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REVIEW 3 major objections 5 minor 72 references

Bulk and surface Dirac states accompanied by two superconducting domes in FeSe-based superconductors

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Pith's one-line read 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…

desk verdict 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. read the letter →

arxiv 2412.16171 v1 pith:PYBPOEVV submitted 2024-12-06 cond-mat.supr-con cond-mat.str-el

Qiang Hou , Wei Wei , Xin Zhou , Wenhui Liu , Ke Wang , Xiangzhuo Xing , Yufeng Zhang , Nan Zhou
show 3 more authors
Yongqiang Pan Yue Sun Zhixiang Shi
This is my paper · ORCID
classification cond-mat.supr-concond-mat.str-el
keywords FeSe1-xTextwosuperconductingdomesbulkDiracstatetopologicalsurfacestrangemetalnematicquantumcriticalpointHallresistivitythree-bandmodel
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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.

What would settle it

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.

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Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • 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.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

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.

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 (3)
  1. [Supplemental Material, 'Three band model', Constraint 3] 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.
  2. [Supplemental Material, 'Three band model', Constraint 1 and Table I] 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.
  3. [Main text, 'Another interesting phenomenon...' (discussion of sign change near the nematic QCP)] 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.
minor comments (5)
  1. [Figure 4 caption] The caption contains typographical errors: 'magniffed' should be 'magnified' and 'deffined' should be 'defined'.
  2. [Main text, 'See Fig. S7 and Table S1 [59]'] 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.
  3. [Main text, 'Magnetotransport properties of FeSe1−xSx suggests'] Subject–verb agreement: 'properties ... suggests' should be 'properties ... suggest'.
  4. [Supplemental Material, 'Two band model'] 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.
  5. [Figure 3 and related text] 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.

Circularity Check

1 steps flagged · score 6.0 of 10

The claimed hole-to-electron sign change of the topological surface Dirac state near the nematic QCP is imposed by the three-band model's curvature rule rather than independently determined; the two-dome phase diagram and resistivity exponents remain independent evidence.

  1. fitted input called prediction [Supplemental Information, 'THREE BAND MODEL', constraint 3; main text Fig. 4(f)]
    "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. ... Fig. 4(f) clearly shows the sign change behavior of the Dirac carriers with doping."

    The three-band fit extracts a small high-mobility carrier whose sign is not free: constraint 3 fixes the band-sign assignment from the curvature of ρxy(H). Because constraints 1 and 2 pin the main hole and electron bands to near-equal concentrations, the minority 'Dirac' band must be hole-like when the Hall curve is convex and electron-like when it is concave. The paper's central transport finding—the topological surface Dirac state changes from hole to electron near x(Te)≈0.52—is therefore a direct restatement of the observed convex-to-concave transition under the imposed rule, not an independent inference. No uniqueness tests, error bars, or fits with the opposite sign assignment are reported, so the sign-change 'prediction' reduces by construction to the model input.

full rationale

The paper's empirical core—the two superconducting domes, the power-law resistivity exponents (n∼1 on SC1, n<1 on SC2), and the nonlinear Hall and magnetoresistance data—is new and largely self-contained. The identification of the SC1 bulk Dirac state and the SC2 topological surface Dirac state is anchored in external ARPES literature (refs. 27, 29, 31, 41–43) and does not by itself constitute circularity. The circular step is narrower: the reported sign change of the surface Dirac carrier near the nematic QCP is not an independent result of the three-band fits. Constraint 3 in the Supplemental Information prescribes that concavity means two electron bands plus one hole band and convexity means one electron band plus two hole bands; with the compensation constraint, this forces the small high-mobility band's sign from the Hall-curvature shape. Thus the 'hole-to-electron' Dirac evolution is an encoding of the curvature change, not a separately measured quantity. Because this sign change is one of the two advertised normal-state/Dirac-state distinctions supporting distinct pairing mechanisms, the circularity is partial rather than total; the phase diagram and resistivity exponents still carry independent weight.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The paper's central interpretive layer rests on fitted parameters: the resistivity exponent, the residual resistivity, and especially the small high-mobility carrier from the three-band model. The mapping of that carrier to known Dirac states is anchored in prior ARPES results, which keeps the work from being fully circular, but the claimed Dirac-state evolution is not an independent measurement.

free parameters (3)
  • Power-law resistivity exponent n = n ~ 1 on SC1; n < 1 on SC2
    Extracted from d ln(rho - rho0)/d ln T; both n and rho0 are fit outputs, so the claimed contrast in normal states is a fit-derived quantity rather than a direct observable.
  • Residual resistivity rho0 = Not tabulated per sample
    Used to compute the exponent n; the choice of rho0 influences whether n ~ 1 or n < 1 is reported.
  • Small high-mobility carrier concentration n2 and mobility mu2 (Dirac carrier) = Table I: n2 from 8.06 x 10^18 to 0.04 x 10^18 cm^-3, mu2 ~ 1000-2300 cm^2/Vs at 20 K
    These are the outputs of the constrained three-band fits. The sign of mu2 defines whether the Dirac state is hole-like or electron-like, so the claimed sign change near the nematic QCP is a property of the fitted parameter.
assumptions (5)
  • domain assumption Hole and electron carrier densities are equal at all dopings and temperatures (compensation).
    Used as constraint 1 in the three-band fitting (Supplement). If compensation is not exact, the fitted concentrations and the extracted Dirac band parameters are not unique.
  • domain assumption The carrier concentration of FeSe (~10^20 cm^-3) is a valid initial scale for the entire doping series.
    Constraint 2 in the Supplement; assumes Te substitution is equivalent doping and biases the fit toward FeSe-like concentrations.
  • ad hoc to paper Concave Hall resistivity implies two electron bands and one hole band; convex implies one electron band and two hole bands.
    Constraint 3 in the Supplement; this shape-to-band assignment determines whether the extracted small carrier is hole- or electron-like and is not derived from theory.
  • domain assumption The small high-mobility carrier fitted by the three-band model represents a Dirac state.
    Transport data alone show a small mobile band; identifying it as a bulk or surface Dirac state relies on prior ARPES experiments (refs 27, 29) and is not independently established by the measurements in this paper.
  • ad hoc to paper T* defined by visual onset of nonlinear Hall resistivity is a faithful proxy for the Dirac state appearance temperature.
    The selection is visual (Fig. S4) and the authors state its variation has minimal impact, but no quantitative criterion is given.

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Pith. "Pith review of Bulk and surface Dirac states accompanied by two superconducting domes in FeSe-based superconductors." pith.science (2026). https://pith.science/paper/PYBPOEVV

@misc{pith2026241216171,
  author       = {Pith},
  title        = {Pith review of: Bulk and surface Dirac states accompanied by two superconducting domes in FeSe-based superconductors},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PYBPOEVV}},
  note         = {Machine review of arXiv:2412.16171}
}
abstract

Recent investigations of FeSe-based superconductors have revealed the presence of two superconducting domes, and suggest possible distinct pairing mechanisms. Two superconducting domes are commonly found in unconventional superconductors and exhibit unique normal states and electronic structures. In this study, we conducted electromagnetic transport measurements to establish a complete phase diagram, successfully observing the two superconducting domes in FeSe$_{1-x}$S$_x$ (0 $\le x \le$ 0.25) and FeSe$_{1-x}$Te$_x$ (0 $\le x \le$ 1) superconductors. The normal state resistivity on SC1 shows the strange metal state, with a power exponent approximately equal to 1 ($\rho (T)\propto T^n$ with $n\sim 1$), whereas the exponent on SC2 is less than 1. A bulk Dirac state observed on SC1, completely synchronized with the strange metal behavior, indicating a close relationship between them. While a topological surface Dirac state is witnessed on SC2, and undergoes a sign change near the pure nematic quantum critical point. The evolution of the Dirac states indicates that the appearance of the two superconducting domes may originate from the Fermi surface reconstruction. Our findings highlight distinct Dirac states and normal state resistivity across the two superconducting domes, providing convincing evidence for the existence of the two different pairing mechanisms in FeSe-based superconductors.

Figures

Figures reproduced from arXiv: 2412.16171 by the authors.

Figure 1
Figure 1. FIG. 1. Evolution phase diagram of the Dirac states, superconductivity, magnetic order and crystal structure with S and Te [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Magnetic field dependence of Hall resistivity [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Magnetic field dependence of MR (Upper panel of (a-l)) and the first-order derivative of MR to [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. The cloud diagrams of the main carrier concentrations with (a) hole, (b) electron type, and (c) Dirac carrier concentra [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

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