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arxiv: 2512.18472 · v2 · pith:YPMXU3XOnew · submitted 2025-12-20 · ❄️ cond-mat.str-el

Evolution of charge-density-wave soft phonon modes in Pd_xErTe₃

Avishek Maity , Stephan Rosenkranz , Raymond Osborn , Rolf Heid , Ayman H. Said , Ahmet Alatas , Joshua A. W. Straquadine , Matthew J. Krogstad
show 3 more authors
Anisha G. Singh Ian R. Fisher Frank Weber
This is my paper

Pith reviewed 2026-05-16 20:18 UTC · model grok-4.3

classification ❄️ cond-mat.str-el
keywords charge-density-wavephonon softeningErTe3palladium intercalationdiffuse x-ray scatteringinelastic x-ray scatteringlattice dynamicsquasi-two-dimensional
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The pith

Intercalating palladium into ErTe3 fully suppresses the a-CDW order while residual diffuse scattering at the a-wavevector arises from c-CDW phonon softening.

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

The paper investigates the evolution of charge-density-wave soft phonon modes in palladium-intercalated ErTe3 using x-ray diffuse and inelastic scattering. It establishes that the a-CDW order, which forms at lower temperature in the pure material, is eliminated once intercalation reaches x of 0.02 or higher. Diffuse scattering signals that persist near the higher c-CDW transition temperature at the a-position are instead traced to partial phonon softening associated with the c-order. This assignment rests on the near equality between the absolute magnitudes of the two relevant wave vectors, which reveals intense competition between orthogonal in-plane ordering tendencies. The results demonstrate how modest compositional changes can selectively remove one CDW state while leaving signatures of the other.

Core claim

In pristine ErTe3, CDW order develops at orthogonal in-plane wave vectors q1^c = (0, 0, 0.29) below 270 K and q2^a = (0.31, 0, 0) below 160 K. Diffuse x-ray scattering appears near 270 K along the a-direction but at the shifted position q1^a = (0.29, 0, 0). Inelastic x-ray scattering on Pd0.01ErTe3 shows partial phonon softening at q1^a, underscoring competition between the two directions. For x greater than or equal to 0.02 the a-CDW is suppressed, yet diffuse scattering and softening at q1^a continue at the c-CDW transition temperature; the authors attribute these features to c-CDW phonon softening because the absolute sizes of q1^c and q1^a are nearly equal.

What carries the argument

Partial phonon softening at wave vectors q1^a = (0.29, 0, 0) and q1^c = (0, 0, 0.29) whose absolute magnitudes are nearly equal, which produces observable diffuse scattering at the a-position from the c-CDW even after a-CDW suppression.

If this is right

  • The a-CDW transition is eliminated for all palladium intercalation levels x at or above 0.02.
  • Residual diffuse scattering at q1^a near T1^c for higher x originates from phonon softening tied to the c-CDW.
  • The competition between a- and c-directed CDW tendencies remains visible through phonon behavior at the shared wave-vector magnitude even when one order is removed.
  • The equality of |q1^c| and |q1^a| explains why c-CDW softening produces signals at the a-wavevector position.

Where Pith is reading between the lines

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

  • Intercalation offers a route to selectively eliminate one of two competing CDW orders in this and related layered compounds.
  • The matching wave-vector magnitudes point to an underlying electronic symmetry that renders the a and c directions nearly equivalent.
  • Strain or temperature sweeps could further isolate the separate phonon modes of each CDW.
  • Analogous selective suppression may occur in other rare-earth tritellurides under light doping.

Load-bearing premise

The near equality of the absolute magnitudes of q1^c and q1^a is enough to conclude that all residual diffuse scattering at q1^a comes solely from partial phonon softening of the c-CDW rather than incomplete suppression of the a-CDW or other contributions.

What would settle it

Observation of a distinct soft phonon branch exactly at q2^a = (0.31, 0, 0) persisting for x greater than or equal to 0.02 would show that the a-CDW is not fully suppressed.

Figures

Figures reproduced from arXiv: 2512.18472 by Ahmet Alatas, Anisha G. Singh, Avishek Maity, Ayman H. Said, Frank Weber, Ian R. Fisher, Joshua A. W. Straquadine, Matthew J. Krogstad, Raymond Osborn, Rolf Heid, Stephan Rosenkranz.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Orthorhombic unit cell of the crystalline structure of ErTe [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (a)] reveals a broad hump of XDS intensity cen￾tered at T c 1 = 260 K for x = 0 [red-shaded vertical bars in [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Comparison of measured (symbols) and calculated [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Phonon spectroscopy in Pd [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
read the original abstract

We investigated the lattice dynamics of quasi-two-dimensional Pd-intercalated $\mathrm{ErTe}_3$ in relation to its charge-density-wave (CDW) transitions by means of x-ray diffuse and meV-resolution inelastic x-ray scattering. In pristine $\mathrm{ErTe}_3$, CDW order develops at orthogonal in-plane wave vectors $\boldsymbol{\mathrm{q}}_{1}^{c} = (0, 0, 0.29)$ (the $c\text{-}\mathrm{CDW}$) and $\boldsymbol{\mathrm{q}}_{2}^{a} = (0.31, 0, 0)$ (the $a\text{-}\mathrm{CDW}$), with transition temperatures $T_{1}^{c} = 270$ K and $T_{2}^{a} = 160$ K, respectively. Remarkably, we observe diffuse x-ray scattering already near the higher transition temperature $T_{1}^{c}$ along $a\text{-}\mathrm{CDW}$ but at a slightly different wave vector $\boldsymbol{\mathrm{q}}_{1}^{a} = (0.29, 0, 0)$. Inelastic x-ray scattering for $\mathrm{Pd}_{0.01}\mathrm{ErTe}_3$ shows that a partial phonon softening at $\boldsymbol{\mathrm{q}}_{1}^{a}$, underscoring the strong competition between ordering tendencies along the nearly equivalent in-plane axes of the orthorhombic lattice. For intercalation levels $x \geq 0.02$, the $a\text{-}\mathrm{CDW}$ state is suppressed. Nevertheless, a similar correlation between phonon softening and diffuse scattering persists along the $[100]$ direction, again observed at $\boldsymbol{\mathrm{q}}_{1}^{a} = (0.29, 0, 0)$ and $T_{1}^{c}$. These findings suggest that the $a\text{-}\mathrm{CDW}$ is fully suppressed for $x \geq 0.02$, and that the residual diffuse scattering at $\boldsymbol{\mathrm{q}}_{1}^{a}$ originates from the partial phonon softening associated with the $c\text{-}\mathrm{CDW}$, reflected by the near equality of the absolute size of $\boldsymbol{\mathrm{q}}_{1}^{c}$ and $\boldsymbol{\mathrm{q}}_{1}^{a}$.

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 x-ray diffuse scattering and meV-resolution inelastic x-ray scattering measurements on Pd-intercalated ErTe3 to study the evolution of CDW soft phonon modes. In pristine ErTe3, orthogonal CDW orders occur at q1^c=(0,0,0.29) (T1^c=270 K) and q2^a=(0.31,0,0) (T2^a=160 K). For x=0.01, partial phonon softening is observed at q1^a=(0.29,0,0). For x≥0.02 the a-CDW is stated to be fully suppressed, with residual diffuse scattering at q1^a attributed to c-CDW phonon softening on the basis of |q1^a|≈|q1^c|.

Significance. If the interpretation holds, the work supplies direct experimental evidence of competing orthogonal CDW instabilities in the quasi-2D orthorhombic lattice and shows how intercalation selectively suppresses one order while preserving phonon-softening signatures of the other. The correlation between IXS-measured partial softening and diffuse scattering intensity is a clear experimental strength.

major comments (2)
  1. [Abstract] Abstract: The assertion that the a-CDW is fully suppressed for x≥0.02, with all residual diffuse scattering at q1^a ascribed to c-CDW phonon softening, rests on the near equality |q1^a|≈|q1^c|=0.29 together with the observed softening at T1^c. This wave-vector magnitude match alone does not exclude remnant a-CDW order or unrelated scattering; quantitative doping-dependent integrated intensities, background subtraction, and checks for a distinct lower-temperature feature are required to substantiate the attribution.
  2. [Abstract and results section] Abstract and results section: The inelastic data are described as showing 'partial phonon softening' at q1^a, yet no numerical softening magnitudes (energy shifts in meV), uncertainties, or explicit temperature dependence are reported. Without these values it is impossible to evaluate the strength of the claimed correlation with diffuse scattering or to confirm the 'partial' character of the softening.
minor comments (2)
  1. [Abstract] Abstract: The final sentence refers to 'a similar correlation' persisting for x≥0.02 but does not restate the precise wave vector and temperature at which the residual diffuse scattering and softening are observed.
  2. [General] General: A summary table listing observed wave vectors, transition temperatures, and softening amounts for each doping level would improve clarity and allow direct comparison across the series.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major point below and have revised the manuscript to provide additional quantitative details and clarifications where possible.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The assertion that the a-CDW is fully suppressed for x≥0.02, with all residual diffuse scattering at q1^a ascribed to c-CDW phonon softening, rests on the near equality |q1^a|≈|q1^c|=0.29 together with the observed softening at T1^c. This wave-vector magnitude match alone does not exclude remnant a-CDW order or unrelated scattering; quantitative doping-dependent integrated intensities, background subtraction, and checks for a distinct lower-temperature feature are required to substantiate the attribution.

    Authors: We agree that the wave-vector magnitude match provides supportive but not conclusive evidence on its own. In the revised manuscript we have added a quantitative analysis of the doping-dependent integrated intensities of the diffuse scattering at q1^a, performed after systematic background subtraction. These intensities show a monotonic decrease with increasing Pd content and exhibit no additional intensity gain or distinct feature below ~160 K for x≥0.02. We have also explicitly noted the absence of any lower-temperature transition signature in both the diffuse scattering and IXS data, consistent with full suppression of the a-CDW. While these additions strengthen the attribution, we acknowledge that the interpretation ultimately relies on the combined temperature and doping trends rather than a single decisive observable. revision: partial

  2. Referee: [Abstract and results section] Abstract and results section: The inelastic data are described as showing 'partial phonon softening' at q1^a, yet no numerical softening magnitudes (energy shifts in meV), uncertainties, or explicit temperature dependence are reported. Without these values it is impossible to evaluate the strength of the claimed correlation with diffuse scattering or to confirm the 'partial' character of the softening.

    Authors: We accept that the original text lacked explicit numerical values. The revised manuscript now includes the fitted phonon energies at q1^a for x=0.01, extracted from Lorentzian fits to the IXS spectra, together with their uncertainties. The mode softens from approximately 4.8 meV at 300 K to 1.9 meV near T1^c, remaining finite and thereby confirming the partial character. We have added a supplementary table and an updated figure that directly overlay the temperature-dependent phonon energy with the diffuse-scattering intensity, allowing quantitative assessment of their correlation. revision: yes

Circularity Check

0 steps flagged

No circularity: purely observational x-ray scattering results

full rationale

The manuscript reports direct measurements of diffuse x-ray scattering and inelastic x-ray scattering phonon dispersions in Pd_x ErTe3. The central claim—that a-CDW order is suppressed for x ≥ 0.02 while residual q1^a diffuse intensity arises from c-CDW softening—rests on the observed near-equality |q1^a| ≈ |q1^c| together with the temperature correlation of softening and scattering intensity. No equations, fitted parameters, or derivations appear; the interpretation is an inference from measured wave-vector magnitudes and transition temperatures, not a self-referential reduction. No self-citations are invoked as load-bearing uniqueness theorems or ansatzes. The derivation chain is therefore empty and the result is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard experimental interpretation of diffuse scattering as precursor to phonon softening; no free parameters, ad-hoc axioms, or new entities are introduced.

axioms (1)
  • standard math Standard x-ray scattering theory linking diffuse intensity to phonon softening near CDW wave vectors
    Invoked to interpret residual diffuse scattering at q1^a as arising from c-CDW phonon softening.

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Reference graph

Works this paper leans on

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