{"id":"9e19e906-717a-4271-88a5-cc27519cc0d8","arxiv_id":"2505.21687","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"RIXS on Bi2212 shows that momentum-dependent anisotropic electron scattering is required to explain the low-energy charge response and the derived superconducting gap.","lead":"Using resonant inelastic x-ray scattering on the cuprate superconductor Bi2212, researchers found that the low-energy electronic response in the superconducting state is suppressed below 80 meV with no compensating hump at higher energies. Modeling shows that only a charge susceptibility that includes momentum-dependent anisotropic electron scattering (k-DAES) can reproduce the data, which also affects how the superconducting gap is extracted.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The non-k-dependent benchmark may be an artifact of setting the SC scattering rate to zero at ω=0; adding a realistic residual damping could make the dip-peak discriminator disappear.","rationale":"The reader's weakest assumption identified the phenomenological eight-Gaussian form of Eq. (1) and the chosen A, σ parameters. My concern is more specific and more load-bearing: the energy-dependent factor in Eq. (1) has no additive constant term, so Γ^SC vanishes at ω=0. This zero-width limit is what produces the sharp coherence hump in the non-k-dependent calculation, and the paper uses the presence/absence of that hump as the principal discriminator. A residual zero-energy scattering rate is physically expected and is already included in the normal-state Γ_N via δ=0.002 eV, so its omission in the SC state is an internal inconsistency rather than merely an unconstrained parameter choice. The suggested test is inexpensive and would settle whether the dip-peak is a real consequence of omitting k-DAES or an artifact of an idealized zero-lifetime model. I do not think this concern alone overturns the paper's conditional acceptance, because the k-DAES model is additionally constrained by ARPES data and the comparison is not parameter-free, but it does mean the strong claim of necessity requires an explicit robustness check. Hence the reader's CONDITIONAL verdict remains appropriate with no change.","tokens_in":21092,"tokens_out":4545,"duration_ms":53209,"concrete_test":"Recompute the non-k-dependent simulations (A=0 in Eq. (1)) with an added constant Γ0 of 2, 5, and 10 meV in the first bracket of Γ^SC_Q,k(ω), keeping all other simulation parameters fixed, and compare the SC-N difference at Q=(0.02,0.02), (0.04,0.04), and (0.06,0.06) to Fig. 3(a). If any Γ0 in this range turns the dip-peak into a dip-only shape with a Q-dependent dip position matching the data, the non-k-dependent model cannot be excluded and the k-DAES claim is unsupported. If the dip-peak persists for all Γ0 up to the ARPES-derived low-energy lifetime, the claim is robust.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that only the k-DAES model reproduces the dip-only SC-N difference spectra, because the non-k-dependent calculation produces an additional hump/dip-peak feature (Fig. 1(c,f) and Fig. 3(c)). This discriminator depends on Eq. (1), where Γ^SC_Q,k(ω) is the product of an energy-dependent factor that vanishes at ω=0 (quadratic below 2Δ for n=2) and a momentum-dependent Gaussian term. Thus Γ^SC_Q,k(0)=0 everywhere in k, including in the non-k-dependent case (A=0). The resulting perfectly coherent zero-energy response is what generates the sharp coherence peak and the hump in the SC state. Real Bi2212 has a finite quasiparticle scattering rate even at zero energy from elastic/impurity scattering, and the paper itself includes a small constant δ=0.002 eV in the normal-state Γ_N but no analogous constant in Γ_SC. If a constant Γ0 of order a few meV is added to the non-k-dependent Γ_SC, the coherence peak is broadened and the SC-N dip-peak may collapse to a dip-only feature, removing the main experimental evidence against the non-k-dependent model. The paper does not test this robustness, so the strong statement that only k-DAES captures the data is not yet established against the simpler possibility of a small residual SC-state damping.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This manuscript reports Cu L3-edge RIXS measurements on optimally doped Bi2Sr2CaCu2O8+δ at three momenta along the nodal direction, in the superconducting (40 K) and normal (250 K) states. The data show a spectral suppression below about 80 meV in the SC state and a dip-like 40K-250K difference spectrum whose minimum moves from about 30 to 50 meV with increasing Q. The authors model the RIXS response with a tight-binding charge susceptibility and introduce a phenomenological scattering rate (Eq. 1) that can be switched between a momentum-independent form (A=0) and a k-dependent anisotropic form (k-DAES) consisting of eight Gaussians at the antinodal points. They show that the k-dependent version produces a dip-only SC-N difference, while the non-k-dependent version produces an additional dip-peak/hump feature, and they argue that the experimental absence of the hump selects the k-DAES model. With this model they constrain the superconducting gap to Δ≲40 meV and conclude that k-DAES must be included when extracting quantitative parameters from RIXS data.","tokens_in":21504,"tokens_out":6361,"duration_ms":64379,"significance":"The paper has several strengths: it presents new high-resolution RIXS data at three Q points, it makes an explicit and falsifiable model comparison between two scattering scenarios, it anchors the anisotropy parameters to published ARPES scattering rates, and it gives a specific proposal for extracting the superconducting gap from RIXS difference spectra. If the central claim holds, it means that momentum-dependent anisotropic electron damping must be included in any RIXS-based analysis of low-energy charge excitations in cuprates, and that previous estimates of gap sizes from RIXS could be biased. The main weakness is that the discriminator between the two models relies on the vanishing of the SC scattering rate at zero energy; this assumption is not tested against a realistic residual damping.","major_comments":[{"comment":"Eq. (1) sets Γ_SC(Q,k,ω) to zero at ω=0 for every k because of the prefactor ω^n H(2Δ-ω)+ωH(ω-2Δ). The non-k-dependent scenario (A=0) therefore has a perfectly coherent response at zero energy, which is what produces the sharp coherence peak and the hump in the SC-N difference spectra in Fig. 3(c). The normal-state calculation in the Supplement (Eq. S2 and the text after it) includes a constant δ=0.002 eV in Γ_N, but no analogous constant is included in Γ_SC. Real underdoped and optimally doped cuprates have finite quasiparticle scattering at zero energy from elastic/impurity scattering, so the contrast between the two scenarios may be artificially sharp. If a constant Γ0 of a few meV were added to the non-k-dependent Γ_SC, the coherence peak would broaden and the dip-peak feature could collapse to a dip-only shape, eliminating the main experimental evidence against the non-k-dependent model. The authors should repeat the calculations of Figs. 3(c) and 4 with Γ_SC replaced by Γ_SC + Γ0 for Γ0 values such as 1, 2, and 5 meV, for both A=0 and A≠0, and show that the dip-only discriminator survives. Without this test the abstract's statement that 'only the charge susceptibility with k-DAES captures the RIXS data' is not yet established.","section":"Eq. (1), Fig. 3(c), SM Sec. II"},{"comment":"The central claim is presented as a general necessity of k-DAES, but the calculation implements the anisotropy with a specific ad hoc functional form: eight Gaussians centered at the antinodal points, with width σ and amplitude A. The manuscript varies A and σ for this fixed form, but it does not test whether the qualitative difference between the two scenarios is robust to the chosen functional shape of the k-dependence. If a smoother anisotropy, a different placement of the hot spots, or a momentum-dependent elastic term were used, the non-k-dependent benchmark could behave differently. The authors should test at least one alternative parametrization of the anisotropy (for example, a d-wave-like cos(2θ) or a simple antinodal hotspot function) and show that the dip-only versus dip-peak distinction persists. Without such a test, the conclusion that k-DAES is essential, rather than merely that this particular Gaussian model is essential, is overstated.","section":"Eq. (1) and SM Sec. IV"}],"minor_comments":[{"comment":"The word 'uncapable' should be 'incapable'.","section":"Introduction, paragraph 2"},{"comment":"'scoth-tape' should be 'Scotch tape'.","section":"SM Sec. I"},{"comment":"'paragmanon' should be 'paramagnon'.","section":"SM Fig. S2 caption"},{"comment":"The author name 'T. P. evereaux' should be 'T. P. Devereaux'.","section":"Reference [48]"},{"comment":"The calculation uses T=1.2 K for the SC state and T=120 K for the normal state, while the experimental data are at 40 K and 250 K; the authors should justify this choice or comment on its effect on the Fermi functions and the Bose factor entering S_c(Q,ω).","section":"SM Sec. II"},{"comment":"The statement that all calculated SC-N curves have weak spectral weight up to ~200 meV that is not captured in the data is a clear limitation; it would be helpful to quantify the mismatch or to test whether an additional broad background component could affect the extracted dip positions.","section":"Near Fig. 3 caption"},{"comment":"The claim that 'only' the k-DAES model captures the data is stronger than what can be concluded from three Q points and qualitative comparison; the abstract and conclusions should temper this to 'the present model including k-DAES captures the data, whereas the non-k-dependent model does not' unless the robustness tests are added.","section":"Abstract and Conclusions"}],"recommendation":"major_revision","confidential_remarks":"The experimental data are of high quality and the paper is clearly written. The missing robustness test against a finite zero-energy scattering rate is the key technical issue; I would encourage the editor to request that test before acceptance. The claim of 'only' capturing the data should be softened or supported by additional model comparisons."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Worth reading if you work on RIXS in cuprates. The new experimental result is a clean momentum-dependent dip in the SC-minus-normal low-energy RIXS difference around q=(0.02,0.02)-(0.06,0.06), with no hump at higher energy. The paper also makes a valid point: extracting Delta from such spectra without modelling momentum-dependent damping is dangerous, and the k-dependent scattering-rate model, anchored to ARPES data, suppresses the coherence hump that the k-independent version produces. This is a useful methodological message for the RIXS-gap community.\n\nThe soft spot is in the strength of the claim. Eq. (1) sets Gamma_SC to zero at omega=0. Real Bi2212 has residual elastic scattering, and the normal-state model in this same paper includes a constant delta=0.002 eV. No analogous constant is put into Gamma_SC. The stress-test note is correct: for the non-k-dependent benchmark (A=0), adding a few-meV constant damping will broaden the coherence peak and may turn the dip-peak feature into a dip-only shape, which is exactly the discriminator used to reject that model. The paper does not test this robustness. So the abstract's statement that only k-DAES captures the data is not yet established against a simpler alternative.\n\nOther issues are proportionally minor. The analysis relies on three Q-points along the nodal direction, a simplified single-band susceptibility, and fitted phonon/paramagnon components. The authors themselves note the overestimate at (0.02,0.02) and the high-energy tail mismatch. A, sigma, and Delta are adjusted with ARPES and the same RIXS data in view, which is circular only in a weak sense; the qualitative dip-vs-dip-peak comparison is a genuine model contrast, and the ARPES input anchors the scattering-rate magnitude. No data or code are posted, which limits independent checking.\n\nBottom line: the experimental observation is solid, the modelling caveat is important, and the paper deserves peer review. I would send it to a referee with a request to test the finite-residual-damping alternative and to make the model and fits available. Reading-group material for sure.","headline":"Solid RIXS observation and a useful modelling warning, but the central 'only k-DAES works' claim needs a robustness check against finite residual SC damping.","tokens_in":21988,"tokens_out":3198,"would_cite":true,"duration_ms":32658,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"To explain RIXS data in cuprate superconductors, momentum-dependent anisotropic electron scattering (k-DAES) must be included in the charge susceptibility; without it, the extracted energy gap is wrong.","keywords":["resonant inelastic x-ray scattering","cuprate superconductors","Bi2Sr2CaCu2O8+delta","charge susceptibility","momentum-dependent anisotropic electron scattering","superconducting gap","marginal Fermi liquid","low-energy charge excitations"],"falsifier":"Compute Im chi_c(Q, omega) with an alternative momentum-dependent scattering anisotropy (for example a different functional form fitted to the same ARPES data, or a microscopic spin-fluctuation-derived rate) and compare the superconducting-minus-normal difference against the measured RIXS dip at Q = (0.04, 0.04); if a momentum-independent rate plus a different gap symmetry or phonon background also reproduces the dip, the k-DAES necessity claim fails. Alternatively, measure RIXS along the anti-nodal direction, where the two scenarios differ more strongly, and check whether the dip-only signature persists.","tokens_in":1973,"feed_emoji":"🔬","tokens_out":1939,"duration_ms":78523,"temperature":0.7,"pith_summary":"This paper argues that momentum-resolved measurements of low-energy charge excitations in the cuprate superconductor Bi2212 cannot be interpreted with a momentum-independent electron scattering rate. RIXS spectra taken above and below the superconducting transition show a spectral-weight suppression below about 80 meV whose dip position moves to higher energy with momentum, and no compensating enhancement at higher energies. A charge susceptibility model that includes the momentum-dependent anisotropic electron scattering (k-DAES) measured by ARPES reproduces this behavior, while the same model without it predicts a spurious hump. The authors conclude that k-DAES must be included whenever quantitative parameters such as the superconducting gap are extracted from RIXS data, and that RIXS can serve as a complementary probe of electron dynamics in reciprocal space.","feed_headline":"Cuprate RIXS gap reads hinge on anisotropic electron damping","feed_subtitle":"Modeling scattering anisotropy is essential; without it, the extracted superconducting gap is wrong.","key_machinery":"The load-bearing object is the phenomenological momentum- and energy-dependent scattering rate Gamma_SC_{Q,k}(omega) in Eq. (1). Its energy factor follows an omega-linear marginal-Fermi-liquid form above 2Delta and an $omega^{2}$ suppression below, while its momentum factor adds eight Gaussians centered at the four antinodal points (width $\\sigma$ = 0.45pi, amplitude A = 6) to represent the stronger damping near the antinodes. Inserted into the tight-binding charge susceptibility chi_c(Q, omega), this rate suppresses the collective 'hump' that a momentum-independent rate produces just above the gap and turns the superconducting-minus-normal difference into the observed dip; the same parameters are simultaneously constrained by ARPES scattering rates.","core_discovery":"On its own terms, the central claim is that the Q-dependence of RIXS-measured low-energy charge excitations in the superconducting state of optimally doped Bi2212 is controlled by the momentum-dependent anisotropic electron scattering (k-DAES) previously established by photoemission. In the normal state the spectra show a continuum of charge excitations down to zero energy; in the superconducting state the weight is suppressed below about 80 meV, producing a dip-like superconducting-minus-normal difference whose position moves from roughly 30 meV at Q = (0.02, 0.02) to roughly 50 meV at Q = (0.06, 0.06), with no hump at higher energy. Calculations of Im chi_c(Q, omega) with the scattering rate of Eq. (1) - eight Gaussians at the antinodal points on top of a marginal-Fermi-liquid energy dependence - reproduce the dip and its momentum shift, whereas the same calculation with a momentum-independent rate produces a dip-peak shape that is not observed. Consequently, attempts to quantify the energy gap $\\Delta$ from RIXS data without k-DAES will mis-estimate it; with k-DAES the data constrain $\\Delta$ to be about 40 meV or less, consistent with the known roughly 30 meV gap. The claim extends beyond the gap: k-DAES affects the charge response up to a few eV, so models of plasmons and other charge excitations in cuprates should include it.","pith_inferences":["If k-DAES is as dominant as claimed, finite-momentum probes such as electron energy-loss spectroscopy should show the same dip-only superconducting-minus-normal difference, whereas Raman scattering at Q approximately 0 should remain relatively insensitive to the anisotropy; this contrast could be checked directly.","The eight-Gaussian ansatz is an effective parametrization; a microscopic origin (for example spin-fluctuation scattering or pseudogap anisotropy) would predict specific doping and temperature dependence of the amplitude A and width sigma that could be tested across the cuprate phase diagram.","The claim that the dip position tracks the gap could be tested by measuring a cuprate with a known different gap magnitude, such as an underdoped compound with a pseudogap, and comparing the predicted versus measured dip shift.","The strong near-zone-center suppression of the quasi-elastic peak in the superconducting state could serve as a fast, high-resolution diagnostic of gap opening in other layered superconductors, including those studied under pressure or in heterostructures."],"forward_implications":["RIXS measurements near the zone center can be used to extract the size of the superconducting gap, complementing ARPES and STM, and can be applied to buried layers, heterostructures, and other samples inaccessible to surface-sensitive probes.","Models of charge excitations in cuprates - acoustic and optical plasmons, temperature dependence of the charge response - must include k-DAES up to the few-eV scale, not just near the gap.","The absence of spectral-weight enhancement above the gap in cuprate RIXS is not evidence against gap formation; it is a signature of momentum-dependent damping.","Quantitative gap values extracted from previous RIXS analyses that omitted k-DAES may need revision, since those analyses relied on a dip-peak shape that the anisotropic model shows to be spurious.","The methodology extends to other layered superconductors, such as infinite-layer nickelates and twisted cuprates, where RIXS is one of the few bulk-sensitive momentum-resolved probes."],"supporting_citations":[{"why":"ARPES evidence for quantum critical behavior in optimally doped Bi2212; supplies the measured scattering rates that anchor the momentum-anisotropy parameters.","marker":"[15]"},{"why":"Temperature-dependent ARPES scattering rates at the Fermi surface; constrains the energy dependence of the scattering rate in the superconducting state.","marker":"[16]"},{"why":"Earlier RIXS study probing the cuprate energy gap; its reported hump in the superconducting-minus-normal difference is the baseline that the k-DAES model suppresses.","marker":"[28]"},{"why":"Shows RIXS can probe the phase and excitations of the superconducting order parameter; basis for relating the RIXS cross-section to Im chi_c(Q, omega).","marker":"[27]"},{"why":"Review of the RIXS scattering formalism; provides the relation between RIXS intensity and the charge dynamic structure factor.","marker":"[25]"},{"why":"RIXS study of the charge response in YBa2Cu3O7-delta; supplies the normalization and spectral-weight comparison used here.","marker":"[29]"},{"why":"Provides the tight-binding band structure and d-wave gap form used as input to the chi_c calculation.","marker":"[32]"},{"why":"Momentum-dependent quasiparticle scattering in Bi2212 from quasiparticle interference; supports the anisotropic scattering-rate form adopted in Eq. (1).","marker":"[36]"}],"fun_headline_variants":["Anisotropic damping controls cuprate RIXS gap","Without k-DAES, cuprate RIXS gap is misestimated","k-DAES essential for cuprate gap from RIXS","Momentum-dependent scattering dictates RIXS gap reads","Anisotropic damping sets cuprate RIXS gap scale"],"cache_read_input_tokens":23936,"weakest_assumption_plain":"The eight-Gaussian functional form of the momentum-dependent scattering rate, with parameters fixed by ARPES, faithfully represents the true anisotropic electron scattering in the superconducting state below about 100 meV; if the real anisotropy is different, the conclusion that k-DAES is necessary could be a model artifact.","fun_headline_variants_meta":{"raw":{"variants":["Anisotropic damping controls cuprate RIXS gap","Without k-DAES, cuprate RIXS gap is misestimated","k-DAES essential for cuprate gap from RIXS","Momentum-dependent scattering dictates RIXS gap reads","Anisotropic damping sets cuprate RIXS gap scale"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000689,"raw_usage":{"total_tokens":3224,"prompt_tokens":1148,"completion_tokens":2076,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":764,"completion_tokens_details":{"reasoning_tokens":1984}},"tokens_in":764,"tokens_out":2076,"duration_ms":15545,"temperature":1.0,"reasoning_tokens":1984,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T13:24:17.764201+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute Im chi_c(Q, omega) with an alternative momentum-dependent scattering anisotropy (for example a different functional form fitted to the same ARPES data, or a microscopic spin-fluctuation-derived rate) and compare the superconducting-minus-normal difference against the measured RIXS dip at Q = (0.04, 0.04); if a momentum-independent rate plus a different gap symmetry or phonon background also reproduces the dip, the k-DAES necessity claim fails. Alternatively, measure RIXS along the anti-nodal direction, where the two scenarios differ more strongly, and check whether the dip-only signature persists.","supporting_citations":[{"cited_title":"Valla, A","cited_arxiv_id":null,"evidence_quote":"Temperature-dependent ARPES scattering rates at the Fermi surface; constrains the energy dependence of the scattering rate in the superconducting state."},{"cited_title":"Suzuki, M","cited_arxiv_id":null,"evidence_quote":"Earlier RIXS study probing the cuprate energy gap; its reported hump in the superconducting-minus-normal difference is the baseline that the k-DAES model suppresses."},{"cited_title":"Marra, S","cited_arxiv_id":null,"evidence_quote":"Shows RIXS can probe the phase and excitations of the superconducting order parameter; basis for relating the RIXS cross-section to Im chi_c(Q, omega)."},{"cited_title":"Merzoni, L","cited_arxiv_id":null,"evidence_quote":"RIXS study of the charge response in YBa2Cu3O7-delta; supplies the normalization and spectral-weight comparison used here."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the tight-binding band structure and d-wave gap form used as input to the chi_c calculation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Momentum-dependent quasiparticle scattering in Bi2212 from quasiparticle interference; supports the anisotropic scattering-rate form adopted in Eq. (1)."}],"review_version":1}