{"id":"fc1ddccc-e7ca-4797-bb94-49a5623e0303","arxiv_id":"2509.00940","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"At -2% compressive strain, dynamic electron correlations make a dz2-derived flat band cross the Fermi level in bilayer La3Ni2O7, creating an extra Fermi pocket absent in static DFT+U; at -3% the pocket disappears.","lead":"Using a calculation that includes dynamic electron interactions, this paper finds an extra flat-band Fermi pocket in a strained nickelate superconductor at the exact strain where superconductivity appears. Static methods miss the pocket, and stronger strain removes it, suggesting superconductivity may only work in a narrow strain window.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The -2% gamma-pocket result rests on a single U/J/double-counting parametrization; without a sensitivity scan the central band-crossing claim is not yet robust.","rationale":"The reader's weakest_assumption is the same one I regard as load-bearing: the transferred U/J values and the double-counting choice. I agree with the CONDITIONAL verdict; no additional concern changes it. The reason this is the single most load-bearing issue is structural: the whole novelty of the paper is the reversal of the DFT+U ordering of dz2 relative to EF, and that reversal is achieved in one parameter set. The paper's internal logic is sound, the eDMFT methodology is state-of-the-art, and the 100 K supplementary results support the qualitative picture, so I do not see an internal inconsistency. But computational claims that hinge on a near-degeneracy need a sensitivity analysis; without it, the central claim is more fragile than the text acknowledges. A targeted U/J and double-counting grid would settle it. Therefore I keep the reader's verdict: conditional acceptance is appropriate, but the claim should be confirmed by a sensitivity scan before being treated as definitive.","tokens_in":13049,"tokens_out":7902,"duration_ms":105838,"concrete_test":"At the -2% Fmmm structure, rerun the fully charge-self-consistent eDMFT for U = 6, 7, 8 eV at fixed J = 1 eV, and for J = 0.7, 1.0, 1.3 eV at fixed U = 7 eV (T = 300 K, same hybridization window and projectors); in each run record the dz2 bonding-band energy at X-M-Gamma and whether a gamma pocket remains in the kz = 0 Fermi surface. Additionally repeat U = 7 eV, J = 1 eV with the exact-d double counting replaced by an FLL or AMF form. If the dz2 crossing at EF persists across the grid and the double-counting variant, the central claim is robust; if the pocket appears only for U = 7 eV, J = 1 eV, exact-d, or its position shifts by more than ~100 meV, the abstract's central assertion is parametrization-dependent and should be qualified.","verdict_should_be":"UNCHANGED","load_bearing_attack":"At -2% strain, the central claim is that the bonding dz2 band moves from below EF in DFT/DFT+U to a flat band crossing EF in eDMFT, producing the gamma pocket. This is a cancellation among the bare DFT level, the static Hartree shift, and the dynamical self-energy. The paper fixes U=7 eV and J=1 eV by reference to constrained DMFT for infinite-layer nickelates (Ref. [41]) and uses the exact-d double-counting scheme (Ref. [39]) (Methods, eDMFT paragraph). No U/J sensitivity scan, no alternative double-counting check, and no comparison with another DMFT implementation is reported. The self-consistent occupation is nd ~ 8.2, against a nominal 7.5, indicating the correlated solution is not simply at the nominal filling; small changes in U or in the double-counting potential can shift the dz2 level by tens of meV, which is the energy scale that decides whether the pocket exists. Because DFT+U and eDMFT bracket EF from opposite sides, the claim is precisely the kind of result that needs a demonstration of robustness in the interaction parameters.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports fully charge self-consistent DFT+embedded DMFT (eDMFT) calculations for bilayer Ruddlesden-Popper nickelate La3Ni2O7 under compressive strain, using a CTQMC impurity solver for the Ni-3d shell. Three strain states are studied: unstrained Amam (0%) and Fmmm (-2% and -3%). The central claim is that at -2% strain—the strain level at which superconductivity is observed—the bonding dz2 band crosses the Fermi level, producing an extra gamma/mu Fermi-surface pocket with flat-band-like character, in contrast to DFT and DFT+U results where this band lies below EF. At -3% strain the pocket is suppressed. The authors further report orbital-selective coherence: dx2-y2 becomes coherent at 300 K, while dz2 is still incoherent at 300 K and only becomes coherent at lower temperature. They conclude that multi-orbital eg physics is relevant for the strained bilayer and that the mu pocket may exist only in a narrow strain window.","tokens_in":13376,"tokens_out":4460,"duration_ms":63150,"significance":"If correct, the result is significant: it challenges the prevailing DFT+U-based picture that the dz2 bonding band is inert at the superconducting strain and would place strained La327 in a two-orbital (dx2-y2 + dz2) description with consequences for pairing-symmetry calculations. The methodological strengths are real: the calculations are fully charge self-consistent, use a spin-rotation-invariant Slater interaction, cover several strain levels with experimentally motivated structures, and compare against DFT/DFT+U. However, the central band-crossing result rests on a single interaction parametrization and a single double-counting scheme, with no sensitivity analysis. Because the claimed crossing is a cancellation between static Hartree shifts and dynamical self-energy effects, the result is not yet quantitatively robust. An explicit U/J and double-counting sensitivity study is needed before the gamma pocket can be treated as a firm prediction.","major_comments":[{"comment":"The central claim—the emergence of the gamma/mu pocket at -2% strain—depends on a single interaction parametrization, U=7 eV and J=1 eV, transferred from constrained DMFT results for infinite-layer nickelates (Ref. [41]), and on the 'exact-d' double-counting scheme (Ref. [39]). No sensitivity scan over U/J or double-counting is reported. Since DFT and DFT+U bracket EF from opposite sides, the eDMFT crossing is a cancellation between the Hartree shift and the dynamical self-energy; a change of tens of meV in the dz2 level determines whether the pocket exists. I request at least a U/J scan (e.g., U=6-8 eV, J=0.5-1.5 eV) and, ideally, a check with an alternative double-counting prescription. The reported self-consistent occupation nd~8.2 versus the nominal 7.5 (Sec. II, 'eDMFT density of states and hybridization functions') underlines that the solution is not at a simple nominal filling, ma","section":"Methods, eDMFT paragraph; Results, Sec. II"},{"comment":"The flat-band crossing at -2% strain is extracted from maximum-entropy analytic continuation of CTQMC data at 300 K. At this temperature the dz2 imaginary self-energy does not extrapolate to zero at zero Matsubara frequency (Fig. 3b), so the dz2 spectral function is broad and the 'flat-band' feature is not a sharp quasiparticle peak. The paper provides no quantitative estimate of the energy separation between the dz2 band and EF, nor any uncertainty/quality-of-fit measure for the MaxEnt result. The authors should provide a direct estimate of the crossing energy (for instance from the real-axis self-energy or from the 100 K spectral functions in Supplementary Note 2) and state how robust the crossing is to the analytic-continuation procedure.","section":"Results, Fig. 1(c), Fig. 3(b); Methods, analytic continuation"}],"minor_comments":[{"comment":"The notation for the Fermi-surface pocket is inconsistent: the abstract and main text call it the mu pocket, the abstract also refers to the gamma/mu pocket, and Supplementary Figure 1d calls it the gamma sheet. Please unify the notation.","section":"Abstract and Sec. II"},{"comment":"The title contains a typo: 'compress ive' should be 'compressive'.","section":"Title/header"},{"comment":"The color scale for the orbital-resolved spectral functions is not defined. A color bar or explicit statement of what the color encodes (e.g., orbital weight/hybridization) would improve readability.","section":"Fig. 1"},{"comment":"The statement 'at least 15 x 10^6 MC steps' is ambiguous. Please specify whether this is the total number of Monte Carlo steps or the number per measurement bin/sweep, and how the number was increased at lower temperature.","section":"Methods, eDMFT paragraph"},{"comment":"The data availability statement relies on 'reasonable request'. Given the community interest in this material and the sensitivity of the central result, depositing input files and representative output (e.g., self-energies, spectral functions) in a public repository would be more consistent with best practices.","section":"Data availability"}],"recommendation":"major_revision","confidential_remarks":"The manuscript addresses a timely and important question with a state-of-the-art method. My main concern is not the method but the robustness of the central crossing: a single (U,J) parametrization and a single double-counting scheme separate the main result from a null result. I would be comfortable with publication after the authors add a sensitivity study, even if it only brackets the uncertainty. The fact that Ref. [41], the source of U/J, is coauthored by two of the current authors makes the transfer assumption easier to check but does not by itself weaken the paper; it does, however, make the requested sensitivity analysis more incumbent. The manuscript is within scope for a condensed-matter theory journal."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Worth a look. The genuinely new thing is the method: no one has yet run fully charge self-consistent eDMFT on strained La3Ni2O7, and the headline result is that at -2% strain the d_z2 bonding band that DFT+U pushes below E_F comes back up and forms the gamma/mu pocket once correlations are treated dynamically. That is a real contrast with the static picture and, if it holds, it changes the multi-orbital discussion and the pairing-symmetry debate.\n\nThe method side is solid: charge self-consistency between DFT and DMFT, CTQMC solver, paramagnetism, 300 K and 100 K runs for the key case, and clear Fermi-surface and spectral-function figures. The 100 K check showing the d_z2 self-energy going to zero while it does not at 300 K is well done. They also cite the conflicting ARPES experiments honestly and do not overclaim consistency with either.\n\nThe soft spot is the one the stress-test flags. The entire -2% pocket rests on a single interaction parametrization, U=7 eV and J=1 eV, taken from a constrained-DMFT paper for infinite-layer nickelates with overlapping authors, plus one double-counting scheme (exact-d). No U or J sweep, no alternative double counting, no second DMFT implementation. The energy scale deciding the crossing is tens of meV, and the d-occupation comes out at 8.2 rather than the nominal 7.5, so small changes in U can plausibly move the band. That does not mean the result is wrong; it means the central claim is not yet robust. The stress-test's analogy to DFT+U bracketing E_F from the opposite side is fair.\n\nAlso, the data availability says \"on request,\" which makes independent checking harder for a computational paper whose main output is a spectral function. I would want at least the self-energies, DOS, and Fermi-surface files released. The Summary's wording that a \"flat band of pure d_z2 character\" crosses E_F is stronger than what the body shows, given the hybridization and the 300 K incoherence. That is minor.\n\nWho is this for? People working on nickelate superconductivity, especially the strain window and pairing symmetry. It deserves a serious referee: the approach is appropriate, the claim is new and important, and the missing sensitivity analysis is an addressable revision, not a fatal flaw.","headline":"First charge-self-consistent eDMFT for strained La327, claiming dynamical correlations resurrect the d_z2 pocket at -2% strain; plausible and new, but the central crossing rests on one U/J setting and needs a sensitivity check.","tokens_in":13848,"tokens_out":2398,"would_cite":true,"duration_ms":29330,"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":"This paper claims that at -2% compressive strain, dynamical correlations place a flat Ni-dz2 band at the Fermi level of La3Ni2O7, reviving the μ Fermi-surface pocket that DFT+U suppresses.","keywords":["Ruddlesden-Popper nickelates","La3Ni2O7","compressive strain","dynamical mean-field theory","Fermi surface pocket","flat band","orbital selectivity","superconductivity"],"falsifier":"A direct photoemission measurement on stoichiometric La3Ni2O7 films under -2% biaxial strain: if the bonding dz2 band is unambiguously observed below the Fermi level and not crossing it, the paper's central claim fails. A complementary computational falsifier is an eDMFT scan over U = 6-8 eV at -2% strain; if the dz2 band stays below the Fermi level throughout that range, the pocket is an artifact of a single parametrization.","tokens_in":12993,"feed_emoji":"⚡","tokens_out":7008,"duration_ms":82121,"temperature":0.7,"pith_summary":"Compressive strain has recently made the bilayer nickelate La3Ni2O7 superconducting at ambient pressure, but the normal state it emerges from is unresolved. This paper argues that dynamical electron correlations—not the static correlations of DFT+U—control that normal state. Using fully charge-self-consistent DFT plus embedded dynamical mean-field theory, it finds that at the experimentally relevant -2% strain a bonding Ni-dz2 band crosses the Fermi level as a flat band, creating the μ Fermi-surface pocket that static calculations push below the Fermi level. If correct, the low-energy physics of strained La327 is genuinely multi-orbital, with both dz2 and dx2-y2 active, and the strain window in which superconductivity appears may be tied to the presence of this pocket.","feed_headline":"Correlations restore a flat band in strained La327","feed_subtitle":"At the -2% strain where superconductivity appears, a dz2 band crosses the Fermi level, unlike in DFT+U.","key_machinery":"The machinery is fully charge self-consistent DFT + embedded dynamical mean-field theory (eDMFT), using localized Ni-3d orbitals, a five-orbital Slater Hamiltonian with U = 7 eV and J = 1 eV, an exact double-counting correction, and a continuous-time quantum Monte Carlo impurity solver. The dynamical self-energy renormalizes the dz2 bands, drastically reducing the bonding-antibonding splitting so that the bonding dz2 band crosses the Fermi level at -2% strain, while dx2-y2 remains more strongly hybridized and coherent. This dynamical renormalization is what distinguishes the eDMFT result from the static DFT+U picture.","core_discovery":"The central claim is that at -2% compressive strain—the strain at which superconductivity has been observed—the bonding dz2 band, which in DFT and DFT+U lies below the Fermi level, is pushed back across the Fermi level by dynamical correlations, producing the μ pocket and a flat-band feature along the X-M-Γ path. Both Ni-eg orbitals then cross the Fermi level, so a two-orbital description is needed for the normal state. At -3% strain the μ pocket is suppressed, and at 0% strain neither eg orbital is fully coherent at 300 K, whereas at -2% strain dx2-y2 is coherent at 300 K but dz2 only reaches coherence at 100 K. The results are presented as a direct contrast with static DFT+U and as compati","pith_inferences":["If the μ pocket is what enables the observed ~30-40 K superconductivity in strained La327, the same mechanism should operate under pressure in unstrained La327, where the pocket also appears; comparing the two could isolate strain's specific role.","The flat dz2 band near the Fermi level may act as a pairing-enhancement source, so a strain series that tunes this band through the Fermi level could produce a non-monotonic Tc versus strain—an experimentally testable signature.","Because dz2 is incoherent near 300 K while dx2-y2 is coherent, resistivity or optical conductivity may show orbital-selective fingerprints, providing an experimentally accessible check of the two distinct coherence scales.","The U and J values are inherited from infinite-layer nickelates and are not scanned here; a constrained-RPA or GW estimate of U for the strained bilayer would be a direct check on whether the μ pocket survives at -2% strain."],"forward_implications":["Because the μ pocket reappears only when correlations are treated dynamically, DFT+U-based predictions for strained La327 miss a Fermi-surface sheet that may be decisive for pairing.","Both dz2 and dx2-y2 eg orbitals cross the Fermi level at -2% strain, so the normal state is multi-orbital and single-orbital effective models are incomplete.","Strain tunes the μ pocket: it is present at -2% but gone by -3%, so if superconductivity depends on the pocket, it should be confined to a narrow strain window.","The flat dz2 band at the Fermi level and its slower coherence onset indicate orbital-selective correlation effects in the normal state.","A strain series across the -2% to -3% range would directly test the predicted Fermi-surface evolution and its link to superconductivity.","Since the paper does not compute pairing, its results set the normal-state Fermi surface that any pairing-symmetry calculation for strained La327 should start from."],"supporting_citations":[{"why":"Supplies the U = 7 eV and J = 1 eV Coulomb parameters adopted for the Ni-d impurity problem.","marker":"[41]"},{"why":"Provides the exact double-counting scheme that sets the placement of the correlated d bands relative to the Fermi level.","marker":"[39]"},{"why":"Describes the full-potential eDMFT implementation and spin-rotation-invariant Coulomb interaction used in the calculation.","marker":"[38]"},{"why":"Gives the strained La327 structures (Fmmm at -2% and -3%, Amam at 0%) that the eDMFT calculations start from.","marker":"[29]"},{"why":"Static DFT+U calculation at -2% strain whose prediction of the bonding dz2 band below the Fermi level this paper directly contradicts.","marker":"[30]"},{"why":"Another DFT+U study reporting the dz2 band below the Fermi level under strain, used as a comparison for the static-correlation picture.","marker":"[32]"},{"why":"ARPES finding the μ pocket below the Fermi level by about 70 meV in strained La2PrNi2O7, used to discuss sensitivity to stoichiometry.","marker":"[34]"},{"why":"ARPES finding the μ band crossing the Fermi level in hole-doped strained films, used to support the eDMFT result.","marker":"[35]"},{"why":"Connects suppression of the μ pocket to possible d-wave pairing, used in the discussion of pairing-symmetry implications.","marker":"[21]"}],"fun_headline_variants":["Strain plus correlations revive flat band in nickelate","Dynamic correlations flip dz2 band across Fermi level","At -2% strain, correlations restore key band in La327","DFT+U misses flat band that eDMFT reveals"],"cache_read_input_tokens":2688,"weakest_assumption_plain":"The results assume the interaction strengths and the way the DFT and correlated parts are reconciled are correct; the band that matters crosses the Fermi level only under that assumption, and the paper does not test how much those choices can vary.","fun_headline_variants_meta":{"raw":{"variants":["Strain plus correlations revive flat band in nickelate","Dynamic correlations flip dz2 band across Fermi level","At -2% strain, correlations restore key band in La327","DFT+U misses flat band that eDMFT reveals"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000184,"raw_usage":{"total_tokens":1159,"prompt_tokens":750,"completion_tokens":409,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":494,"completion_tokens_details":{"reasoning_tokens":342}},"tokens_in":494,"tokens_out":409,"duration_ms":4791,"temperature":1.0,"reasoning_tokens":342,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T13:03:30.788203+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A direct photoemission measurement on stoichiometric La3Ni2O7 films under -2% biaxial strain: if the bonding dz2 band is unambiguously observed below the Fermi level and not crossing it, the paper's central claim fails. A complementary computational falsifier is an eDMFT scan over U = 6-8 eV at -2% strain; if the dz2 band stays below the Fermi level throughout that range, the pocket is an artifact of a single parametrization.","supporting_citations":[{"cited_title":"L., Cosovanu, L., Haule, K","cited_arxiv_id":null,"evidence_quote":"Supplies the U = 7 eV and J = 1 eV Coulomb parameters adopted for the Ni-d impurity problem."},{"cited_title":"& Botana, A","cited_arxiv_id":null,"evidence_quote":"Gives the strained La327 structures (Fmmm at -2% and -3%, Amam at 0%) that the eDMFT calculations start from."},{"cited_title":"& Wang, Q.-H","cited_arxiv_id":null,"evidence_quote":"Connects suppression of the μ pocket to possible d-wave pairing, used in the discussion of pairing-symmetry implications."}],"review_version":1}