{"id":"afb0fbe1-fe2f-4288-a9c5-50d7cc7e92d0","arxiv_id":"2507.20139","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"77Se-NMR shows the anomalous low-temperature relaxation upturn in FeSe0.82S0.18 is suppressed but persists under pressure up to 2 GPa, consistent with Bogoliubov Fermi surface quasiparticle interactions.","lead":"This paper measures nuclear magnetic resonance signals in an iron-based superconductor under high pressure, finding that a strange low-temperature signal weakens but does not disappear. The results support the idea that the superconductor hosts exotic 'Bogoliubov Fermi surfaces' where quasiparticles interact unusually.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central claim that the SC-state 1/T1T upturn persists at 2 GPa is not quantitatively supported: Fig. 1 shows no error bars, and no data are deposited, so 'weak but nonzero' may rest on noise rather than an intrinsic BFS signal.","rationale":"The reader's conditional verdict already identifies the missing error bars and the absence of a dedicated pressure control for extrinsic contributions. My read agrees that this is the principal weakness, but I sharpen it to the specific statistical question: is the SC-state upturn at 2.0 GPa significant relative to noise? The reader also lists the Kspin assumption as a second fragile premise; I consider that secondary because even a factor-of-two change in Kspin would keep K(α) well above unity, so the qualitative conclusion of nonzero U would survive. The theoretical BFS-C2 interpretation is not the load-bearing issue: the paper only claims consistency with that model, and the experimental fact of a persistent upturn is what must be secure. The lack of deposited data is a reproducibility concern that amplifies the statistical issue. Overall, the paper is a plausible and potentially important extension, but its headline claim requires the quantitative check I propose. This does not change the reader's CONDITIONAL verdict.","tokens_in":11976,"tokens_out":4096,"duration_ms":45067,"concrete_test":"Obtain the raw T1 recovery curves for the 2.0 GPa run below Tc (or a high-resolution digitization of Fig. 1b) and compute 1/T1T with proper pointwise error bars. Fit the data below Tc to (a) a constant and (b) a constant plus an upturn term (e.g., A/T^α or A log(Tc/T)). Report the change in chi-squared per degree of freedom and the fitted amplitude A with its uncertainty. If the improvement from the upturn term is not significant at the 95% confidence level, the claim that the upturn persists at 2 GPa is unsupported and the central conclusion must be weakened.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's headline conclusion is that pressure suppresses but does not eliminate the anomalous SC-state upturn, implying nonzero Bogoliubov quasiparticle interactions at 2 GPa. The only evidence for persistence is the visual behavior of 1/T1T below Tc in Fig. 1(b), which is presented without error bars or any statistical test. At 2 GPa the SC-state signal is a small deviation from an approximately flat baseline; without point-by-point uncertainties, the upturn cannot be distinguished from scatter, a slow vortex-core contribution, or a pressure-induced inhomogeneous broaden­ing effect. The exclusion arguments in the text against Volovik and impurity effects were made at ambient pressure, comparing x=0.18 with x=0.05 and 0.10 (Ref. 15); they are not repeated under pressure, where the Lifshitz reconstruction, altered Tc, and the pressure cell itself change the background. Because the abstract and conclusion rely on 'suppressed but persists', the persistence claim is the load-bearing element. If the 2 GPa upturn is not statistically significant, the conclusion reduces to 'suppression under pressure', which would not establish nonzero interactions. The supporting K(α)≈15 estimate depends on an assumed pressure-independent Kspin=0.03%; even though K(α)>1 is robust to reasonable Kspin variations, the quantitative link to 'U nonzero' inherits this assumption. The absence of deposited data prevents an independent check of the key figure.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports 77Se-NMR measurements on FeSe0.82S0.18 under hydrostatic pressure up to 2.0 GPa and temperatures down to ~100 mK. The authors find that the anomalous low-temperature upturn of 1/T1T below Tc, previously attributed to Bogoliubov quasiparticle interactions, is suppressed under pressure but still apparently present at 2 GPa, while the normal-state 1/T1T becomes roughly T-independent at 2 GPa. They interpret these observations as evidence that the quasiparticle interaction U weakens but remains nonzero under pressure, and they claim consistency with a theoretical model of Bogoliubov Fermi surfaces with C2 symmetry at the Γ point. The paper also estimates a Korringa enhancement factor K(α)≈15 at 2 GPa using an assumed pressure-independent Kspin=0.03%.","tokens_in":12223,"tokens_out":5494,"duration_ms":48227,"significance":"If the central claim—that the SC-state upturn persists at 2 GPa—is quantitatively robust, the paper would provide one of the first pressure-dependent experimental constraints on Bogoliubov Fermi surface quasiparticle interactions, extending the ambient-pressure evidence of Ref. 15. The observation that the normal-state and SC-state temperature dependences differ across Tc at 2 GPa is an interesting and potentially falsifiable feature. However, the persistence claim currently rests on visual inspection of a small signal in Fig. 1 without error bars, and the quantitative link to U through K(α) inherits an assumed pressure-independent Kspin. The paper does not deposit data, so independent verification is not possible at present. The qualitative trend (pressure suppresses the upturn) is plausible, but the 'nonzero' conclusion requires additional statistical and theoretical support.","major_comments":[{"comment":"The claim that the upturn of 1/T1T 'persists' at 2.0 GPa is not quantitatively supported. Fig. 1(b) shows no error bars on the 1/T1T data, and no statistical test is provided to distinguish the small deviation from a constant baseline from scatter or residual vortex-core contributions. The ambient-pressure exclusion of Volovik and impurity effects (based on the x=0.05 and x=0.10 comparison in Ref. 15) is not repeated under pressure, where the Lifshitz transition, the strongly pressure-dependent Tc (4.0→12.4 K at zero field, from Supplementary Fig. 1), and the pressure-cell environment change the background. The authors should provide point-by-point uncertainties, fit the 2 GPa SC-state data against a constant versus an upturn, and report a significance measure; if the upturn at 2 GPa is not significant, the conclusion should be revised to 'suppressed' rather than 'suppressed but nonzero'.","section":"Experimental Results, Fig. 1"},{"comment":"The estimate K(α)≈15 assumes Kspin=0.03% is independent of pressure. The argument that Kspin is constant because the DOS of a two-dimensional electron system is constant is not obviously valid in the presence of the pressure-induced Lifshitz transition invoked in the preceding subsection, which changes the Fermi-surface topology. Since K(α) feeds the conclusion that U is nonzero at 2 GPa, the authors should either justify the constant-Kspin assumption under pressure more rigorously, test the sensitivity of K(α) to reasonable Kspin variations, or soften the quantitative claim to a qualitative statement that AFM fluctuations remain.","section":"Spin correlation at 2.0 GPa (T>Tc), Eqs. (3)-(4)"},{"comment":"The inference from the suppression of the upturn to 'U becomes weak but nonzero' is not uniquely determined: the upturn depends both on the interaction U and on the nesting factor χ0(q) in Eq. (4), and the pressure-induced Lifshitz transition changes χ0(q) as the authors themselves discuss. The paper acknowledges that 'it is difficult to specify which contribution is larger from the experiments alone', but then attributes the pressure effect specifically to U. To make the central claim load-bearing, the authors should either demonstrate that the observed pressure dependence cannot be explained by the change in nesting alone, or present a model calculation of the expected 1/T1T under pressure with U fixed.","section":"Theoretical model based on BFSs with C2 symmetry (T<Tc)"}],"minor_comments":[{"comment":"The heading 'Data avaiavirity' should read 'Data availability', and the statement that data are available from the corresponding author upon reasonable request should be replaced or supplemented by deposition of the raw 1/T1T and Knight-shift data in a public repository to enable independent verification of the key figure.","section":"Data availability"},{"comment":"The caption should specify the symbol styles for each pressure level and clearly state that plotted points are measured values; currently only dashed/solid lines are described as guides to the eye.","section":"Fig. 1 caption"},{"comment":"The text uses non-standard full-width characters (e.g., '＝' in Eq. (3)) and Unicode math symbols that render inconsistently; the equations should be formatted in standard LaTeX for journal production.","section":"Equations (1)-(4)"},{"comment":"The sentence 'The results measured at zero field and 6.02 T were shown in Supplementa ry Fig. 1' contains an odd spacing; also correct the inconsistent notation for the substitution level x=0.12 (written as '0.1220' in the main text discussion of Fig. 3).","section":"Supplementary Material, Section I"},{"comment":"The experimental field orientation B//ab should be explicitly related to the spin-triplet quantization axis z used in Ref. 16, so the claim that the B⊥z calculation reproduces the data better is meaningful.","section":"Discussion of theoretical model"},{"comment":"The phrase 'the scattering between the segments on nodal areas becomes weak but nonzero' is ambiguous about whether it refers to the interaction U, the scattering amplitude, or the resulting χ(q); clarify this in the conclusion.","section":"Conclusion"}],"recommendation":"major_revision","confidential_remarks":"The paper is a direct follow-up to the authors' previous work (Ref. 15) and leans heavily on that paper for the ambient-pressure exclusion arguments; the editor may wish to stress self-containedness in the revision. The pressure-dependent study is a valuable addition to the BFS debate, but the central quantitative claim (nonzero interactions at 2 GPa) currently relies on error-bar-free visual inspection and an assumed pressure-independent Kspin. The absence of deposited data is a reproducibility concern for a key empirical figure."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear [Colleague],\n\nThe one-sentence take: this is a useful pressure-dependent NMR dataset that extends the group's ambient-pressure finding, but the central claim that the SC-state 1/T1T upturn 'persists but weakens' at 2 GPa is presented without error bars, which leaves the load-bearing inference exposed. The paper is worth refereeing, not desk-rejecting, but it needs a revision that shows uncertainties and deposits data.\n\nWhat's actually new: the pressure dependence of the anomalous SC-state relaxation in FeSe0.82S0.18. They show that at 2 GPa the normal-state 1/T1T becomes T-independent (a plausible Lifshitz-transition effect), while below Tc it still rises on cooling. That normal-versus-SC difference at the same pressure is the cleanest new fact, and it is the kind of observation that constrains the BFS scenario. The paper also verifies the sample remains tetragonal and paramagnetic up to 2 GPa, reports Tc at zero field and 6.02 T, and excludes the obvious extrinsic backgrounds at ambient pressure. The writing is honest: they explicitly note that the alternative nematic-fluctuation model is untested against their data, and they admit that the upturn's origin could be either nesting or interaction U.\n\nThe soft spots are real. First and most important: Fig. 1 has no error bars, and no raw data are deposited. The 2 GPa upturn is a small deviation from a flat baseline; without point-by-point uncertainties, I cannot tell if 'weak but nonzero' is signal or scatter. The persistence claim is load-bearing—if the 2 GPa upturn is within noise, the conclusion reduces to 'suppressed under pressure', which would not establish nonzero quasiparticle interactions. Second, the exclusion of Volovik and impurity effects was done at ambient pressure by comparing x=0.18 with x=0.05 and 0.10; under pressure the background could change, and no dedicated control is shown. That is a minor issue relative to the first. Third, the K(α)≈15 estimate assumes Kspin=0.03% and its pressure independence; the argument is plausible but it is an assumption, and the quantitative link to U inherits it.\n\nThe circularity concern is less severe than it first looks: the ambient-pressure upturn was used to infer BFS interactions, and the pressure suppression is a new external constraint rather than a refit of the same data.\n\nWho gets value: condensed-matter experimentalists working on FeSe-S and on ultranodal superconductivity. I'd bring it to a group meeting, and I'd cite it if the error bars confirm the persistence. For peer review: send it out, with a request for error bars, deposited data, and a statistical test on the 2 GPa upturn.\n\nBest,\n[Your name]","headline":"Useful pressure-dependent NMR data, but the load-bearing 'persists at 2 GPa' claim lacks error bars; worth refereeing with a request for uncertainties and raw data.","tokens_in":12874,"tokens_out":4128,"would_cite":true,"duration_ms":40339,"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 uses NMR under pressure to argue that the anomalous upturn in 1/T1T deep in the superconducting state of 18%-S-substituted FeSe, a signature of scattering between Bogoliubov Fermi-surface segments, persists at 2 GPa and is thus…","keywords":["77Se NMR","Bogoliubov Fermi surfaces","FeSe1-xSx","ultranodal superconductivity","spin-lattice relaxation rate","pressure","spin fluctuations","iron-based superconductors"],"falsifier":"A 77Se-NMR experiment at 2 GPa on samples with controlled electron-irradiation damage, measuring 1/T1T as a function of field and disorder level, would settle the claim: if the residual upturn tracks disorder or field strength, it is not an intrinsic Bogoliubov Fermi-surface interaction.","tokens_in":11729,"feed_emoji":"🧲","tokens_out":9033,"duration_ms":83347,"temperature":0.7,"pith_summary":"This paper reports 77Se NMR measurements of the iron-based superconductor FeSe0.82S0.18 (18% S substitution) under pressures up to 2.0 GPa and temperatures down to about 100 mK. The authors aim to establish that the anomalous upturn in the spin-lattice relaxation rate 1/T1T deep in the superconducting state—previously seen at ambient pressure and attributed to scattering between segments of Bogoliubov Fermi surfaces (topologically protected nodal surfaces inside the gap)—is suppressed but not eliminated by pressure. Such a result matters because it would confirm that Bogoliubov quasiparticles in this material interact with one another and that the ultranodal superconducting state survives under pressure. The paper also finds that in the normal state the same relaxation signal becomes temperature-independent at 2 GPa while the superconducting-state upturn persists, indicating that Bogoliubov quasiparticles nest differently from normal electrons.","feed_headline":"Anomalous NMR upturn survives 2 GPa in S-substituted FeSe","feed_subtitle":"The relaxation upturn tied to Bogoliubov Fermi surfaces persists, evidence that quasiparticle interactions remain nonzero.","key_machinery":"The quantity that carries the argument is the nuclear spin-lattice relaxation rate divided by temperature, $1/T_1T \\propto (1/\\omega)\\sum_{\\mathbf q} \\mathrm{Im}\\,\\chi(\\mathbf q)$, which measures low-energy spin fluctuations. The central object is the Bogoliubov Fermi surface (BFS), a topologically protected set of zero-energy nodal surfaces in a superconductor with broken time-reversal symmetry, which keeps a finite density of states inside the superconducting gap. The comparison model is an RPA spin-fluctuation calculation for a two-hole-pocket system with C2-symmetric BFSs at the Γ point, in which scattering between BFS segments at $\\mathbf q\\simeq(0.4\\pi,0)$ under a strong Hubbard interaction $U$ produces the upturn in $1/T_1T$; the paper reads the pressure suppression of the upturn as $U$ becoming weaker but nonzero. In the normal state, a standard Korringa relation, $1/(T_1T)=(4\\pi k_B/\\hbar)(\\gamma_n/\\gamma_e)^2 K_{\\rm spin}^2 K(\\alpha)$, connects the measured rate to the correlation factor $K(\\alpha)$, giving $K(\\alpha)\\simeq 15$ at 2 GPa, which the authors take as evidence that antiferromagnetic fluctuations persist even though the normal-state upturn is gone.","core_discovery":"The central discovery is that the low-temperature upturn of 1/T1T in the superconducting state of FeSe0.82S0.18, which at ambient pressure was interpreted as enhanced spin fluctuations from scattering between Bogoliubov Fermi-surface segments, is weakened but still visible at 2.0 GPa. The authors conclude that the interaction strength U between Bogoliubov quasiparticles becomes smaller under pressure but remains nonzero. In the normal state, by contrast, 1/T1T flattens to a constant at 2.0 GPa, which they attribute to a pressure-induced Lifshitz transition that changes the dominant nesting wave vector; the persistence of the upturn below Tc shows that Bogoliubov quasiparticles nest differently from normal electrons. These observations are interpreted as consistent with the theoretical model of Bogoliubov Fermi surfaces with C2 symmetry at the Γ point, where the upturn arises from enhanced χ(q) at q≈(0.4π,0) between BFS segments carrying interband spin-triplet particle-hole mixing.","pith_inferences":["Inference: Because the paper estimates K(α) from the normal-state Korringa relation and then uses that picture below Tc, one could test the model directly by measuring the field-angle dependence of the upturn, which the theory predicts is stronger for B perpendicular to the triplet quantization axis than for B parallel to it.","Inference: The arguments used to exclude impurity and vortex contributions at ambient pressure are not repeated at 2 GPa; a controlled irradiation or field-sweep study at 2 GPa would tell whether the surviving upturn has the same intrinsic origin.","Inference: If the interaction U is the controlling parameter, fine pressure tuning across the Lifshitz transition should show the superconducting-state upturn amplitude tracking the normal-state K(α) rather than following Tc; that correlation is not presented in the paper."],"forward_implications":["If the upturn is truly a BFS scattering signature, then the superconducting state of FeSe0.82S0.18 contains zero-energy Bogoliubov quasiparticles that interact, not simply a nodal gap with noninteracting quasiparticles.","The persistence at 2 GPa means BFS behavior is not confined to ambient pressure, so pressure is a tunable knob for the interaction strength in this material.","The different temperature dependence of 1/T1T above and below Tc at 2 GPa implies that the relevant nesting wave vector changes from q≈(π,0) for normal electrons to q≈(0.4π,0) for Bogoliubov quasiparticles, a testable spectral prediction.","The estimated K(α) ≈ 15 at 2 GPa in the normal state says antiferromagnetic correlations remain fairly strong even where the 1/T1T upturn disappears, so pressure mainly disrupts the nesting that produces the upturn."],"supporting_citations":[{"why":"Provided the ambient-pressure 1/T1T upturn and its attribution to BFS-related spin fluctuations that this paper extends under pressure.","marker":"[15]"},{"why":"Supplies the RPA calculation of 1/T1T showing the upturn arises from scattering between BFS segments at q~(0.4π,0), the model the data are matched against.","marker":"[16]"},{"why":"Laser ARPES observation of wide C2-symmetric nodal regions that motivates the BFS geometry at the Γ point.","marker":"[13]"},{"why":"Introduced the topological ultranodal pair-state concept and BFS model for iron-based superconductors that frames the interpretation.","marker":"[8]"},{"why":"Provided prior pressure-dependent 77Se-NMR data on 12%-S FeSe and the Lifshitz-transition interpretation used here for the normal-state suppression.","marker":"[22]"},{"why":"Theory of pressure-induced Fermi-surface reconstruction in FeSe that explains why normal-state spin fluctuations become temperature-independent at 2 GPa.","marker":"[35]"},{"why":"Electron-irradiation study of disorder effects on gap nodes, used to argue the upturn is not an impurity effect.","marker":"[17]"}],"fun_headline_variants":["NMR upturn from BFS persists under 2 GPa in FeSe0.82S0.18","Pressure study confirms Bogoliubov Fermi surfaces in S-substituted FeSe","FeSe0.82S0.18: Pressure weakens but doesn't kill BFS spin signal","Bogoliubov Fermi surface signature survives pressure in FeSe0.82S0.18"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing assumption is that the 1/T1T upturn in the superconducting state is an intrinsic bulk signal from scattering between Bogoliubov Fermi-surface segments, not a vortex-core, impurity, or pressure-cell artifact, and that the spin contribution to the Knight shift stays at 0.03% under pressure.","fun_headline_variants_meta":{"raw":{"variants":["NMR upturn from BFS persists under 2 GPa in FeSe0.82S0.18","Pressure study confirms Bogoliubov Fermi surfaces in S-substituted FeSe","FeSe0.82S0.18: Pressure weakens but doesn't kill BFS spin signal","Bogoliubov Fermi surface signature survives pressure in FeSe0.82S0.18"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000674,"raw_usage":{"total_tokens":3121,"prompt_tokens":1050,"completion_tokens":2071,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":666,"completion_tokens_details":{"reasoning_tokens":1969}},"tokens_in":666,"tokens_out":2071,"duration_ms":17549,"temperature":1.0,"reasoning_tokens":1969,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T17:48:27.824350+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A 77Se-NMR experiment at 2 GPa on samples with controlled electron-irradiation damage, measuring 1/T1T as a function of field and disorder level, would settle the claim: if the residual upturn tracks disorder or field strength, it is not an intrinsic Bogoliubov Fermi-surface interaction.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provided the ambient-pressure 1/T1T upturn and its attribution to BFS-related spin fluctuations that this paper extends under pressure."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the RPA calculation of 1/T1T showing the upturn arises from scattering between BFS segments at q~(0.4π,0), the model the data are matched against."},{"cited_title":"Nagashima, T","cited_arxiv_id":null,"evidence_quote":"Laser ARPES observation of wide C2-symmetric nodal regions that motivates the BFS geometry at the Γ point."},{"cited_title":"Setty, S","cited_arxiv_id":null,"evidence_quote":"Introduced the topological ultranodal pair-state concept and BFS model for iron-based superconductors that frames the interpretation."},{"cited_title":"Kuwayama, K","cited_arxiv_id":null,"evidence_quote":"Provided prior pressure-dependent 77Se-NMR data on 12%-S FeSe and the Lifshitz-transition interpretation used here for the normal-state suppression."},{"cited_title":"Yamakawa, and H","cited_arxiv_id":null,"evidence_quote":"Theory of pressure-induced Fermi-surface reconstruction in FeSe that explains why normal-state spin fluctuations become temperature-independent at 2 GPa."},{"cited_title":"Nagashima, K","cited_arxiv_id":null,"evidence_quote":"Electron-irradiation study of disorder effects on gap nodes, used to argue the upturn is not an impurity effect."}],"review_version":1}