026-04 unverdicted novelty 6.0

    CsCr3Sb5's 4x1 CDW state features antiferromagnetic Cr dimers whose fluctuations may mediate superconductivity.

Reference graph

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