{"id":"4aa0292b-7a28-4e40-93b2-7b9f047a1c84","arxiv_id":"1909.02743","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"New measurements and DFT+DMFT calculations show that electronic correlations, especially orbital-dependent Coulomb interactions, bring the Lifshitz transition strain in Sr2RuO4 down to the experimentally observed value.","lead":"This paper combines new strain measurements with theory to show that electronic correlations, and particularly the orbital anisotropy of the Coulomb interaction, control the strain at which the Fermi surface of the superconductor Sr2RuO4 changes topology. The result explains why the transition occurs at a much smaller strain than standard calculations predict, and highlights the value of precision strain experiments as a constraint on electronic structure theory.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The fitted orbital-anisotropy parameter u, not an ab initio value, carries the quantitative agreement; an independent cRPA or QMC cross-check is needed to confirm the central claim.","rationale":"The paper is a careful combined experimental/theoretical study. The new stress cell and elastic-moduli measurements are credible; the error bars on ε_VHS are properly propagated; the DFT calculations are cross-checked with multiple codes and k-meshes; and the qualitative reduction of ε_VHS under correlations is consistent with earlier work (Facio et al.). The reader's identified assumption—that the resistivity peak marks the Lifshitz transition—is explicitly stated and supported by scattering arguments, and its numerical impact lies within the quoted error bars. The load-bearing soft spot is instead on the theoretical side: the quantitative conclusion that anisotropy of the local Coulomb interaction is essential is obtained by tuning u to the measured value. The paper does not provide an ab initio value for u, and the RISB solver is approximate. Because the entire 'only by accounting for orbital anisotropy' claim rests on this one fitted parameter, an independent cRPA calculation or a QMC solver cross-check is the natural condition for acceptance. Hence the verdict remains CONDITIONAL.","tokens_in":10367,"tokens_out":14340,"duration_ms":144881,"concrete_test":"Perform a constrained-RPA calculation for Sr2RuO4 with the same Wannier basis and strain used here (εxx = -0.44×10^-2 and zero strain) to obtain the orbital-resolved U matrix; compute u_cRPA = U_xy,xy − U_xz,yz. If u_cRPA lies in 0.10–0.15 eV, the fitted anisotropy is first-principles supported; if it is outside this window, the paper's quantitative agreement is not independently motivated. As a secondary check, run DFT+DMFT with a continuous-time QMC impurity solver at U = 3.1 eV, J_H = 0.7 eV, and u = 0.10–0.15 eV to see whether ε_VHS remains near the experimental value; a significant deviation would indicate RISB solver dependence.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central conclusion—that orbital anisotropy of the local Coulomb interaction is required to bring the theoretical Lifshitz strain into agreement with experiment—rests on Eq. (1), in which u = U_xy,xy − U_{xz,yz},{xz,yz} is introduced as an adjustable parameter. The paper fits u ≈ 0.10–0.15 eV to the measured ε_VHS but does not report an independent cRPA value for this anisotropy; Ref. 18 is cited only for the qualitative statement that U_xy exceeds U_xz,yz. Since the isotropic calculation already has U and J_H fixed by the mass renormalization, matching ε_VHS with a single free u is a one-parameter fit, not a prediction. If an ab initio constrained-RPA calculation gave u outside 0.10–0.15 eV, the agreement would be a fitting artifact rather than evidence for the anisotropy mechanism. The RISB solver is also approximate; its static, orbital-dependent self-energy could bias the orbital differentiation, and no cross-check with an exact impurity solver is provided. The reader's alternative concern—that the transition may sit at the Tc peak rather than the resistivity peak—is real but less decisive: the 5–12% offset lies inside the quoted ±0.06×10^-2 experimental error bar and would shift the fitted u by only about 0.01 eV, keeping it in the stated range.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports a refined experimental determination of the strain at which the gamma Fermi surface sheet of Sr2RuO4 undergoes a Lifshitz transition under uniaxial pressure, yielding a longitudinal strain of (-0.44 +/- 0.06) x 10^-2 and a B1g strain of (-0.66 +/- 0.09) x 10^-2. The measurement uses a force-sensor-based stress cell and new low-temperature elastic moduli. The authors then compare this experimental benchmark with density functional theory (DFT) and DFT+DMFT calculations. DFT with and without spin-orbit coupling overestimates the critical strain in magnitude. DFT+DMFT with isotropic Coulomb interactions (U = 3.1 eV, J_H = 0.7 eV) overcorrects, giving a critical strain close to zero. Introducing an orbital anisotropy u = U_xy,xy - U_{xz,yz},{xz,yz} of 0.10-0.15 eV (with inter-orbital anisotropy u' = u/3) brings the calculated critical strain into agreement with experiment. The authors conclude that electronic correlations reduce the critical strain and that orbital anisotropy of the local Coulomb interaction is required to reproduce the experimental value.","tokens_in":10627,"tokens_out":8134,"duration_ms":81171,"significance":"The experimental part is careful and provides a reliable benchmark: two samples, force-sensor calibration, and new low-temperature elastic moduli give a credible value of the Lifshitz strain. The qualitative finding that correlations reduce the critical strain relative to DFT is robust and important, as it reconciles the observed strain with theoretical expectations. The demonstration that the orbital anisotropy of the Hubbard interaction can shift the Lifshitz strain by several tenths of a percent is a valuable constraint on electronic-structure methods. However, the quantitative agreement is obtained by fitting the anisotropy parameter u, not by an ab initio calculation, so the paper's central quantitative claim is a model-dependent inference rather than a prediction. The paper is honest about this limitation, and it provides a clear motivation for future constrained-RPA or other calculations of the orbital-dependent Coulomb interaction.","major_comments":[{"comment":"The orbital-anisotropy parameter u is introduced as an adjustable parameter, and the agreement with the experimental epsilon_VHS is used to set u ~ 0.10-0.15 eV. Reference 18 is cited only for the qualitative statement that U_xy exceeds U_{xz,yz}; no independent ab initio value for this anisotropy in Sr2RuO4 is provided. If a constrained-RPA calculation yielded u outside this range, the agreement would be a fitting artifact rather than evidence for the anisotropy mechanism. The authors should either report such a calculation (or a strong estimate from other sources) or explicitly reframe the conclusion as a demonstration of sensitivity rather than a quantitative prediction.","section":"Calculation results, Eq. (1)"},{"comment":"The claim that agreement with experiment 'can be achieved only by accounting for orbital anisotropy' is supported by only two isotropic parameter sets (U = 3.1 eV, J_H = 0.7 eV and U = 2.3 eV, J_H = 0.4 eV). It is not demonstrated that no isotropic (U, J_H) combination consistent with the observed mass renormalization (m*/m ~ 2.5-4.4) can reproduce the experimental critical strain. A more systematic scan over the isotropic parameter space, or a mapping of the region consistent with the experimental mass renormalization, is needed to establish that anisotropy is truly necessary rather than merely a convenient knob.","section":"Conclusions and isotropic parameter comparison"},{"comment":"The RISB impurity solver has a restricted self-energy form (static plus linear in frequency), which could bias the orbital-dependent renormalizations that are central to the proposed mechanism. The paper itself recommends verification with other impurity solvers for the carrier redistribution, but no cross-check is provided for the key quantity epsilon_VHS. A test with a more exact solver (e.g., continuous-time QMC) for at least one strain and one u value would materially strengthen the central quantitative claim.","section":"Appendix (RISB solver)"}],"minor_comments":[{"comment":"In the text near Fig. 4, 'For both u = 0.10 and 0.15 meV' should read 'eV', since the parameter u is introduced in electron-volt units.","section":"Fig. 4 discussion"},{"comment":"The sentence 'for comparison with experiment they should be scaled by 1.39/1.51' is clear, but it would help to state explicitly whether the quoted DMFT values (-0.38 x 10^-2 and -0.70 x 10^-2) have already been scaled or should be scaled by the reader; the current wording leaves some ambiguity.","section":"Strain conversion paragraph"},{"comment":"The statement 'all experimental error bars are 2 sigma' appears in the experimental section; it would be useful to remind the reader of this convention when the final epsilon_VHS uncertainty is quoted in the abstract and conclusions.","section":"Experimental error bars"},{"comment":"The phrase 'new uniaxial stress apparatus' could be clarified as 'recently developed' because the apparatus was previously described in Ref. 7.","section":"Abstract"}],"recommendation":"major_revision","confidential_remarks":"The paper is a strong candidate for publication, but the central quantitative claim rests on a fitted parameter u without an independent ab initio estimate. I would encourage the editor to request a cRPA calculation or an explicit reframing of the conclusion as a sensitivity demonstration. The RISB approximation is a known limitation, but a cross-check with a more exact impurity solver would substantially raise the confidence in the quantitative result. These are fixable within revision, hence major_revision rather than reject."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The experimental part is the real story here, and it is solid. The new force-sensor apparatus, two samples, and the new low-temperature elastic moduli give a credible, well-characterized value of the Lifshitz strain, epsilon_xx = (-0.44 +/- 0.06) x 10^-2. That is a genuine metrological improvement over the scattered -5 to -7 x 10^-3 estimates floating around. The paper is worth reading for that alone.\n\nThe theory section makes a clear qualitative point: plain DFT overestimates the critical strain, and electronic correlations, treated in DMFT, push it down. That qualitative conclusion is not circular—it comes from comparing DFT and DMFT results, not from fitting anything. The paper also properly credits Facio et al. and Zhang et al. for the earlier findings that correlations shift the Van Hove singularity and that orbital anisotropy matters for the unstrained Fermi surface. The citation pattern looks honest.\n\nThe soft spot is the quantitative mechanism. The orbital-anisotropy parameter u is introduced in Eq. (1) and then tuned to reproduce the measured strain. The paper says u ~ 0.10-0.15 eV, but there is no independent cRPA estimate of that anisotropy to show that the fitted range is where an ab initio calculation would land. If a constrained-RPA calculation gives u outside that range, the agreement is a fitting artifact rather than evidence for the anisotropy mechanism. The RISB impurity solver is approximate and no cross-check with an exact solver is provided; that is a real limitation, though not fatal, because the qualitative reduction of the critical strain is robust across the solver choice within the paper's own argument.\n\nThe reader's alternative concern—that the resistivity peak might not mark the transition—is less damaging than it looks. The authors discuss it explicitly, and the 5-12% offset from the Tc peak sits mostly within the quoted error bar. The stress-test note is right that this would only shift the fitted u by about 0.01 eV. So that is a minor caveat, not a load-bearing flaw.\n\nThe paper is honest about its own fitting: the fixed U and JH reproduce the band renormalizations, and then a single anisotropy parameter adjusts the critical strain. That is a legitimate way to make a mechanism plausible, but it stops short of a prediction. What would move it from plausible to convincing is an independent determination of u or a second impurity solver.\n\nVerdict: this deserves serious peer review. The experiment alone justifies referee time, and the theory is a testable proposal with clear next steps. I would send it out and ask for the cRPA check or a QMC cross-check, but I would not desk reject it.","headline":"A careful experimental refinement of the Lifshitz strain in Sr2RuO4, paired with a plausible but not yet fully independent DMFT mechanism for why correlations reduce it.","tokens_in":11194,"tokens_out":1484,"would_cite":true,"duration_ms":19052,"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":"Electronic correlations, and specifically the orbital anisotropy of the Coulomb interaction, determine the uniaxial strain at which Sr2RuO4 undergoes a Lifshitz transition; new measurements put that strain at $(-0.44 \\pm 0.06)\\times…","keywords":["Lifshitz transition","Sr2RuO4","uniaxial strain","Van Hove singularity","dynamical mean-field theory","orbital anisotropy","Coulomb correlations","Fermi surface"],"falsifier":"Measure the Fermi-surface topology directly — for example with quantum oscillations or ARPES on a sample under the same uniaxial strain — at strains between the resistivity peak and the Tc peak. If no topology change occurs until the Tc peak strain, the paper's assignment of $\\varepsilon_{\\rm VHS}$ and the inferred value of $u$ would need revision.","tokens_in":10189,"feed_emoji":"🔬","tokens_out":7472,"duration_ms":65293,"temperature":0.7,"pith_summary":"This paper pins down the uniaxial strain at which the largest Fermi surface of the superconductor Sr2RuO4 changes topology — a Lifshitz transition — and shows that electronic correlations determine that strain. New measurements place the critical longitudinal strain at $\\varepsilon_{xx} = (-0.44 \\pm 0.06) \\times 10^{-2}$, corresponding to a B$_{1g}$ strain of $(-0.66 \\pm 0.09) \\times 10^{-2}$. Density functional theory alone predicts a strain more than twice as large. The authors show, with dynamical mean-field theory, that Coulomb repulsion shrinks the predicted strain, and that only an orbital-dependent Coulomb interaction on the ruthenium site brings theory into agreement with experiment. The result makes high-precision strain measurements a sharp test of correlated-electron calculations.","feed_headline":"Coulomb repulsion sets Sr2RuO4's Lifshitz strain","feed_subtitle":"Measurements and DMFT calculations agree only when the ruthenium orbitals feel unequal Coulomb repulsion.","key_machinery":"The central object is the energy of the $xy$ band at the Y point of the Brillouin zone, $E_{xy} - E_F$, whose zero crossing as a function of compressive $\\varepsilon_{xx}$ defines the Van Hove strain $\\varepsilon_{\\rm VHS}$ and the Lifshitz transition. The argument is carried by the orbital anisotropy parameter $u = U_{xy,xy} - U_{\\{xz,yz\\},\\{xz,yz\\}}$, which raises the Coulomb repulsion felt by electrons in the $xy$ orbital (the $\\gamma$ sheet) relative to the $xz,yz$ orbitals. Correlations grow the $\\gamma$ sheet and, for isotropic $U$, push $\\varepsilon_{\\rm VHS}$ essentially to zero; a nonzero $u$ partially counteracts that growth, moving the crossing back to the experimentally observed strain. This parameterization lets the calculation connect the measured critical strain to a microscopic Coulomb quantity.","core_discovery":"The paper establishes that the strain-induced Lifshitz transition in Sr2RuO4 — where the $\\gamma$ Fermi-surface sheet becomes open and a Van Hove singularity crosses the Fermi level — occurs at a longitudinal strain $\\varepsilon_{\\rm VHS} = (-0.44 \\pm 0.06)\\times 10^{-2}$, corresponding to a B$_{1g}$ strain of $(-0.66 \\pm 0.09)\\times 10^{-2}$. This value is considerably smaller than density functional theory predicts, even with spin-orbit coupling. Using DFT+DMFT with a rotationally invariant slave-boson solver, the authors show that Coulomb correlations reduce the critical strain, but that an isotropic Coulomb interaction strong enough to match measured mass renormalizations overshoots, pushing the transition essentially to zero strain. Adding an orbital anisotropy $u = U_{xy,xy} - U_{\\{xz,yz\\},\\{xz,yz\\}}$ in the range 0.10–0.15 eV restores agreement with experiment. The paper concludes that the orbital anisotropy of the local Coulomb interaction on the Ru site is essential, and that the measured critical strain provides a new quantitative constraint on electronic structure theory.","pith_inferences":["If the same anisotropy mechanism operates in other layered ruthenates, strain experiments could serve as a direct probe of orbital-resolved Coulomb repulsion, complementing spectroscopy.","The 5–12% offset between the Tc peak and the resistivity peak leaves open the possibility that the true topology change sits at the Tc peak; a direct Fermi-surface probe in the same stress cell could settle which feature marks the transition.","Because the fitted $u$ lies in the range predicted by constrained-RPA calculations, the experiment effectively measures a microscopic interaction parameter; similar strain metrology could test Hubbard parameters in other correlated oxides."],"forward_implications":["The measured $\\varepsilon_{\\rm VHS}$ becomes a benchmark for future electronic-structure methods applied to Sr2RuO4: a method must reproduce both the mass renormalization and the critical strain.","Strain tuning toward a Van Hove singularity in other multi-orbital correlated metals will require correlation-aware methods, not just DFT, to predict the required strain.","The orbital anisotropy of the Coulomb interaction is an essential ingredient of the Hubbard model for Sr2RuO4; an isotropic $U$ misplaces the Lifshitz transition even when it reproduces band masses.","Because the Tc peak and the resistivity peak occur at slightly different strains, identifying $\\varepsilon_{\\rm VHS}$ with the resistivity peak sharpens the separation between the topology change and the pairing-enhancement mechanism."],"supporting_citations":[{"why":"Supplies the force-sensor uniaxial stress apparatus that measures stress accurately, and the resistivity data from sample 1.","marker":"[7]"},{"why":"Provides the strain-optimized crystal structures used in all calculations and the prior observation of a strong Tc peak.","marker":"[2]"},{"why":"Earlier room-temperature elastic moduli of Sr2RuO4, the baseline against which the new low-temperature moduli are compared.","marker":"[12]"},{"why":"Direct ARPES observation of the stress-driven Lifshitz transition; used to confirm the strain sensitivity and the Fermi-surface geometry.","marker":"[6]"},{"why":"Shows that orbital-dependent Coulomb parameters improve the calculated Fermi surface, motivating the anisotropic u used here.","marker":"[17]"},{"why":"Constrained-RPA calculation indicating a larger Coulomb repulsion for the xy orbital, the theoretical basis for the anisotropy.","marker":"[18]"},{"why":"Prior DFT+DMFT work showing that correlations reduce the critical strain, which this paper extends.","marker":"[22]"},{"why":"High-resolution ARPES Fermi surface at zero strain, used to validate the correlated calculations at zero strain.","marker":"[26]"}],"fun_headline_variants":["Orbital anisotropy sets Sr2RuO4's Lifshitz strain","Unequal Coulomb repulsion explains Sr2RuO4's strain transition","DMFT matches Sr2RuO4's Lifshitz strain with anisotropic U","Anisotropic Coulomb interaction tunes Lifshitz strain in Sr2RuO4","Correlated electrons and orbital anisotropy set Lifshitz strain"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The paper identifies the peak in low-temperature resistivity with the Lifshitz transition; if the true transition occurs at the slightly larger strain where Tc peaks, the experimental benchmark and the fitted Coulomb anisotropy would shift.","fun_headline_variants_meta":{"raw":{"variants":["Orbital anisotropy sets Sr2RuO4's Lifshitz strain","Unequal Coulomb repulsion explains Sr2RuO4's strain transition","DMFT matches Sr2RuO4's Lifshitz strain with anisotropic U","Anisotropic Coulomb interaction tunes Lifshitz strain in Sr2RuO4","Correlated electrons and orbital anisotropy set Lifshitz strain"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000322,"raw_usage":{"total_tokens":1857,"prompt_tokens":1037,"completion_tokens":820,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":653,"completion_tokens_details":{"reasoning_tokens":722}},"tokens_in":653,"tokens_out":820,"duration_ms":8370,"temperature":1.0,"reasoning_tokens":722,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T04:41:02.048502+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the Fermi-surface topology directly — for example with quantum oscillations or ARPES on a sample under the same uniaxial strain — at strains between the resistivity peak and the Tc peak. If no topology change occurs until the Tc peak strain, the paper's assignment of $\\varepsilon_{\\rm VHS}$ and the inferred value of $u$ would need revision.","supporting_citations":[{"cited_title":"Paglione , author C","cited_arxiv_id":null,"evidence_quote":"Earlier room-temperature elastic moduli of Sr2RuO4, the baseline against which the new low-temperature moduli are compared."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Prior DFT+DMFT work showing that correlations reduce the critical strain, which this paper extends."}],"review_version":1}