{"id":"9136d2f5-abc2-43a4-9315-3111e9c15691","arxiv_id":"2411.14746","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"M-EELS measurements of ErTe3 reveal relaxational, diffusive charge dynamics near the CDW transition and a static charge susceptibility that increases with decreasing temperature, but no actual divergence.","lead":"This paper measures the dynamic charge susceptibility of the charge density wave material ErTe3 using momentum-resolved electron energy loss spectroscopy, finding purely relaxational electronic dynamics and a static susceptibility that grows as temperature drops. The result is significant as the first meV-resolution measurement of the charge response near a CDW transition, though the claimed divergence is not directly observed.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The reported divergence/increase in χ'(q,0) rests on A/γ from raw Glauber fits to M-EELS spectra, but the 5.6 meV resolution is never deconvolved; once γ approaches this scale, the extracted static susceptibility is not the intrinsic value.","rationale":"The reader's weakest assumption is surface sensitivity. That concern is legitimate, but the paper partially addresses it by showing that the elastic CDW signal yields Tc = 268(7) K, consistent with bulk x-ray measurements, so the surface appears to undergo the same bulk transition. The more immediate threat to the central claim is that the static susceptibility is not measured directly; it is the ratio A/γ obtained from fits to a model that may be distorted by the finite instrument resolution. Critical slowing down implies γ decreases toward low T near q0, so the regime where γ is comparable to 5.6 meV is precisely where the claimed increase in χ' is largest. Without a resolution-deconvolved analysis, the temperature dependence of χ'(q0,0) cannot be separated from resolution effects. This concern targets the quantitative content of the 'first observation' claim, not just its framing. The abstract overstates a divergence that the body qualifies, but the body's qualifier is openly stated; the resolution issue is unaddressed and would survive even if the text were reworded. I therefore retain the reader's CONDITIONAL verdict, with the condition that the analysis be redone or justified with respect to resolution convolution and model uniqueness.","tokens_in":11743,"tokens_out":7675,"duration_ms":84219,"concrete_test":"Re-fit all raw energy-loss spectra after explicit convolution of Eq. (3) with the measured 5.6 meV resolution function; if the deconvolved γ(q0,T) values at low T differ from the reported values by more than the resolution width, recompute χ' = A/γ and test whether the increase persists. Additionally, fit the same data with an overdamped harmonic oscillator, Im χ = Aωγ/[(ω0^2 - ω^2)^2 + ω^2γ^2]; if the goodness of fit is comparable, the Glauber identification and the A/γ static limit are not unique. Report the ratio γ(q0,T)/R_Res as a function of temperature; any points with γ/R_Res < 1 should be flagged as resolution-limited.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The headline claim that χ'(q,0) = A/γ (Eq. 6) increases and 'diverges' is derived exclusively from two-parameter Glauber fits (Eq. 3) to raw M-EELS spectra. The stated 5.6 meV FWHM instrument resolution is not mentioned in the fitting procedure or SI, so the fits appear to ignore resolution convolution. Near the CDW wavevector, the data show critical slowing down: γ(q0,T) drops sharply below Tc (Fig. 3d). Once γ becomes comparable to or smaller than the 5.6 meV resolution width, the fitted Lorentzian width and amplitude are dominated by the resolution function rather than by intrinsic charge dynamics. In that regime A/γ is not the true static susceptibility, and the continued rise of χ'(q0,0) to the lowest temperature (Fig. 4b) may be an artifact of fitting a resolution-broadened quasi-elastic line. The abstract's word 'divergence' is also stronger than the body's admission that χ' 'does not diverge at TC1'; however, the deeper problem is that even the reported monotonic increase is model- and resolution-dependent. No error bars are given for A, γ, or χ', and no comparison is made with alternative line shapes, such as an overdamped oscillator with finite frequency, so the uniqueness of the Glauber interpretation and of the A/γ static limit is not established.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports momentum-resolved electron energy-loss spectroscopy (M-EELS) measurements of ErTe3 near its higher charge-density-wave transition at TC1 ≈ 267 K. Elastic scans track the CDW satellite and its correlation length, while inelastic spectra are fit to a Glauber/diffusive model, χ''(q,ω,T) = A(q,T) ω / (ω² + γ²(q,T)). The extracted relaxation rate γ(q,T) shows a minimum near the CDW wavevector q0, which the authors interpret as critical slowing down, and a parabolic q-dependence that yields a diffusion constant D(T) peaking near 250 K. The static susceptibility is then obtained as χ'(q,0) = A/γ, which increases with decreasing temperature and is presented as the first observation of the predicted divergence of χ(q) at a CDW transition. The body text, however, explicitly states that the susceptibility does not diverge at TC1 but continues to rise to the lowest measured temperature.","tokens_in":12078,"tokens_out":3595,"duration_ms":36082,"significance":"If the central analysis is correct, this would be a notable experimental advance: a meV-resolution, momentum-resolved measurement of the dynamic charge susceptibility near a CDW transition, showing purely relaxational electronic dynamics that behave differently from the phonon softening seen by inelastic x-ray scattering. The observation of a q-dependent relaxation rate and a diffusivity peak just below Tc is potentially interesting and could motivate further work. However, the headline claim about the static susceptibility is model-derived rather than independently measured, and it is sensitive to instrumental resolution and to the choice of lineshape. These issues must be addressed before the result can be regarded as established.","major_comments":[{"comment":"The fits to the M-EELS loss spectra use the raw data without any apparent deconvolution of the stated 5.6 meV FWHM energy resolution. Once γ(q0,T) falls near or below this energy scale, as it does below Tc in Fig. 3(d), the fitted Lorentzian width and amplitude become dominated by the instrument resolution rather than by the intrinsic charge dynamics. In that regime the quantity χ'(q0,0) = A/γ from Eq. (6) is not the true static susceptibility, and the continued rise in Fig. 4(b) may be an artifact. Please include a resolution convolution in the fit model or otherwise demonstrate that the extracted A and γ are unaffected down to the lowest temperatures and momenta shown.","section":"§4, Eq. (4) and Fig. 3(d)"},{"comment":"The static susceptibility is not measured independently; it is defined as A/γ from the same Glauber model, Eq. (3), used to fit the spectra. The increase of χ'(q,0) with decreasing temperature is therefore a consequence of the fitted parameters, not an independent experimental observation. To support the claim that this increase reflects an intrinsic divergence, the authors should compare against alternative lineshapes (for example, an overdamped oscillator with a finite bare frequency) and report the fitted A(q,T) and γ(q,T) with uncertainties. Currently no error bars are given for any extracted quantity, which makes it impossible to assess the significance of the reported trends.","section":"§4, Eq. (6)"},{"comment":"The abstract claims 'a divergence in the real part of χ(q,ω) in the static limit' and describes it as 'the first time' such a phenomenon has been observed, but the body text in §5 explicitly states that the susceptibility 'does not diverge at TC1' and instead continues to rise to the lowest temperature measured. The abstract should be reconciled with the body: the data support a monotonic increase, not a divergence at the transition. The wording 'first experimental observation' should also be moderated given that the quantity is extracted from a model fit rather than measured directly.","section":"Abstract and §5, Fig. 4"},{"comment":"The 50 eV incident electron energy used in the M-EELS experiment makes the measurement strongly surface sensitive, yet the paper compares the extracted susceptibility and dynamics with bulk TC1 and bulk transport and thermodynamic properties without discussing possible surface-versus-bulk differences. If the surface CDW transition temperature or fluctuation spectrum differs from the bulk, the extracted χ(q,ω) would not describe the bulk CDW transition. Please address this limitation explicitly or qualify the conclusions accordingly.","section":"§2, Fig. 1(c)"}],"minor_comments":[{"comment":"The phrase 'CDW mehavior' in the second paragraph is a typo and should read 'CDW behavior'.","section":"Introduction"},{"comment":"There are missing spaces in 'TC1≈ 267K and TC2≈ 159K withqC1≈ (5/7)c∗'; please format these quantities consistently.","section":"§3, text and Fig. 2"},{"comment":"The caption uses t in χ′(q,ω=0,t) where the text and figure axes refer to temperature T; please correct the symbol.","section":"Fig. 4 caption"},{"comment":"The global fit to the disorder model reports the minima at σ = 2.6 and κ = 2500 but gives no uncertainties on these parameters; provide confidence intervals or standard errors to support the claim that the two fits are comparable.","section":"Supplemental Information, Eq. (S2)"},{"comment":"The notation ℏD(T) implies D has units of energy divided by squared momentum, but the paper later refers to a 'diffusion constant' and a diffusion length λ ∼ √(Dτ). Please define the units of D explicitly and check consistency between Eqs. (5) and the definition of λ.","section":"§4, Eq. (5)"},{"comment":"The text calls the fit a 'BCS interpolation formula' but the expression used is a mean-field order-parameter interpolation; please clarify the terminology.","section":"§3, Fig. 2(b)"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is within scope for cond-mat.str-el and addresses a question of genuine interest. The main issue is that the central claim about the static susceptibility is derived from a two-parameter model fit to resolution-limited data, and the paper does not provide the deconvolution or error analysis needed to make that claim robust. With a careful revision that includes resolution treatment, error bars, alternative lineshape tests, and a moderated abstract, this could become a valuable contribution. I do not see any indication of data fabrication or misconduct."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Let me give you my read. The genuinely new thing here is the measurement itself: first meV-resolution dynamic charge susceptibility across a CDW transition, and it shows the electronic response is purely relaxational, not the soft phonon behavior seen by IXS. That is a real result and likely stands regardless of the static susceptibility issues. The elastic scattering analysis is careful, the Tc they extract matches x-ray data, and the Glauber model fits the loss spectra well with only two parameters.\n\nThe soft spots are real but not fatal to the relaxational claim. The abstract says 'divergence' while the body admits the static susceptibility does not diverge at Tc and keeps rising to low T. That's an overclaim, and the body's explanation—bare vs dressed susceptibility—is speculative. More importantly, the stress-test note is on point: the data are never deconvolved from the 5.6 meV resolution. Near q0, γ drops below the resolution scale, so A and γ from the Glauber fits are not independent. The ratio A/γ then reflects the resolution function as much as the intrinsic response. The continued rise of χ'(q0,0) to lowest temperature could be a resolution artifact. There are no error bars on A, γ, or χ', and no comparison with alternative line shapes, so the A/γ route to the static susceptibility is model-dependent. The surface sensitivity of 50 eV M-EELS is also an unaddressed assumption; the authors should at least justify that the surface response tracks the bulk CDW.\n\nNone of this kills the paper. The relaxational dynamics and the diffusivity peak near 250 K are interesting and worth reporting, and the measurement technique is genuinely new in this context. But the static susceptibility claim needs to be either backed with a resolution-deconvolved analysis or pulled back to what the data actually show.\n\nWho is this for? CDW experimentalists and theorists who care about order-parameter fluctuations. It deserves a serious referee: the experimental window is valuable, and the issues are addressable in revision. I'd recommend sending it out, with a referee who will push on the resolution handling and the abstract/body mismatch.","headline":"First meV-resolved dynamic susceptibility across a CDW transition, with a promising relaxational-dynamics result, but the static susceptibility claim is overreached and likely resolution-limited.","tokens_in":12637,"tokens_out":2163,"would_cite":true,"duration_ms":20654,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Using meV-resolved M-EELS, this paper measures the dynamic charge susceptibility of ErTe3 near its CDW transition and finds purely relaxational dynamics with a static susceptibility that grows near the ordering wavevector as temperature…","keywords":["charge density wave","dynamic charge susceptibility","momentum-resolved electron energy loss spectroscopy","ErTe3","Glauber model","relaxational dynamics","critical slowing down","diffusive charge order"],"falsifier":"A direct test would be to measure the same dynamic response with a bulk-sensitive probe, such as meV-resolved inelastic x-ray scattering at the CDW wavevector, and check whether the static susceptibility $\\chi'(q_0,0)$ still rises with decreasing temperature and whether the line shape remains purely relaxational; if the bulk shows a softening collective mode or a $\\chi'$ that peaks at $T_c$, the surface assumption would be invalidated. A second falsifier: extend the measurement below $T_{C2}$ and see whether $\\chi'(q_0,0)$ continues to grow, saturates, or turns over, which would distinguish a genuine near-divergence from a disorder-rounded rise.","tokens_in":11586,"feed_emoji":"⚡","tokens_out":8633,"duration_ms":67831,"temperature":0.7,"pith_summary":"Using momentum-resolved electron energy loss spectroscopy (M-EELS) with about 5.6 meV energy resolution, this paper measures the dynamic charge susceptibility $\\chi(q,\\omega)$ of the canonical charge density wave (CDW) material ErTe3 across its primary transition at about 267 K. The electronic charge excitations are found to be purely relaxational, with no propagating collective mode, and the spectra are well described by a Glauber (diffusive) model. The relaxation rate is minimized near the CDW wavevector, indicating critical slowing down, and the extracted diffusion constant peaks around 250 K, just below the transition. In the static limit, the real part of the susceptibility grows sharply near $q_0$ as temperature decreases; the authors present this as the first experimental observation of the long-predicted divergence of $\\chi(q)$ at a CDW transition, while noting that the rise continues below $T_c$ rather than peaking there.","feed_headline":"M-EELS captures charge susceptibility at a CDW transition","feed_subtitle":"Electronic excitations in ErTe3 are diffusive; static susceptibility grows at ordering wavevector as temperature drops.","key_machinery":"The central object is the dynamic charge susceptibility $\\chi(q,\\omega)$ measured by M-EELS, parameterized by the Glauber (model A) form $\\chi''(q,\\omega) = A(q,T) \\omega / (\\omega^2 + \\gamma^2(q,T))$, where $\\gamma$ is a relaxation rate and $A$ sets the overall scale. The loss intensity is modeled as $I = V_{\\text{eff}}^2 n(\\omega,T) \\chi''$, with $V_{\\text{eff}}$ the Coulomb matrix element and $n$ the Bose factor, so that $A$ and $\\gamma$ are extracted directly from the data. The relaxation rate near the CDW wavevector is then described by a diffusion model $\\gamma(q,T) = \\hbar \\tau^{-1} + \\hbar D(T)(q-q_0)^2$, and the static susceptibility follows from $\\chi'(q,0) = A/\\gamma$. This chain converts raw energy-loss spectra into a temperature- and momentum-resolved picture of the charge fluctuations, including the diffusion constant and the static susceptibility.","core_discovery":"The paper's central claim is that the dynamic charge susceptibility of ErTe3 near its CDW transition is dominated by relaxational, diffusive fluctuations rather than by a propagating soft electronic mode, and that the static limit of this susceptibility rises strongly near the CDW wavevector as the temperature is lowered. Fitting the M-EELS loss spectra to the Glauber (model A) form for a non-conserved order parameter, $\\chi''(q,\\omega) = A \\omega/(\\omega^2+\\gamma^2)$, yields an excellent two-parameter description at all measured temperatures and momenta. The relaxation rate $\\gamma$ shows a pronounced minimum at $q_0$, the signature of critical slowing down, and a parabolic momentum dependence that defines a diffusion constant $D(T)$ with a maximum near 250 K. The real part of the susceptibility in the static limit, $\\chi'(q,0) = A/\\gamma$, develops a peak at $q_0$ that increases with decreasing temperature, which the authors identify as the first observation of the susceptibility divergence predicted for CDW transitions since the 1970s. They also carefully note that the rise does not diverge at $T_c$ but continues to the lowest temperature measured, offering possible explanations including weak disorder or gapping of only a small fraction of the Fermi surface.","pith_inferences":["Because 50 eV electrons probe only a few atomic layers near the surface, the measured susceptibility could differ from the bulk; a bulk-sensitive measurement would test whether the surface transition and dynamics are representative.","The exponential rather than logarithmic temperature dependence of $\\chi'(q_0,0)$ hints that the divergence mechanism is not simple 1D nesting; applying the same measurement to other RTe3 compounds with different rare-earth ions could map how this depends on Fermi surface morphology.","If the rise in $\\chi'(q_0,0)$ continues below the second transition $T_{C2}$ or saturates at low temperature, that would discriminate between a true near-divergence and a disorder-rounded response; this is a direct extension of the reported data.","The finding that the electronic response is relaxational while phonons soften suggests that the electron-phonon coupling that drives the CDW may itself be governed by the diffusive electronic fluctuations; a time-resolved extension could test whether these relaxational dynamics control the CDW ordering kinetics."],"forward_implications":["The charge dynamics in ErTe3 near its CDW transition are relaxational, so theories of the transition must account for diffusive order-parameter fluctuations rather than solely soft propagating modes.","The static charge susceptibility $\\chi'(q,0)$ grows near the CDW wavevector as the temperature is lowered, providing the first direct experimental evidence for the predicted divergence of $\\chi(q)$ at a CDW transition, albeit with a rise that continues below $T_c$.","The diffusion constant $D(T)$ peaks around 250 K, just below $T_c$, coinciding with the temperature where a strong violation of the Wiedemann-Franz law was previously reported.","The characteristic diffusion length of the CDW fluctuations is roughly 2 to 10 lattice constants, similar to diffusive charge order in a stripe-ordered cuprate.","Density fluctuations are present at all measured momenta, indicating that a substantial fraction of valence electrons contributes to the charge response even away from $q_0$."],"supporting_citations":[{"why":"Supplies the M-EELS technique and the expression for the loss intensity used to extract the dynamic charge susceptibility.","marker":"[32]"},{"why":"Provides the crystal growth, the transition temperatures $T_{C1}$ and $T_{C2}$, and the CDW wavevector $q_{C1}$ for ErTe3.","marker":"[19]"},{"why":"Gives the ARPES gap values and the evidence that only a small fraction of the Fermi surface is gapped by the CDW order.","marker":"[20]"},{"why":"Shows the phonon softening at the CDW wavevector, providing the contrast to the purely relaxational electronic response.","marker":"[25]"},{"why":"Predicts the divergence of the static charge susceptibility at a CDW transition and discusses the unrenormalized susceptibility.","marker":"[1]"},{"why":"Supplies the Glauber (model A) form for the dynamic susceptibility of a non-conserved order parameter.","marker":"[52]"},{"why":"Reports the anomalous thermal transport and Wiedemann-Franz violation just below $T_c$, connected to the diffusivity peak.","marker":"[53]"},{"why":"Provides the diffusive charge-order dynamics and the diffusion-length estimate used for comparison.","marker":"[54]"}],"fun_headline_variants":["Static charge susceptibility divergence seen in ErTe3 CDW","M-EELS shows diffusive charge dynamics in ErTe3 near CDW","Charge susceptibility in ErTe3 purely relaxational near CDW","Diffusive modes dominate charge response in ErTe3 CDW transition","First meV-resolved glimpse of dynamic charge susceptibility"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The central assumption is that the surface charge dynamics measured with 50 eV electrons accurately represent the bulk CDW transition in ErTe3.","fun_headline_variants_meta":{"raw":{"variants":["Static charge susceptibility divergence seen in ErTe3 CDW","M-EELS shows diffusive charge dynamics in ErTe3 near CDW","Charge susceptibility in ErTe3 purely relaxational near CDW","Diffusive modes dominate charge response in ErTe3 CDW transition","First meV-resolved glimpse of dynamic charge susceptibility"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000329,"raw_usage":{"total_tokens":1897,"prompt_tokens":1070,"completion_tokens":827,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":686,"completion_tokens_details":{"reasoning_tokens":740}},"tokens_in":686,"tokens_out":827,"duration_ms":10333,"temperature":1.0,"reasoning_tokens":740,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T14:56:16.886798+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A direct test would be to measure the same dynamic response with a bulk-sensitive probe, such as meV-resolved inelastic x-ray scattering at the CDW wavevector, and check whether the static susceptibility $\\chi'(q_0,0)$ still rises with decreasing temperature and whether the line shape remains purely relaxational; if the bulk shows a softening collective mode or a $\\chi'$ that peaks at $T_c$, the surface assumption would be invalidated. A second falsifier: extend the measurement below $T_{C2}$ and see whether $\\chi'(q_0,0)$ continues to grow, saturates, or turns over, which would distinguish a genuine near-divergence from a disorder-rounded rise.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the M-EELS technique and the expression for the loss intensity used to extract the dynamic charge susceptibility."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the crystal growth, the transition temperatures $T_{C1}$ and $T_{C2}$, and the CDW wavevector $q_{C1}$ for ErTe3."},{"cited_title":"Moore, V","cited_arxiv_id":null,"evidence_quote":"Gives the ARPES gap values and the evidence that only a small fraction of the Fermi surface is gapped by the CDW order."},{"cited_title":"Maschek, S","cited_arxiv_id":null,"evidence_quote":"Shows the phonon softening at the CDW wavevector, providing the contrast to the purely relaxational electronic response."},{"cited_title":"Gr¨ uner,Density waves in solids (CRC press, 2018)","cited_arxiv_id":null,"evidence_quote":"Predicts the divergence of the static charge susceptibility at a CDW transition and discusses the unrenormalized susceptibility."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Reports the anomalous thermal transport and Wiedemann-Franz violation just below $T_c$, connected to the diffusivity peak."},{"cited_title":"Measurement of the dynamic charge susceptibility near the charge density wave transition in ErTe$_3$","cited_arxiv_id":"2411.14746","evidence_quote":"Provides the diffusive charge-order dynamics and the diffusion-length estimate used for comparison."}],"review_version":1}