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REVIEW 4 major objections 6 minor 56 references

Superconducting density of states of PtPb4

T0 review · 4 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Millikelvin STM of PtPb4 finds a fully open BCS gap, while defect-rich surface patches stay superconducting up to 5 K and 1.5 T.

desk verdict Solid BCS-gap measurement with an intriguing but under-supported claim of defect-enhanced superconductivity above bulk Tc and Hc2. read the letter →

arxiv 2507.21013 v1 pith:KEL3XRS2 submitted 2025-07-28 cond-mat.supr-con cond-mat.mes-hallcond-mat.str-el

Pablo García Talavera , Jose Antonio Moreno , Edwin Herrera , Alexander I. Buzdin , Sergey L. Bud'ko , Paul C. Canfield , Isabel Guillamón , Hermann Suderow This is my paper · ORCID
classification cond-mat.supr-concond-mat.mes-hallcond-mat.str-el
keywords superconductivityscanningtunnelingmicroscopyPtPb4BCStheorysuperconductinggaptwinning-planestackingfaultstype-IIsuperconductor
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

This paper uses millikelvin scanning tunneling microscopy to measure the local superconducting density of states of the layered compound PtPb4. The authors find that over large areas the tunneling spectra open a full s-wave gap of 0.48 meV, close to the BCS value 1.76 kBTc = 0.49 meV for Tc ≈ 3 K, and that the gap closes with temperature approximately along the BCS curve. The central claim that goes beyond bulk physics is that on some surface regions the gap persists at temperatures up to 5 K and fields up to 1.5 T, well above the bulk Tc ≈ 2.8–3 K and Hc2 = 0.36 T. The authors attribute these regions to superconductivity locally enhanced by structural defects such as stacking faults and twinning planes, fitting the temperature dependence to a Ginzburg-Landau model of defect-localized superconductivity. If correct, PtPb4 is a conventional BCS superconductor whose defect-rich surface hosts patches with critical parameters several times higher than the bulk, suggesting a practical route to enhanced interface superconductivity in layered metals.

What carries the argument

The measurement machinery is STM conductance spectroscopy at 0.1 K in a dilution refrigerator. To extract the density of states from the spectra, the paper models the superconducting density of states as a sum over a Gaussian distribution of gaps, $N(E)\propto \sum_i \gamma_i(\Delta_i) \,\mathrm{Re}\left[E/\sqrt{E^2-\Delta_i^2}\right]$, then convolutes with the derivative of the Fermi function to fit the measured conductance; the fitted distribution stays centered at 0.48 meV for the bulk-like regions. For the enhanced regions, the load-bearing mechanism is the twinning-plane Ginzburg-Landau solution: above bulk Tc the local order parameter is $\varphi=\sqrt{2t}/\sinh(|d|t^{1/2}+p)$, with $t=(T-T_c)/(T_{cd}-T_c)$, $p=0.5\ln\left((1+t^{1/2})/(1-t^{1/2})\right)$, $d$ the distance to the defect in units of the coherence length, and $T_{cd}$ the defect critical temperature. The fit fixes $T_c=2.4$ K, $T_{cd}=5.8$ K, and $d=1.2$, showing that a defect buried a few tens of nanometers below the surface can leave observable gap-like tunneling signatures well above bulk Tc.

What would settle it

Fix the tip over one of the high-field superconducting patches at 0.1 K and sweep the field up and down while recording the zero-bias conductance and full spectra: genuine superconductivity requires the gap to close reversibly at a well-defined local Hc2, whereas an artifact would not follow a reversible, field-dependent closure; the paper reports no such same-location sweep.

Watch

Extended reading notes

Core claim

On its own terms, the paper establishes three things. First, the surface density of states at 0.1 K is fully gapped, with a Gaussian distribution of gap values centered at Δ0 = 0.48 meV and width 0.1 meV; the temperature evolution of the gap follows BCS theory with Tc ≈ 3 K, and the surface is spatially homogeneous in zero field. Second, at 1.5 T, far above bulk Hc2 = 0.36 T, the surface splits into a patchwork of normal and superconducting regions, and the superconducting patches coincide with topographic grains. Third, at zero field in a few locations, gap-like spectra survive up to 5 K, with a temperature dependence that deviates from BCS and is described by the Ginzburg-Landau solution for a superconducting order parameter enhanced at a twinning plane located about 1.2 coherence lengths from the surface. The paper concludes that defect networks created by nearly degenerate layer stackings locally raise Tc almost twofold and Hc2 almost fivefold.

Load-bearing premise

The entire enhanced-superconductivity claim rests on the assumption that the gap-like spectra seen above 3 K and 0.36 T are genuine superconductivity at those locations, rather than an STM artifact, an electronic resonance, or a normal-state pseudogap-like feature.

Editorial extensions

If this is right

  • PtPb4 provides a bulk BCS reference spectrum against which future surface and interface effects can be compared.
  • Defect engineering, rather than chemistry alone, becomes a lever for raising Tc and Hc2 in layered intermetallic compounds.
  • Local critical fields can vary by a factor of four across a single cleaved surface, so macroscopic measurements will mix regions with different intrinsic behavior.
  • Because the measured surface lacks atomically flat terraces, no surface states form, leaving the search for topological superconductivity in PtPb4 to samples with better-defined surfaces.

Reading between the lines

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

  • A targeted field sweep with the tip parked over a single enhanced region would decide the matter: the paper reports no measurement in which the gap closes and reopens at a well-defined local Hc2.
  • It would be informative to search for the same 5 K feature in non-superconducting PtSn4, which shares the layer stacking; if the feature survives there, it is likely a structural resonance rather than superconductivity.
  • If genuine, defect-enhanced superconductivity in PtPb4 should be reproducible in thin films or deliberately created stacking faults, which would be a testable materials-engineering route.
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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

4 major / 6 minor

Summary. The manuscript reports millikelvin scanning tunneling microscopy (STM) measurements of the superconducting density of states of PtPb4. At zero field, dI/dV spectra are fit by a Gaussian-distributed set of BCS gaps centered at 0.48 meV, and the temperature dependence of the extracted gap follows BCS down to a closing temperature Tc near 3 K. At 1.5 T, well above the reported bulk Hc2 = 0.36 T, some surface regions show gap-like conductance suppression, and at zero field some locations show gap-like signatures up to 5 K. The authors attribute these enhanced regions to superconductivity locally strengthened near structural defects such as stacking faults or twinning planes, and they support this interpretation with a Ginzburg-Landau twinning-plane model from Ref. [55]. The paper also includes powder XRD data relevant to polytype identification. The central tension is whether the above-bulk-Tc and above-bulk-Hc2 features are genuine local superconductivity or artifacts.

Significance. If the above-bulk results hold, PtPb4 would be a striking case of a conventional s-wave superconductor whose defect-rich surface hosts regions with substantially enhanced local Tc and Hc2, a result of clear interest for interface superconductivity and for the broader search for topological or enhanced superconductivity in PtSn4-related materials. The zero-field BCS-gap measurement is a solid and valuable result in itself, providing the first low-temperature local density-of-states characterization of this superconductor; the fully open gap, the BCS ratio, and the measured gap closure near 3 K are internally consistent and benchmarked against an external BCS prediction. The authors are also appropriately cautious about the absence of atomic resolution and about not excluding topological surface states. However, the enhanced-Tc and enhanced-Hc2 claim currently rests on a small number of selected spectra and on a multi-parameter model fit, so the significance of the paper is conditional on additional control measurements.

major comments (4)
  1. [§Results, Fig. 3] The claim of superconductivity above bulk Hc2 is load-bearing for the paper, but it is supported only by a small number of selected conductance curves at 1.5 T. No field sweep at a fixed topographic location is shown in which the gap closes and reopens at a well-defined local Hc2, and no normal-state dI/dV spectrum is presented at the same location after the feature is suppressed (for example at 2 T). Without such a control, the zero-bias suppression in the 'blue' regions of Fig. 3(a) could in principle be produced by topography-induced tip changes or by field-dependent normal-state features in this semimetal with strong magnetoresistance. Please add a field-cycle measurement at a representative hotspot and at a representative normal location, or state explicitly why such a measurement is not possible.
  2. [§Results, Fig. 4] The above-Tc claim rests on 'a few locations' at zero field, and only one set of temperature-dependent curves is shown. The manuscript does not provide statistics over multiple hotspots, does not state how many locations were measured and how many showed the effect, and does not show a reproducibility test such as cycling between 0.1 K and 5.65 K at the same location and returning to 0.1 K. The 5.65 K curve in Fig. 4(a) may be intended as a normal-state reference, but the text does not explicitly use it to exclude a temperature-dependent tip or electronic artifact. Please provide a clearer normal-state reference and quantitative reproducibility information.
  3. [§Discussion and Fig. 4(c)] The fit to the twinning-plane Ginzburg-Landau expression uses d, Tc, and Tcd as free parameters and is not accompanied by independent structural identification of a twinning plane or stacking fault beneath the hotspot. With three adjustable parameters, the dashed line in Fig. 4(c) demonstrates consistency with the model of Ref. [55], but it cannot by itself establish that defect-enhanced superconductivity is the mechanism. Please either constrain these parameters with independent data (for example a local Hc2 measurement or the coherence length at the hotspot) or explicitly present the fit as an illustrative consistency check rather than as a quantitative validation.
  4. [§Results, Figs. 3 and 4] The paper does not define an objective criterion for classifying a spectrum as 'superconducting' at 1.5 T or above Tc. This matters because the claim depends on which regions and curves are selected from the zero-bias maps. Please specify how the presence of a gap was determined for each spectrum (for example a fit threshold or a zero-bias conductance criterion) and report the total number of measured locations, the number classified as superconducting, and the spatial statistics across the maps.
minor comments (6)
  1. [Figure 4(c) caption] The caption states that the black line is the expected BCS tendency for Δ0 = 0.52 meV, but the text does not explain how this Δ0 value for the anomalous region was obtained; please add this information.
  2. [Experimental section] Please state the lock-in modulation voltage and the effective energy resolution of the STM measurements, since these are needed to assess whether the residual subgap density of states and the fitted gap width are resolution-limited.
  3. [Figure 2 caption] The caption refers to conductance curves taken 'along the red line in (a)', but the red line is not visible in the figure as presented; please ensure the line is clearly shown in the figure.
  4. [Appendix] The statement that the powder XRD data are 'also compatible with the Ccce space group' is useful, but please clarify the quantitative confidence in distinguishing P4/nbm from Ccce from this refinement, since the polytype distinction is invoked later in the Discussion.
  5. [References] Reference [23] appears incomplete: 'Superconducting properties of ptpb4 single crystals, 2021, 1 (2021)' needs the journal or thesis information and a proper page/article identifier.
  6. [Conclusions] The phrase 'A-priori preparation' should read 'A priori preparation'; please also check the use of 'A-priori' elsewhere in the manuscript.

Circularity Check

1 steps flagged · score 4.0 of 10

The BCS gap measurement is independent, but the defect-enhanced Tc conclusion reduces to a fitted parameter in a self-cited GL model.

  1. fitted input called prediction [Discussion, paragraph 'Interestingly, the temperature dependence...' and Fig. 4(c)]
    "From Ref. [55] we find that, above the bulk critical temperature Tc, the temperature dependence of the order parameter φ can be written as φ = √(2t)/sinh(|d|t^{1/2}+p), where t = (T−Tc)/(Tcd−Tc), p = 0.5ln((1+t^{1/2})/(1−t^{1/2})), Tcd the critical temperature close to the defect ... We find a good fit ... if we take d = 1.2, Tc = 2.4 K and Tcd = 5.8 K. This shows that the superconducting Tc can be considerably enhanced close to structural defects."

    Tcd is a free parameter in the fitted GL expression, and the fit sets Tcd = 5.8 K. The paper then presents Tcd > Tc as the conclusion that 'the superconducting Tc can be considerably enhanced close to structural defects.' This is a fitted input restated as a finding: the model already assumes an enhanced local Tc, and the data are not used to independently predict that enhancement. The model is imported from Ref. [55], coauthored by A.I. Buzdin, so the interpretive chain relies on a self-citation. The raw observation of gap-like features above bulk Tc/Hc2 remains an independent experimental fact, but the attribution to twinning-plane enhancement reduces to fitting rather than to an external prediction.

full rationale

The core BCS result is self-contained: the STM conductance curves are fitted with a Gaussian gap distribution and the resulting Δ0 = 0.48 meV is compared to the external BCS expectation Δ0 = 1.76kBTc = 0.49 meV. This is a benchmark against an external formula, not a circular derivation. Likewise, the observation of gap-like features at fields up to 1.5 T and temperatures up to 5 K is a direct experimental statement, though it lacks a normal-state reference at the same locations and is therefore experimentally underdetermined. The only step approaching circularity is the use of the twinning-plane GL model from Ref. [55] to convert the fitted Tcd into the claim that Tc is enhanced near defects. Because Tcd is a fitted parameter in a model that presupposes defect-enhanced superconductivity, and because Ref. [55] shares an author with the present paper, this interpretive step does not independently validate the enhancement. It is a partial circularity in the discussion, but it does not undermine the main BCS measurement, which is externally benchmarked.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central BCS-gap measurement is anchored to independent STM data and an external BCS benchmark, but the defect-enhanced superconductivity interpretation rests on a fitted GL model and on assumptions about how the local field and the local DOS model relate to the measured spectra. The adjustable parameters and the domain assumptions listed here are the things the reader pays for upstream of the central claim.

free parameters (4)
  • Gaussian gap distribution center Δ0 (surface DOS fit) = 0.48 meV
    Chosen as the center of a Gaussian distribution of gap values to reproduce the tunneling conductance at 0.1 K; also used as the zero-temperature BCS gap for comparison.
  • Gaussian gap distribution width σ1 = 0.1 meV
    Adjusted to reproduce the rounded quasiparticle peaks in the conductance spectra; no independent constraint is given.
  • Gap distribution width in anomalous high-Tc region = about 0.1 meV
    Used in the DOS model for Fig. 4(b) to fit conductance curves up to 5.65 K; obtained by fitting.
  • Twinning-plane model parameters (d, Tc, Tcd) = d=1.2, Tc=2.4 K, Tcd=5.8 K
    Three free parameters chosen to fit the gap versus temperature data in the anomalous region. There is no independent measurement of the distance to the defect or the local critical temperature.
assumptions (5)
  • domain assumption STM differential conductance dI/dV is proportional to the quasiparticle density of states convolved with the thermal derivative of the Fermi function.
    Standard STM model used to extract N(E) from measured spectra, invoked in Results when fitting the curves.
  • domain assumption The superconducting DOS is represented as a sum over Gaussian-distributed gaps: N(E) proportional to sum_i gamma_i(Delta_i) Re[E / sqrt(E^2 - Delta_i^2)].
    Assumed multigap or gap-distribution model borrowed from prior work (Refs. [16,33,38-42]); not derived for PtPb4.
  • ad hoc to paper The Ginzburg-Landau solution for twinning-plane superconductivity from Ref. [55] applies to the defect-enhanced regions in PtPb4.
    Used to fit the gap temperature dependence above bulk Tc; its applicability to PtPb4 stacking faults is assumed rather than independently tested.
  • domain assumption The coherence length xi = 32 nm, obtained from Hc2 = 0.36 T via Hc2 = Phi0 / (2 pi xi^2), is relevant for the surface region.
    Standard relation; assumes a single-band isotropic Hc2 and that the bulk value applies to the surface patches.
  • domain assumption The magnetic field at the STM junction is equal to the reported applied field, which is perpendicular to the surface, with no correction for misalignment or demagnetization.
    The comparison '1.5 T is above Hc2 = 0.36 T' assumes the local field matches the applied perpendicular field.

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Cite this review

Pith. "Pith review of Superconducting density of states of PtPb4." pith.science (2026). https://pith.science/paper/KEL3XRS2

@misc{pith2026250721013,
  author       = {Pith},
  title        = {Pith review of: Superconducting density of states of PtPb4},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KEL3XRS2}},
  note         = {Machine review of arXiv:2507.21013}
}
abstract

PtPb$_4$ is a type II superconductor with a bulk critical temperature $T_{c}\approx 3 $K and an upper critical field of $H_{c2}=0.36 $T. PtPb$_4$ is related to non-superconducting PtSn$_4$, which presents nodal arc states at the surface. Here we measure the superconducting density of states of PtPb$_4$ using millikelvin Scanning Tunneling Microscopy (STM). We observe a fully opened superconducting gap of $\Delta=0.48$\ meV similar to expectations from Bardeen Cooper and Schrieffer (BCS) theory ($\Delta_0=1.76k_BT_{c}=0.49 $meV). Measurements under magnetic fields applied perpendicular to the surface show a spatially inhomogeneous gap structure, presenting superconducting signatures at fields as high as 1.5 T, significantly above $H_{c2}=0.36 $T. On some locations we find that the superconducting density of states does not vanish above $T_{c}$. We can find signatures of a superconducting gap up to 5K. We discuss possible reasons for the observation of superconducting properties above $T_{c}$ and $H_{c2}$, emphasizing the role played by structural defects.

Figures

Figures reproduced from arXiv: 2507.21013 by the authors.

Figure 1
Figure 1. (a) We show as colored lines the tunneling conduc [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. (a) Conductance map at zero bias and 0 T, at a [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. (a) Tunneling conductance versus bias voltage [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figures from the paper (1 more)
Figure 5
Figure 5. Figure 5: X-ray diffraction pattern of PtPb4 powder is shown by black circles. The best pattern obtained with the P4/nbm structure by refinement is shown by a red solid line. The dif￾ference between the experimental and the refined diffraction pattern is shown by a blue line. Ma…

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