{"id":"3ea8b420-00dd-40ce-9c58-19d35a040d06","arxiv_id":"2606.21323","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":5.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Large-scale computational study of cuprates finds Tc correlates most strongly with p-orbital Coulomb coupling in the three-band Emery model.","lead":"The paper collects data on ~40 cuprates and computes parameters of single-band Hubbard and three-band Emery models via DFT, MLWFs, and cRPA downfolding. It reports that experimental Tc correlates most strongly with the Coulomb interaction strength on oxygen p-orbitals.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.3","headline":"Automated MLWF+cRPA downfolding may not produce parameters whose compound-to-compound variations faithfully track the interactions controlling Tc","rationale":"The reader's weakest assumption is precisely the load-bearing step; the full-text methods section would need to contain explicit validation or sensitivity checks for the claim to be secure. Because the statistical analysis is post-hoc on the output of that pipeline, confirming or refuting the fidelity of the downfolding directly tests whether the observed correlation can be trusted. No other internal inconsistency is visible from the abstract alone.","tokens_in":1846,"tokens_out":465,"duration_ms":19247,"concrete_test":"Take the five cuprates with published manual cRPA or constrained-DFT values for the 3-band Emery parameters (e.g., La2CuO4, HgBa2CuO4, Bi2212, YBCO, Nd2CuO4); rerun the paper's exact automated MLWF+cRPA workflow on the same DFT bands and compare the resulting U_p values and their ordering to the literature numbers. If the automated U_p deviates by >1 eV or changes the rank order for more than two compounds, recompute the Tc correlation using the literature parameters instead.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The headline correlation (Tc most strongly with U_p on oxygen p-orbitals in the 3-band model) is obtained by feeding the output of a fully automated MLWF+cRPA pipeline into a statistical analysis. For this correlation to reflect the microscopic physics rather than a methodological artifact, two conditions must hold: (1) the downfolding must yield effective U_p, U_d, t_pd etc. whose relative ordering and magnitudes across the ~40 compounds are accurate, and (2) any systematic errors in the procedure must be uncorrelated with the structural or chemical features that also correlate with experimental Tc. The abstract and methods paragraph give no indication that the pipeline was benchmarked against manual cRPA results or subjected to window/screener sensitivity tests on multiple cuprates; DFT starting points are known to be sensitive to the choice of functional and to the treatment of self-interaction in cuprates, both of which can shift the screened interactions by several eV in a compound-dependent way.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript conducts a large-scale study of ~40 cuprate compounds by compiling experimental Tc and crystal structures, computing DFT band structures, and downfolding them via an automated MLWF+cRPA procedure to single-band Hubbard and three-band Emery models. Statistical analysis of the resulting effective parameters identifies the strongest correlation between experimental Tc and the Coulomb interaction U_p on oxygen p-orbitals in the three-band model, while also confirming a trend with t' in the single-band model and noting that Tc appears to vanish below a finite t' value.","tokens_in":2047,"tokens_out":440,"duration_ms":19046,"significance":"If the downfolded parameters accurately reflect compound-to-compound variations in microscopic interactions, the result would indicate that oxygen-site Coulomb couplings are the dominant factor controlling Tc variations across cuprates, with implications for materials design. The alignment with recent Hubbard-model ground-state calculations on the t' threshold adds supporting context. The automated pipeline and statistical approach enable the scale of the study, but the significance hinges on validation of the downfolding procedure.","major_comments":[{"comment":"Methods paragraph (and any associated supplementary details on the pipeline): The central claim that Tc correlates most strongly with U_p relies on the automated MLWF+cRPA downfolding producing parameters whose variations across compounds faithfully track the interactions controlling experimental Tc. No benchmarks against manual cRPA results, no sensitivity tests to DFT functional choice or energy windows on multiple cuprates, and no assessment of compound-dependent self-interaction errors are reported, despite known sensitivities that can shift screened interactions by several eV.","section":"Methods"}],"minor_comments":[{"comment":"Abstract: The phrase 'more sophisticated models might be needed to describe all cuprates on the same footing' is stated without specifying which discrepancies in the data support this conclusion.","section":"Abstract"},{"comment":"Abstract: The 'previously observed trend' for t' should include a citation to the relevant prior work.","section":"Abstract"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for their careful review and constructive feedback on our manuscript. We address the major comment on the methods and validation of the automated downfolding procedure below.","responses":[{"response":"We agree that the absence of explicit benchmarks and sensitivity analyses represents a limitation, as the referee notes. A comprehensive set of manual cRPA validations or tests across all ~40 compounds would be computationally prohibitive for this large-scale study. We will revise the methods section and supplementary information to include (i) a discussion of known cRPA sensitivities to DFT functionals, energy windows, and self-interaction errors with references to the literature, and (ii) results from sensitivity tests performed on a representative subset of compounds. This will clarify that while absolute parameter values may carry systematic uncertainties, the automated and consistent treatment across the dataset supports the reliability of relative trends, including the observed correlation with U_p.","revision_made":"partial","referee_comment":"[Methods] Methods paragraph (and any associated supplementary details on the pipeline): The central claim that Tc correlates most strongly with U_p relies on the automated MLWF+cRPA downfolding producing parameters whose variations across compounds faithfully track the interactions controlling experimental Tc. No benchmarks against manual cRPA results, no sensitivity tests to DFT functional choice or energy windows on multiple cuprates, and no assessment of compound-dependent self-interaction errors are reported, despite known sensitivities that can shift screened interactions by several eV."}],"tokens_in":1475,"tokens_out":317,"duration_ms":17046,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main thing to know is that across their set of roughly 40 cuprates the experimental Tc shows its strongest correlation with the effective Coulomb interaction on the oxygen p orbitals in the three-band Emery model obtained from automated MLWF+cRPA downfolding. They also recover the known t' trend in the single-band model and note that Tc appears to drop to zero below some finite t' value.\n\nWhat the work does reasonably well is assemble a consistent dataset of structures and Tc values and apply the same automated pipeline to every compound. That scale is not common, and the statistical comparison is presented without obvious cherry-picking. The emphasis on oxygen-site interactions follows directly from the numbers they report.\n\nThe soft spot is exactly the one flagged in the stress-test note. The downfolding is fully automated with no reported benchmarks against manual cRPA runs, no tests of window or functional sensitivity, and no checks on how DFT self-interaction errors shift the screened U's differently across compounds. Cuprate DFT is known to be sensitive on these points, so the compound-to-compound spread in U_p could contain methodological artifacts that happen to align with structural trends also linked to Tc. The abstract and methods paragraph give no sign that this was addressed.\n\nThis paper is for theorists who work with effective models for cuprates and want a broad statistical look at parameter trends. A reader already convinced that three-band physics matters will find the U_p ranking worth checking against their own calculations.\n\nIt deserves peer review. The dataset size and the clear claim make it worth a referee's time even if the central correlation needs stronger validation of the downfolding step.","headline":"The paper's new angle is a dataset-wide correlation showing Tc tracks most strongly with U_p from the three-band model, but the automated downfolding leaves the result on shaky ground.","tokens_in":2560,"tokens_out":414,"would_cite":false,"duration_ms":31333,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"In cuprates, Tc correlates most strongly with the effective Coulomb repulsion on oxygen p-orbitals in the three-band model.","keywords":["cuprates","Tc","Coulomb interactions","three-band Emery model","single-band Hubbard model","oxygen p-orbitals","DFT downfolding","statistical correlation"],"falsifier":"A cuprate compound or set of compounds in which the computed p-orbital Coulomb coupling fails to correlate with measured Tc while some other parameter shows a stronger correlation when an alternative downfolding procedure is used.","tokens_in":2771,"feed_emoji":"⚛","tokens_out":774,"duration_ms":34028,"temperature":0.7,"pith_summary":"The paper compiles data on about 40 cuprate compounds and their experimental Tc values, then uses an automated procedure to compute DFT band structures and downfold them to the single-band Hubbard model and the three-band Emery model via MLWFs and cRPA. Statistical analysis of the resulting parameters against Tc shows that the Coulomb coupling on the p-orbitals exhibits the strongest correlation across the full dataset. This points to the oxygen sites in the copper-oxide planes as central to Tc variations, while also confirming a correlation with t' in the single-band model where Tc appears to require a minimum t' value. A sympathetic reader would care because identifying the dominant interaction parameter offers a route to understanding why Tc differs between compounds and potentially to guiding higher-Tc material design.","feed_headline":"Oxygen p-orbital Coulomb coupling tracks cuprate Tc best","feed_subtitle":"Across 40 compounds, statistical analysis finds strongest link to p-site repulsion in three-band model rather than hopping or d-orbital term","key_machinery":"The fully automated MLWF + cRPA downfolding of DFT band structures to the single-band Hubbard and three-band Emery models, followed by statistical correlation analysis with experimental Tc.","core_discovery":"Through a large-scale systematic study that downfolds DFT band structures for dozens of cuprates to effective lattice models and applies unbiased statistical analysis, Tc scales well with simple functions of the model parameters; throughout the dataset Tc correlates the most with the Coulomb coupling on the p-orbitals in the three-band model, highlighting the importance of the oxygen sites in the copper-oxide planes, while also confirming the previously observed trend that t' in the single-band model correlates with experimental Tc and that Tc appears to vanish below a finite value of t'.","pith_inferences":["If p-orbital Coulomb terms dominate, then structural modifications that change oxygen coordination or environment could tune Tc more directly than changes focused on copper sites.","The observed correlation implies that differences in screening of interactions at oxygen atoms vary enough across crystal structures to control Tc differences.","Three-band model simulations that vary only the p-orbital U could be compared directly to experimental Tc trends for specific compounds to test predictive power.","Extending the same downfolding and correlation procedure to pressure-dependent Tc data or additional compounds would provide a direct test of whether the p-orbital trend persists."],"forward_implications":["Tc correlates with t' in the single-band model and appears to vanish below a finite value of t'.","The coupling strength plays a role in addition to the hopping parameters.","More sophisticated models might be needed to describe all cuprates on the same footing.","The oxygen p-orbitals are important for understanding variations in Tc."],"fun_headline_variants":["P-orbital Coulomb coupling correlates most with cuprate Tc","Oxygen p-site repulsion tracks Tc in cuprate three-band models","Coulomb interactions on p orbitals predict cuprate Tc best","Across cuprates p-orbital Coulomb strength best predicts Tc"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The automated MLWF + cRPA downfolding procedure from DFT band structures produces effective model parameters whose variations across compounds faithfully reflect the microscopic interactions that control experimental Tc.","fun_headline_variants_meta":{"raw":{"variants":["P-orbital Coulomb coupling correlates most with cuprate Tc","Oxygen p-site repulsion tracks Tc in cuprate three-band models","Coulomb interactions on p orbitals predict cuprate Tc best","Across cuprates p-orbital Coulomb strength best predicts Tc"]},"model":"grok-4.3","cost_usd":0.004324,"raw_usage":{"total_tokens":2253,"prompt_tokens":832,"num_sources_used":0,"completion_tokens":67,"cost_in_usd_ticks":43237000,"prompt_tokens_details":{"text_tokens":832,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1354,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":832,"tokens_out":67,"duration_ms":14618,"temperature":1.0,"reasoning_tokens":1354,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-26T13:04:40.741925+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"A cuprate compound or set of compounds in which the computed p-orbital Coulomb coupling fails to correlate with measured Tc while some other parameter shows a stronger correlation when an alternative downfolding procedure is used.","supporting_citations":[],"review_version":1}