{"id":"7cca6f34-3725-4f0e-b88b-b7d34dbb1f47","arxiv_id":"2412.16171","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"FeSe1-xSx and FeSe1-xTex transport data reveal two superconducting domes with different Dirac states and resistivity exponents, suggesting distinct pairing mechanisms.","lead":"Transport measurements on FeSe-based superconductors map two superconducting domes with different normal-state resistivity and different Dirac states. The results suggest the two domes may have distinct pairing mechanisms, one tied to a bulk Dirac state and strange metal behavior, the other to a surface Dirac state near a nematic quantum critical point.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The claimed sign change of the topological surface Dirac state near the nematic QCP rests on an unvalidated hall-shape rule in the three-band model, so the Dirac-state evolution supporting two distinct pairing mechanisms is not yet established.","rationale":"The two superconducting domes and the n≈1 versus n<1 resistivity exponents are direct, reproducible transport observations and are not called into question. The paper's added value lies in connecting these domes to distinct Dirac states—a bulk Dirac state on SC1, a surface Dirac state on SC2, with a sign change near the pure nematic QCP—and in using that connection to argue for two pairing mechanisms. The reader's weakest-assumption analysis correctly locates the three-band model as the fragile link. My stress-test sharpens this to constraint 3, because the sign of the small high-mobility band is the only basis for the 'hole-to-electron sign change' and for distinguishing electron-type versus hole-type surface Dirac states in Fig. 4(f). Constraint 3 is plausible for the special case where the two main bands have similar mobilities (as in FeSe), but it is not derived or justified generally. The authors' own admission that the origin of the sign change is unclear (main text) shows that this feature is not independently corroborated. The proposed refit with the sign free would settle the matter directly. If the sign is not robust, the paper should present the Dirac-state evolution as one plausible interpretation rather than a demonstrated fact; the two-dome phase diagram and n-exponent contrast would remain useful but would no longer 'strongly support' two distinct pairing mechanisms. Therefore the conditional verdict stands, with the condition being a uniqueness/stability analysis of the three-band fits. No ad hominem is intended; this is a modeling-assumption critique.","tokens_in":18543,"tokens_out":7114,"duration_ms":73036,"concrete_test":"Refit the 20 K ρxy(H) and MR data for x(Te) = 0.44, 0.5, and 0.6 using the same three-band model and total-compensation constraint, but with the small band's sign left free (not fixed by the concavity/convexity rule). Compare the reduced chi-squared for the best electron-like versus hole-like small-band solutions. If the opposite-sign solution fits equally well (Δχ²_red < 0.1), the claimed sign change is not determined by transport data. Additionally, vary the starting carrier concentrations over a factor of two and check whether the fitted sign and Dirac concentration n2 remain stable.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's distinctive claim that SC2 is accompanied by a topological surface Dirac state that changes from hole-type to electron-type near x_Te ≈ 0.52 is derived entirely from three-band fits whose sign assignment relies on constraint 3 in the Supplemental Information: 'the concave shape of hall behavior represents two electron bands and one hole band, while the convex shape ... one electron band and two hole bands.' This rule is not generally valid: for a multiband compensated system, the curvature of ρxy(H) depends on carrier mobilities and concentrations, not only on the number of electron versus hole bands. The authors do not demonstrate that the fits are unique, report no error bars, and do not test the opposite sign assignment for the small high-mobility band. Since the authors themselves state that 'the origin of the change is not yet clear' (main text), the sign change near the QCP is an interpretation rather than an established observation. If constraint 3 is relaxed, the sign change—and with it the claimed dichotomy between bulk and surface Dirac states across the two domes—may vanish; the central pairing-mechanism conclusion would then rest only on the observed two-dome phase diagram and resistivity exponents, which are less specific.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports electromagnetic transport measurements on FeSe1−xSx (0 ≤ x ≤ 0.25) and FeSe1−xTex (0 ≤ x ≤ 1) single crystals, establishing a temperature–doping phase diagram with two superconducting domes (SC1 near FeSe and SC2 near FeSe0.5Te0.5). The authors identify a bulk Dirac state accompanying SC1, synchronized with strange-metal resistivity (n ≈ 1), and a topological surface Dirac state accompanying SC2, which they claim changes from hole- to electron-type near the pure nematic quantum critical point at x(Te) ≈ 0.52. Based on the distinct normal-state resistivity exponents and the evolution of the Dirac states, the paper concludes that the two superconducting domes have two different pairing mechanisms, with SC1 associated with antiferromagnetic fluctuations and SC2 with nematic fluctuations. The phase diagram, Hall resistivity, and magnetoresistance data are presented for the full doping range, with the Dirac-state analysis based on simultaneous three-band and two-band fits described in the Supplemental Material.","tokens_in":18864,"tokens_out":3343,"duration_ms":35406,"significance":"If the central claims hold, the paper provides a complete normal-state phase diagram for an entire FeSe-based family and offers a concrete scenario in which two superconducting domes are associated with different electronic structure contexts: a bulk Dirac state plus strange metal for SC1, and a topological surface Dirac state plus sub-linear resistivity for SC2. This would be a valuable contribution to the ongoing discussion of pairing mechanisms in FeSe-based superconductors and to the broader phenomenology of two-dome superconductors. The paper is also commendable for presenting transport data over a wide doping range, for making the fitting constraints explicit in the Supplemental Material, and for combining Hall and magnetoresistance analyses. However, the load-bearing identification of the Dirac state type and its sign change rests on a constrained three-band model whose uniqueness and validity are not demonstrated; unless that analysis is made robust, the central pairing-mechanism conclusion is only as strong as the phase diagram and resistivity exponents, which are less specific.","major_comments":[{"comment":"The sign change of the Dirac carrier near the nematic QCP, which is central to the claim that the topological surface Dirac state evolves from hole-type to electron-type, is imposed rather than tested by Constraint 3: 'The concave shape of hall behavior represents two electron bands and one hole band, while the convex shape of hall behavior represents one electron band and two hole bands.' This rule is not generally valid for multiband compensated systems: the curvature of ρxy(H) depends on the mobilities and concentrations of all bands, not only on the number of electron versus hole bands. The authors do not report confidence intervals for the fitted n2 and μ2, do not test whether an opposite sign assignment for the small high-mobility band can also describe the same Hall and MR data, and do not demonstrate that the three-band fit is unique. Since the main text states that 'the origin of the change is not yet clear,' the hole-to-electron sign change near x(Te) ≈ 0.52 is an interpretation contingent on Constraint 3 rather than an established observation. This needs to be addressed with a model-selection analysis (e.g., fits without the concavity/convexity rule, error bars or bootstrap uncertainties, and a test of alternative band assignments) before the Dirac-state dichotomy across the two domes can be considered established.","section":"Supplemental Material, 'Three band model', Constraint 3"},{"comment":"The three-band analysis imposes full electron–hole compensation at all dopings (Constraint 1) and uses FeSe-like carrier concentrations as the starting scale (Constraint 2). While compensation is supported by several experimental probes, the fits in Table I yield Dirac carrier concentrations as small as 0.04–0.07 × 10^18 cm^-3 near x(Te) = 0.5–0.6, about three orders of magnitude smaller than the main carrier concentrations. With no error bars or sensitivity analysis reported, it is unclear whether the Dirac band parameters, and especially their sign, are meaningfully constrained by the transport data at these dopings. The authors should provide quantitative uncertainties for n2 and μ2 from the simultaneous Hall/MR fits, and show how the fitted values change when the compensation and initial-value constraints are relaxed within reasonable bounds.","section":"Supplemental Material, 'Three band model', Constraint 1 and Table I"},{"comment":"The conclusion that the two superconducting domes exhibit 'completely different Dirac and normal transport behaviors, strongly supporting the two distinct superconducting pairing mechanisms' depends on the Dirac-state assignment. The normal-state resistivity exponents (n ≈ 1 on SC1, n < 1 on SC2) and the two-dome phase diagram are direct observables and are credible. However, the paper uses these observables to argue for two pairing mechanisms while also attributing the SC2 dome to the topological surface Dirac state and to pure nematic fluctuations. The latter attribution relies on the Dirac-state sign change, which is not yet robust for the reasons above. The authors should either strengthen the transport evidence for the sign change or soften the claim that the Dirac-state evolution provides 'convincing evidence' for two distinct pairing mechanisms, clearly separating the direct transport observables from the model-dependent interpretation.","section":"Main text, 'Another interesting phenomenon...' (discussion of sign change near the nematic QCP)"}],"minor_comments":[{"comment":"The caption contains typographical errors: 'magniffed' should be 'magnified' and 'deffined' should be 'defined'.","section":"Figure 4 caption"},{"comment":"The table in the Supplemental Material is labeled 'TABLE I', but the main text refers to it as 'Table S1'. Please harmonize the numbering and the citation.","section":"Main text, 'See Fig. S7 and Table S1 [59]'"},{"comment":"Subject–verb agreement: 'properties ... suggests' should be 'properties ... suggest'.","section":"Main text, 'Magnetotransport properties of FeSe1−xSx suggests'"},{"comment":"In Eqs. (S6)–(S8), the notation n is used for the common carrier concentration of the compensated two-band model; this should be defined explicitly, since the main text uses n for the resistivity exponent and n2 for the Dirac carrier concentration.","section":"Supplemental Material, 'Two band model'"},{"comment":"The magnetoresistance data for x(Te) ≥ 0.7 are described as 'nearly zero' and not analyzed quantitatively, yet Fig. 1 includes the full doping range in the phase diagram. A brief statement explaining why these data do not affect the Dirac-state classification at high Te content would improve clarity.","section":"Figure 3 and related text"}],"recommendation":"major_revision","confidential_remarks":"The phase diagram and transport data set are a solid contribution, and the explicit statement of fitting constraints in the SI is good practice. My main concern is that the Dirac-state sign change, which is the linchpin of the pairing-mechanism conclusion, is an artifact of a modeling constraint rather than an independent observable. This is fixable within the manuscript's scope by adding uncertainty quantification, testing alternative band assignments, and either confirming or downplaying the sign-change claim. If the sign change cannot be robustly established, the paper would still be valuable as a comprehensive phase diagram and normal-state transport study, but the 'two distinct pairing mechanisms' conclusion would need to be substantially softened. The manuscript is within the scope of cond-mat.supr-con."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a useful systematic transport study of FeSe1-xSx and FeSe1-xTex, and the phase diagram with the two domes and the resistivity exponent contrast is worth having. But the claim that the two domes are accompanied by different Dirac states—especially the sign change near the nematic QCP—rests on a three-band fit with imposed constraints, so the Dirac-state evolution is an interpretation, not an established observation.\n\nWhat's actually new: the continuous doping series on the Te side, and the correlation between the reappearance of nonlinear Hall and MR around x(Te)=0.41–0.6 and the SC2 dome. That is a real dataset. The S-side largely reuses published data, and the bulk Dirac cone in FeSe and the topological surface states in FeSe0.5Te0.5 are already known from ARPES, so the novelty is the synthesis and the proposed evolution across doping.\n\nWhat's good: the paper is honest about the limits of the sign-change interpretation (\"the origin of the change is not yet clear\"), and the T* construction is transparent. The resistivity exponent n contrast, with n~1 on SC1 and n<1 on SC2, is a plausible and useful observation even if the T* selection is visual.\n\nWhere it's soft: the sign change of the surface Dirac state is a change in the sign of a fitted mobility in a compensated three-band model. Constraint 3 in the SI—concave Hall means two electron bands plus one hole band, convex means one electron plus two hole bands—is not generally valid. Hall curvature depends on mobilities and concentrations, not just band count. There are no error bars, no test of alternative sign assignments, and no demonstration that the fits are unique. So the hole-to-electron crossing of the surface Dirac state near x=0.52 is model-dependent. If that constraint is relaxed, the sign change could vanish. The pairing-mechanism conclusion is an inference from this plus the two-dome phase diagram; it's suggestive, not convincing.\n\nThere is also a minor concern: the paper doesn't provide raw data or fitting residuals, which makes the three-band results hard to evaluate. That's fixable.\n\nWho it's for: people working on FeSe-based superconductors and the two-dome paradigm. It deserves a serious referee, but the referee should ask for data sharing, error analysis, and a robustness check of the three-band constraints. I'd accept it after that, likely as a solid phase-diagram paper with a more cautious Dirac-state narrative.","headline":"Useful systematic transport phase diagram for the two domes in FeSe-based superconductors, but the Dirac-state evolution and sign change rest on a constrained three-band fit and are not yet established.","tokens_in":19327,"tokens_out":2197,"would_cite":false,"duration_ms":22987,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper claims that the two superconducting domes in FeSe-based superconductors are accompanied by entirely different normal states and Dirac states, and that this difference is evidence for two distinct superconducting pairing…","keywords":["FeSe1-xTex","two superconducting domes","bulk Dirac state","topological surface Dirac state","strange metal","nematic quantum critical point","Hall resistivity","three-band model"],"falsifier":"Angle-resolved photoemission on FeSe$_{1-x}$Te$_x$ samples across the nematic quantum critical point ($x(\\mathrm{Te}) \\approx 0.4$–$0.7$) could directly test whether a topological surface Dirac cone exists on both sides of the QCP and whether its carrier character flips from hole-like to electron-like near $x \\approx 0.52$; if no such surface Dirac cone is found, or the sign change does not follow the QCP, the transport-based assignment of the SC2 Dirac state would fail.","tokens_in":18387,"feed_emoji":"🧲","tokens_out":10344,"duration_ms":274657,"temperature":0.7,"pith_summary":"The paper sets out to show that the two superconducting domes seen in FeSe$_{1-x}$S$_x$ and FeSe$_{1-x}$Te$_x$ are not the same pairing phenomenon twice. Transport measurements map a complete doping-temperature phase diagram in which the first dome (SC1) is synchronized with a bulk Dirac state and a strange-metal resistivity with exponent $n \\sim 1$, while the second dome (SC2) sits near a pure nematic quantum critical point and is accompanied by a topological surface Dirac state whose carrier sign changes across that point. If this reading is right, the two domes arise from different electronic-structure contexts and therefore different pairing mechanisms, placing FeSe-based materials inside the same two-dome paradigm as other unconventional superconductors.","feed_headline":"Two superconducting domes in FeSe host different Dirac states","feed_subtitle":"Bulk Dirac cone and strange metal mark dome 1; a surface Dirac cone flips sign at dome 2—two pairing mechanisms.","key_machinery":"The load-bearing object is the constrained three-band magnetotransport model used to separate ordinary carriers from a small high-mobility Dirac carrier species. The model, applied simultaneously to Hall resistivity $\\rho_{xy}(H)$ and magnetoresistance $\\rho_{xx}(H)$, imposes charge compensation, an FeSe-like carrier concentration scale, and the rule that a concave Hall shape means two electron bands plus one hole band while a convex shape means one electron band plus two hole bands. This fitting is what assigns the small carrier to a bulk Dirac cone on the SC1 side and to a hole- or electron-type topological surface Dirac cone on the SC2 side, and it yields the carrier concentrations, mobilities, and sign change displayed in the phase diagram.","core_discovery":"On its own terms, the paper's central discovery is that the normal state and the Dirac electronic state track the two superconducting domes separately rather than changing continuously. Around FeSe (SC1), a topologically trivial bulk Dirac cone at the Brillouin-zone corner appears together with a non-Fermi-liquid strange metal ($\\rho(T) \\propto T^n$, $n \\sim 1$) and superconductivity; with Te doping this Dirac state is gradually suppressed. Near FeSe$_{0.5}$Te$_{0.5}$ (SC2), where a pure nematic quantum critical point sits, a topologically nontrivial surface Dirac cone appears due to stronger spin–orbit coupling, survives above the structural transition, and changes from hole-like to electron-like as the system crosses the quantum critical point, while the normal-state exponent falls below 1 and no strange metal reappears. The authors take this evolution as evidence that the two domes originate from a Fermi-surface reconstruction and are associated with distinct pairing mechanisms, one linked to antiferromagnetic fluctuations and the other to nematic fluctuations.","pith_inferences":["Beyond the paper, the same transport analysis could be applied to S-substituted FeSe under pressure, where the nematic QCP moves; the model predicts the surface-Dirac sign change should track the QCP rather than the chemical substitution itself.","Beyond the paper, the causal link between the bulk Dirac cone and the strange metal is left open: the two could be one phenomenon (the Dirac cone producing $T$-linear resistivity) or two parallel consequences of nematic fluctuations.","Beyond the paper, quantum oscillation measurements on FeSe$_{1-x}$Te$_x$ in the SC2 region could test the tiny Dirac carrier densities ($\\sim 10^{17}$ cm$^{-3}$) extracted from the three-band fit; an independent pocket with that density would confirm the assignment."],"forward_implications":["If the picture holds, SC1 is tied to antiferromagnetic-fluctuation pairing and SC2 to pure nematic-fluctuation pairing, with the $T_c$ dip between the domes marking a switch of electronic structure rather than a smooth crossover.","At the junction doping the bulk Dirac state disappears, the strange metal gives way to Fermi-liquid behavior, and no surface Dirac state has yet appeared, locating the structural crossover near $x(\\mathrm{Te}) \\approx 0.3$.","The sign change of the topological surface Dirac state near the pure nematic QCP provides a transport-accessible marker for the Fermi level crossing the Dirac point.","The combination of nonlinear Hall effect and linear magnetoresistance offers a bulk transport route for identifying topological surface Dirac states in iron chalcogenides, complementing surface-sensitive probes."],"supporting_citations":[{"why":"Supplies the pure nematic quantum critical point associated with the SC2 dome, which anchors the second superconducting dome in the phase diagram.","marker":"[13]"},{"why":"Provides the high-field shrinkage of SC1 and SC2 that the paper cites as evidence that the two domes are mediated by antiferromagnetic and nematic fluctuations, respectively.","marker":"[14]"},{"why":"Establishes the strange-metal Hall response in FeSe$_{1-x}$S$_x$ that links the bulk Dirac state to the strange metal on the SC1 side.","marker":"[21]"},{"why":"Defines the compensated semimetal band structure of FeSe with hole and electron pockets that the three-band fitting assumes.","marker":"[26]"},{"why":"Identifies the electron-type bulk Dirac cone at the Brillouin-zone corner in FeSe, the reference state for SC1.","marker":"[27]"},{"why":"Identifies the topologically nontrivial surface Dirac states induced by spin-orbit coupling in FeSe$_{0.45}$Te$_{0.55}$, the reference state for SC2.","marker":"[29]"},{"why":"Origin of the concave Hall and high-mobility minority-carrier interpretation used to detect the bulk Dirac state in FeSe.","marker":"[38]"},{"why":"Provides the electron Dirac state and linear magnetoresistance signature in Fe$_{1+y}$Te$_{0.6}$Se$_{0.4}$ used for comparison on the Te-rich side.","marker":"[44]"},{"why":"Contains the constrained three-band model (compensation, FeSe-like carrier scale, Hall-shape rule) from which the carrier concentrations, mobilities, and Dirac sign change are extracted.","marker":"[59]"}],"fun_headline_variants":["Two FeSe domes, two Dirac states, two pairing mechanisms","Bulk Dirac for SC1, surface Dirac for SC2","Two superconducting domes share distinct normal-state and Dirac behaviors","FeSe superconductors: two domes, two Dirac cones, distinct origin","Distinct Dirac states expose two pairing mechanisms in FeSe"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The identification of which Dirac state is present, and of the sign change, rests on the three-band fitting constraints in the supplementary material: exact electron-hole compensation, an FeSe-like carrier concentration as the starting scale, and the rule that concave Hall curvature means two electron bands plus one hole band while convex means one electron band plus two hole bands.","fun_headline_variants_meta":{"raw":{"variants":["Two FeSe domes, two Dirac states, two pairing mechanisms","Bulk Dirac for SC1, surface Dirac for SC2","Two superconducting domes share distinct normal-state and Dirac behaviors","FeSe superconductors: two domes, two Dirac cones, distinct origin","Distinct Dirac states expose two pairing mechanisms in FeSe"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000349,"raw_usage":{"total_tokens":1948,"prompt_tokens":1027,"completion_tokens":921,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":643,"completion_tokens_details":{"reasoning_tokens":833}},"tokens_in":643,"tokens_out":921,"duration_ms":9254,"temperature":1.0,"reasoning_tokens":833,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T20:57:20.620909+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Angle-resolved photoemission on FeSe$_{1-x}$Te$_x$ samples across the nematic quantum critical point ($x(\\mathrm{Te}) \\approx 0.4$–$0.7$) could directly test whether a topological surface Dirac cone exists on both sides of the QCP and whether its carrier character flips from hole-like to electron-like near $x \\approx 0.52$; if no such surface Dirac cone is found, or the sign change does not follow the QCP, the transport-based assignment of the SC2 Dirac state would fail.","supporting_citations":[{"cited_title":"Pure nematic quan- tum critical point accompanied by a superconducting dome","cited_arxiv_id":null,"evidence_quote":"Supplies the pure nematic quantum critical point associated with the SC2 dome, which anchors the second superconducting dome in the phase diagram."},{"cited_title":"Hussey, Takao Watanabe, Koichi Kindo, and Takasada Shibauchi","cited_arxiv_id":null,"evidence_quote":"Provides the high-field shrinkage of SC1 and SC2 that the paper cites as evidence that the two domes are mediated by antiferromagnetic and nematic fluctuations, respectively."},{"cited_title":"ˇCulo, M","cited_arxiv_id":null,"evidence_quote":"Establishes the strange-metal Hall response in FeSe$_{1-x}$S$_x$ that links the bulk Dirac state to the strange metal on the SC1 side."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Identifies the electron-type bulk Dirac cone at the Brillouin-zone corner in FeSe, the reference state for SC1."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Identifies the topologically nontrivial surface Dirac states induced by spin-orbit coupling in FeSe$_{0.45}$Te$_{0.55}$, the reference state for SC2."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Origin of the concave Hall and high-mobility minority-carrier interpretation used to detect the bulk Dirac state in FeSe."},{"cited_title":"Multiband effects and possible dirac fermions in Fe1+yTe0.6Se0.4","cited_arxiv_id":null,"evidence_quote":"Provides the electron Dirac state and linear magnetoresistance signature in Fe$_{1+y}$Te$_{0.6}$Se$_{0.4}$ used for comparison on the Te-rich side."}],"review_version":1}