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REVIEW 5 major objections 6 minor 34 references

Two-gap superconductivity in the noncentrosymmetric La$_3$Se$_4$ compound

T0 review · 5 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read La3Se4 is a two-gap superconductor: a strong-coupling gap of about 2.05 meV and a weak-coupling gap of about 0.85 meV close together at Tc ≈ 8 K, with heat capacity and magnetometry supporting the same picture.

desk verdict First PCAR on La3Se4 makes a plausible but not airtight case for two-gap superconductivity; worth sending to referees. read the letter →

arxiv 2411.16399 v1 pith:RLYMIWCL submitted 2024-11-25 cond-mat.supr-con

F. Košuth , N. Potomová , Z. Pribulová , J. Kačmarčík , M. Naskar , D.S. Inosov , S. Ash , A.K. Ganguli
show 4 more authors
J. Šoltýs V. Cambel P. Szabó P. Samuely
This is my paper · ORCID
classification cond-mat.supr-con
keywords two-gapsuperconductivitynoncentrosymmetricsuperconductorLa3Se4point-contactAndreevreflectionBlonder-Tinkham-KlapwijkmodelheatcapacityHall-probemagnetometrypenetrationfield
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

La3Se4, a noncentrosymmetric superconductor with Tc ≈ 8 K, is claimed to be a two-gap superconductor. Point-contact Andreev reflection spectra show a large gap of about 2.05 meV and a small gap of about 0.85 meV; in most junctions the small gap is invisible at low temperature and only emerges as a central peak when the spectrum is warmed or a magnetic field is applied. Both gaps follow BCS-like temperature curves and close at the same Tc, which the paper takes as evidence of strong interband coupling. The same two-gap parameters reproduce the heat capacity via the two-gap alpha model and the Hall-probe penetration field, so the finding is presented as a bulk property, not a surface effect.

What carries the argument

The analysis rides on point-contact Andreev reflection (PCAR) spectroscopy interpreted with the Blonder–Tinkham–Klapwijk (BTK) model. The conductance spectrum is written as a weighted sum of two BTK contributions, σ_tot = ασ1 + (1−α)σ2, each with its own gap Δi, spectral smearing Γi, and barrier strength Zi. The key trick is that the two gaps respond differently to temperature and magnetic field: warming toward Tc or applying a field shrinks the large-gap features and exposes the previously hidden small gap as a zero-bias maximum. Bulk support comes from ac heat capacity fitted with the phenomenological two-gap alpha model and from Hall-probe measurements of the penetration field Bp(T), whose superfluid-density curve is a weighted sum of two gap contributions with the same parameters.

What would settle it

Perform phase-purity analysis (x-ray diffraction, electron microscopy) and measure heat capacity and PCAR on single crystals: if the small-gap feature or the 2.4 K heat-capacity anomaly vanishes or splits into a separate transition, the two-gap interpretation fails. Alternatively, track the zero-bias feature in magnetic field: a small superconducting gap should be suppressed and vanish at Bc2, whereas an Andreev bound state would persist or grow with field.

Watch

Extended reading notes

Core claim

The paper's central claim is that the noncentrosymmetric compound La3Se4 is a two-gap superconductor with a large gap Δ1 ≈ 2.05 ± 0.15 meV (2Δ1/kBTc ≈ 5.8, strong coupling) and a small gap Δ2 ≈ 0.85 ± 0.15 meV (2Δ2/kBTc ≈ 2.3), both closing at the same Tc = 8.1 ± 0.3 K. In direct spectra where both gaps are visible, the large gap carries 85–90% of the spectral weight. On the majority of junctions, only the large gap is apparent at low temperature, but the small-gap feature appears as a central maximum when the temperature approaches Tc or when a magnetic field selectively suppresses the large-gap contribution. Both gaps follow BCS-like Δ(T) curves, and the same two-gap parameters (2Δ1/kBTc = 5.75, 2Δ2/kBTc = 2, α = 0.9) describe the heat capacity and the temperature dependence of the penetration field, leading the authors to conclude that two-gap superconductivity is an intrinsic bulk property.

Load-bearing premise

The argument assumes the polycrystalline La3Se4 pieces are a single bulk superconducting phase, so the small gap is an intrinsic second band gap rather than a signature of a secondary phase, grain-boundary magnetism, or an interfacial Andreev bound state.

Editorial extensions

If this is right

  • The ground state of La3Se4 must be described by at least two superconducting bands with strong interband coupling; single-band or nodal single-gap models cannot account for the spectra.
  • The absence of positive curvature in the temperature dependence of the upper critical field near Tc does not rule out two-gap superconductivity, because strong interband coupling can flatten the curvature into the linear shape observed.
  • The 2.4 K heat-capacity anomaly is not a superconducting transition of the bulk sample; its field insensitivity and the saturation of the penetration field at low temperature place its origin in grain-boundary magnetism or a minority phase.
  • The same two-gap parameters from point-contact spectroscopy quantitatively reproduce both heat capacity and penetration depth, meaning the gap structure is a bulk thermodynamic property and not restricted to the contact region.

Reading between the lines

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

  • If single crystals or thoroughly phase-characterized polycrystals were measured, the same PCAR protocol should reveal the small gap directly at low temperature with roughly 10–15% weight; if the feature appears only in polycrystalline samples, a grain-boundary or secondary-phase origin becomes more likely.
  • The paper dismisses the zero-bias conductance peak (ZBCP) alternative largely on the 65 meV spin-orbit splitting scale; a directional measurement on an oriented sample could separate an intrinsic second gap from an interfacial Andreev bound state.
  • A testable extension is to tune the antisymmetric spin-orbit coupling via pressure or chemical substitution: if the two-gap structure changes discontinuously with the splitting, the second gap is tied to the spin-split bands, whereas smooth evolution would suggest a more conventional multiband origin.
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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

5 major / 6 minor

Summary. The manuscript reports point-contact Andreev reflection (PCAR) spectroscopy, heat capacity, and Hall-probe magnetometry on the noncentrosymmetric superconductor La3Se4 with Tc ≈ 8 K. Most PCAR spectra show a single gap near 2 meV, while a subset of contacts reveals a second smaller gap near 0.85 meV. The authors fit the temperature and magnetic field evolution with a two-gap BTK model, obtaining 2Δ1/kBTc ≈ 5.8 and 2Δ2/kBTc ≈ 2.3, and they argue that both gaps close at the same Tc. Bulk measurements are presented as consistent with two-gap superconductivity: an alpha-model fit to the heat capacity and a theoretical curve for the penetration field Bp(T).

Significance. If the two-gap interpretation is correct, La3Se4 would join a small group of noncentrosymmetric superconductors with multigap, largely s-wave-like order, and the inferred strong interband coupling would be of interest. The paper's strengths are its multi-probe approach, the direct observation of two-gap structure in a subset of PCAR spectra, and the explicit discussion of alternative ZBCP and secondary-phase explanations. However, the thermodynamic and magnetometry evidence is currently too permissive to independently establish the two-gap scenario, and the temperature dependence of the small gap is strongly constrained by the fitting procedure.

major comments (5)
  1. [Sec. 3, Fig. 2 and inset] The temperature dependence of the small gap Δ2 is not independently measured. The authors start the two-gap fit at T = 5.5 K, where the two gaps are resolved, and then allow Z, Γ, and α to vary by only about 10% at all other temperatures. The resulting Δ2(T) curve that closes near 8 K is therefore largely imposed by the constrained fitting, not by the data. The text itself notes that the lowest-temperature spectra show no apparent two-gap structure. Please fit the full temperature series with a single-gap BTK model and with a two-gap model where all parameters are free at each temperature, and report the goodness-of-fit comparison. This is necessary to support the claim that both gaps close at the same Tc.
  2. [Sec. 3, Fig. 5] The alpha-model fit to the heat capacity does not independently require a second gap. The stated parameter range is α = 0.8–1.0, so α = 1 (zero weight for the small gap) is within the uncertainty. The red curve shown uses α = 0.9, but a single-gap fit with the same large-gap ratio may describe the data nearly as well. Please show the single-gap alpha-model fit and provide confidence intervals for the weight α, so the reader can judge whether the heat capacity actually discriminates between one-gap and two-gap forms.
  3. [Sec. 3, Fig. 6] The Hall-probe Bp(T) comparison is not an independent confirmation of two-gap superconductivity. The red dashed curve is computed with the same parameters obtained from the heat capacity fit and is rescaled vertically to match the data; this is a shape check, not a parameter-free prediction. To make this evidence meaningful, please also show the best single-gap model curve for Bp(T) with its own vertical rescaling, and quantify the difference in quality of the two descriptions.
  4. [Sec. 3, Figs. 2 and 3; Sec. 4] The dismissal of the zero-bias conductance peak (ZBCP) alternative rests mainly on the 65 meV antisymmetric spin-orbit splitting energy. That energy scale does not by itself rule out an unconventional or surface origin for the central feature, and the argument is qualitative. Since the central maximum is the key observable used to infer Δ2, please provide a more quantitative test, for example fitting the 5.5–6.5 K spectra with a single-gap BTK model plus an additive central peak (e.g., a Gaussian or a Δ = 0 component) and comparing the resulting chi-squared with the two-gap fit.
  5. [Sec. 3 and Suppl. Fig. S1] The field-dependent heat capacity and Hall-probe measurements rule out a secondary superconducting phase with Tc ≈ 2.4 K, but they do not exclude a secondary phase with a local Tc in the 4–7 K range, which could produce a small-gap-like feature in PCAR. Given that the sample is polycrystalline and the small-gap weight is only about 10–15%, this is a concrete alternative that should be addressed, for instance by reporting measurements on several independently synthesized batches or by a microstructural study (e.g., EDX or XRD on the actual measured surface).
minor comments (6)
  1. [Abstract and Conclusions] There is a typo in the Conclusions: 'nocentrosymmetric' should be 'noncentrosymmetric'.
  2. [Sec. 3] In the sentence beginning 'In the following we focus on a possibilty', 'possibilty' should be 'possibility'.
  3. [Fig. 1 caption] The caption says 'Curve 2 and 3 are fitted' but should read 'Curves 2 and 3 are fitted'.
  4. [Sec. 4] In the Discussion, the text refers to 'the two-gap alpha model with 2Δ1/kBTc = 5.75, 2Δ2/kBTc = 2, and α = 0.9 (Fig. 4)', but the heat capacity data are shown in Fig. 5, not Fig. 4.
  5. [References] Reference [10] contains a typo: 'Finate-quasiparticle-lifetime' should be 'Finite-quasiparticle-lifetime'. Also, the author list of Reference [30] appears jumbled; it should likely read 'J. M. Edge and A. V. Balatsky'.
  6. [Supplemental Material] In the caption of Fig. S3, 'used in Fig.5 of the article' should refer to Fig. 6, since the penetration field data appear in Fig. 6 of the main text.

Circularity Check

2 steps flagged · score 4.0 of 10

The two-gap claim retains independent PCAR content, but the bulk corroboration and the common-Tc closure partly reuse the same fitted two-gap model, with fitted parameters presented as supporting evidence.

  1. fitted input called prediction [Section 3, Hall-probe paragraph (Fig. 6)]
    "a theoretical curve (red dashed line in Fig. 6) involving two energy gaps, with the same parameters as those obtained from the heat capacity measurements, follows our data in a very good agreement proving the two gap superconductivity in the system."

    The Hall-probe curve is computed from the same two-gap alpha model using parameters already obtained from the heat-capacity fit (2Δ1/kBTc = 5.75, α = 0.9; 2Δ2/kBTc = 2, 1−α = 0.1) and is then vertically rescaled to match the data. The agreement is therefore a consistency re-plot of the fitted hypothesis, not an independent prediction. Moreover, the heat-capacity fit itself returned α = 0.8–1, so zero weight for the small gap is within the stated error bars. Presenting this agreement as 'proving the two gap superconductivity' elevates a parameter-reuse consistency check to an independent confirmation.

  2. fitted input called prediction [Section 3, Fig. 2 temperature-dependence paragraph]
    "Since the spectra at the lowest temperatures do not show any apparent two-gap structure, we started the fit at T = 5.5 K, where the two gaps are resolved. ... We used these Z, Γ and α parameters as the initial-fit values at all temperatures from T = 2.2 K to 8 K allowing for corrections of about 10%."

    The reported Δ2(T), shown as open symbols in the inset and claimed to close at the same Tc near 8 K, is obtained by carrying the Z2, Γ2, α values from the single 5.5 K two-gap fit into all other temperatures with only ±10% freedom. At 2.2–5 K the spectra show no resolved second-gap structure, so the small-gap component there is not independently measured; it is inherited from the anchored 5.5 K fit. The common-Tc closure is thus partly imposed by the fitting constraints rather than derived from separately resolved small-gap maxima at every temperature.

full rationale

The paper does not rest on a self-citation chain or an imported uniqueness theorem; the self-citations to earlier work on the same compound and on MgB2 are methodological and not load-bearing in a circular sense. The primary PCAR evidence does have independent content: curves 2 and 3 in Fig. 1 and the field-evolution spectra in Fig. 3 show additional structure beyond a single-gap BTK line shape, and those are genuine observations. However, the bulk 'proof' is partially circular. The heat-capacity alpha-model fit allows α = 0.8–1, meaning a single-gap scenario is within uncertainty, yet the displayed curve uses α = 0.9. The Hall-probe comparison then reuses those same fitted two-gap parameters and rescales the vertical axis, so its agreement is a shape check of the two-gap hypothesis rather than an independent test. Similarly, the temperature dependence of the small gap is extracted by anchoring all line-shape parameters to one 5.5 K fit and constraining them to ±10% at other temperatures, so the conclusion that both gaps close at the same 8 K is partly inherited from the fit strategy. These are fitted inputs presented as corroboration, but the central two-gap claim does not reduce entirely to them because some spectra directly show two-gap features. Overall circularity is moderate: score 4.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The central claim rests on standard phenomenological models (BTK, alpha model, superfluid-density relation) and on the assumption that the polycrystalline sample is a single bulk superconducting phase. No new entities are postulated.

free parameters (6)
  • PCAR large gap Δ1 = 2.05 ± 0.15 meV (average; per-spectrum values 1.9-2.2 meV)
    Fitted from single- and two-gap BTK model to PCAR spectra; central to the two-gap claim.
  • PCAR small gap Δ2 = 0.85 ± 0.15 meV (average)
    Fitted from two-gap BTK model to selected spectra and to temperature/field evolution; central to the two-gap claim.
  • PCAR spectral weight α (large gap) = 0.85-0.9
    Free weight in weighted-sum two-gap BTK fit; determined per spectrum and used consistently in heat capacity and Hall-probe models.
  • BTK smearing Γ1, Γ2 and barrier Z1, Z2 = e.g., Γ1=1.15±0.1 meV, Z1=0.7±0.1, Γ2=0.15±0.05 meV, Z2=0.1±0.05 in Fig. 2
    Phenomenological fit parameters in BTK model; chosen per spectrum and largely fixed in the temperature run, which constrains the gap extraction.
  • Heat capacity alpha-model ratios and weight = 2Δ1/kBTc=5.75±0.25, 2Δ2/kBTc=2±0.5, α=0.8-1
    Fitted to a broad heat capacity anomaly; the wide ranges reflect the ambiguity of the two-gap description of the bulk data.
  • Hall-probe penetration-field curve vertical scale = not given (rescaled to match data)
    The theoretical two-gap superfluid-density curve is vertically rescaled to the Bp(T) data; only the shape is compared, so the vertical scale is a free parameter.
assumptions (5)
  • domain assumption BTK model describes N-S point-contact conductance in this polycrystalline junction.
    Used throughout Section 3 to fit PCAR spectra; standard in PCAR literature, but polycrystalline contacts with unknown current direction may deviate from the ideal ballistic model.
  • domain assumption The total PCAR conductance is the weighted sum of two independent BTK conductances (σ_tot = ασ1 + (1-α)σ2).
    Equation in Section 2; assumes two independent bands with no interband coherence effects on transport.
  • domain assumption The low-temperature heat capacity anomaly at 2.4 K has non-superconducting origin.
    Section 3: inferred from field independence and from absence of a kink in Bp(T); if false, the superconducting heat capacity fit could be distorted.
  • domain assumption Normal-state heat capacity can be extrapolated as aT + bT^3 + cT^5 from above Tc down to low temperatures.
    Section 3: used to subtract normal state and extract the superconducting contribution; the broad transition may make this extrapolation uncertain.
  • domain assumption The penetration field Bp is proportional to Bc1 and the superfluid density for the bulk sample.
    Section 3 and Suppl. Fig. S2-S3: used to connect Hall-probe data to the gap model; the geometrical factor and demagnetizing effects are not fully quantified.

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Pith. "Pith review of Two-gap superconductivity in the noncentrosymmetric La$_3$Se$_4$ compound." pith.science (2026). https://pith.science/paper/RLYMIWCL

@misc{pith2026241116399,
  author       = {Pith},
  title        = {Pith review of: Two-gap superconductivity in the noncentrosymmetric La$_3$Se$_4$ compound},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RLYMIWCL}},
  note         = {Machine review of arXiv:2411.16399}
}
abstract

Point-contact Andreev reflection spectroscopy at low temperatures and high magnetic fields has been performed on a noncentrosymmetric La$_3$Se$_4$ superconductor with a critical temperature $T_c$ = 8 K. Two superconducting energy gaps $\Delta_1$ and $\Delta_2$ with $2\Delta_{1}/k_{B} T_{c}$ ~ 5.8 and $2\Delta_{2}/k_{B} T_{c}$ ~ 2.3, are directly observed in some of the spectra. The temperature and magnetic field effects help to resolve a two-gap structure even on the most frequent spectra where at low temperatures only a single gap is apparent, reflected in a pair of maxima around the zero bias. Two-gap superconductivity consistently with the point contact Andreev reflection spectroscopy is also supported by the heat capacity and the Hall probe magnetization measurements.

Figures

Figures reproduced from arXiv: 2411.16399 by the authors.

Figure 1
Figure 1. In some cases, usually on spectra with higher contact￾barrier strength, we observed an additional maximum at zero bias ( [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗

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Reviewed August 12, 2026 · model on record in the stance chip above.