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Sizable superconducting gap and anisotropic chiral topological superconductivity in the Weyl semimetal PtBi$_2$

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Scanning tunneling spectroscopy reveals a 10–16 meV superconducting gap and topological in-gap states on PtBi2.

desk verdict Careful STS data with real potential, but the superconducting and chiral-topological conclusions need control measurements this paper does not provide. read the letter →

arxiv 2507.13843 v1 pith:SFRCWG5T submitted 2025-07-18 cond-mat.supr-con cond-mat.mtrl-sci

Xiaochun Huang , Lingxiao Zhao , Sebastian Schimmel , Julia Besproswanny , Patrick Härtl , Christian Hess , Bernd Büchner , Matthias Bode This is my paper · ORCID
classification cond-mat.supr-concond-mat.mtrl-sci
keywords topologicalsuperconductorWeylsemimetalPtBi2scanningtunnelingspectroscopyAndreevboundstateschiralpairingsymmetrysuperconductinggapMajoranazeromodes
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 reports scanning tunneling microscopy and spectroscopy on the decorated honeycomb surface of the Weyl semimetal PtBi2, finding a superconducting gap of 10–16 meV that stays uniform from macroscopic down to atomic length scales. Within this gap the authors observe low-energy in-gap states, which they interpret as Andreev bound states that are spatially extended across the surface rather than pinned to defects. Spectral simulations that combine a Dynes-broadened density of states, surface Andreev bound-state conductance, and an empirical term reproduce the measured spectra as a function of tip–sample distance, using an anisotropic chiral order parameter Δ(k)=Δ0 cos(θ)$e^{{iθ}}$. The authors conclude that PtBi2 realizes intrinsic topological superconductivity with a sizable, accessible gap, making it a platform for studying Majorana modes.

What carries the argument

The central object is the tunneling-current model Itot = IT(1−$e^{{−α}}$) + $e^{{−α}}$(IABS $e^{{−β}}$ + IΓ(1−$e^{{−β}}$)), with IT a Dynes-broadened quasiparticle term, IABS an angle-resolved Andreev bound-state current built from the Kashiwaya transmissivity, and IΓ an empirical inverse-resistance term. A single effective parameter d encodes tip–sample distance and controls the relative weights of these components through α, β, and the barrier strength Z. The order parameter entering the model is anisotropic chiral, Δ = Δ0 cos(θ)$e^{{iθ}}$, whose angular dependence and ±π phase change reproduce the V-shaped gap and the hump-shaped in-gap bound states seen in experiment. The model's ability to match the setpoint-dependent spectral evolution is what argues for chiral topology.

What would settle it

A temperature-dependent tunneling study on the same surface that finds the ~10 meV coherence peaks and in-gap states unchanged while warming through the reported ~10 K surface superconducting transition—or a few-tesla magnetic field that fails to suppress them—would show the gap is not superconducting, falsifying the chiral topological conclusion.

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Extended reading notes

Core claim

On the decorated honeycomb termination of trigonal PtBi2, the authors establish a spatially homogeneous superconducting gap with coherence peaks at 10, 12, and 16 meV in four tunneling configurations, varying by less than 1 meV across hundreds of nanometers and remaining uniform at sub-lattice spacing. By reducing the tip–sample distance they reveal previously unobserved in-gap states that grow with setpoint current in a reversible way and appear across the whole surface, which they identify as Andreev bound states. A theoretical model of the tunneling current—combining a Dynes-broadened density of states, an angle-resolved Andreev bound-state current with phase information, and an empirical conductance term—reproduces the full spectral evolution with a single effective distance parameter, requiring an anisotropic chiral pairing Δ(k)=Δ0 cos(θ)$e^{{iθ}}$. The authors take this as evidence that the bound states originate from a Majorana cone on the surface and that PtBi2 is an intrinsic chiral topological superconductor.

Load-bearing premise

The coherence peaks and in-gap bound states are assumed to be superconducting signatures intrinsic to the PtBi2 surface, even though all spectra were taken at a single temperature of 5.1 K without field or temperature sweeps to verify a superconducting transition.

Editorial extensions

If this is right

  • If PtBi2 is an intrinsic chiral topological superconductor, its ~10 meV surface gap places topological surface Andreev bound states at energies accessible to conventional cryogenic experiments, well above the millikelvin regime needed for many engineered Majorana platforms.
  • The spatial uniformity of the gap and the surface-extended nature of the bound states imply that disorder and structural defects do not destroy the topological surface phase, making the material usable for planar devices.
  • The anisotropic chiral order parameter Δ(k)=Δ0 cos(θ)e^{iθ} predicts a specific spectroscopic fingerprint—V-shaped gap at larger tip distance and hump-shaped in-gap states at closer approach—that can guide searches for similar physics in other Weyl semimetals.
  • The coexistence of a large pairing gap with spin-textured Fermi arcs supports the use of PtBi2 as a test bed for Majorana zero modes and non-Abelian braiding proposals.

Reading between the lines

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

  • A natural next experiment is to drive the same surface through the superconducting transition with temperature and magnetic field; if the coherence peaks and bound states survive above the surface transition or resist fields well above the bulk critical field, the interpretation as superconductivity would need revision.
  • The same tunneling-current decomposition could serve as a spectroscopic fingerprint to distinguish chiral from other nodal pairing symmetries in candidate materials, since the phase-resolved term is what produces the characteristic hump.
  • If the chiral pairing is confirmed, it would imply that the surface superconductivity of PtBi2 belongs to a class of topological phases where the Majorana cone is a bulk-boundary consequence, suggesting that other Weyl semimetals with Fermi-arc surface states and phonon-mediated pairing may also naturally host topological superconductivity.
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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 / 5 minor

Summary. The manuscript reports low-temperature STM/STS measurements on the decorated honeycomb surface of trigonal PtBi2, claiming a spatially uniform surface superconducting gap of 10–16 meV at 5.1 K and the observation of surface-extended in-gap states interpreted as Andreev bound states (ABSs). A phenomenological tunneling model combining a Dynes density of states, an ABS transmission function, and an empirical conductance term is used to simulate the spectra; with an assumed order parameter Δ = Δ0 cos(θ)e^{iθ}, the authors conclude that PtBi2 hosts anisotropic chiral topological superconductivity and that the observed ABSs have topological origin.

Significance. If fully established, a ~10 meV uniform surface superconducting gap in an intrinsic Weyl semimetal at accessible temperatures, together with topological ABSs, would be a significant advance for Majorana physics. The manuscript has real strengths: the gap-like feature is reproducible with multiple tips, spatially homogeneous from hundreds of nanometers down to sub-lattice scales, and the authors have made a serious attempt to build a hierarchical model rather than presenting a single ad hoc fit. However, the significance is conditional on two unproven steps: the superconducting origin of the 10–16 meV gap and the chiral phase structure of the order parameter. Both steps are load-bearing for the central claim, and the current evidence does not exclude non-superconducting or non-chiral alternatives.

major comments (4)
  1. [Section II and Methods] The assignment of the 10–16 meV gap to intrinsic surface superconductivity lacks direct evidence: all spectra were acquired at T = 5.1 K, and the paper reports no temperature sweep through the reported ~10 K surface transition and no magnetic-field dependence. The Introduction itself cites refs. [32,33] as 'fundamentally questioned the existence of surface superconductivity in PtBi2,' but the manuscript never returns to those null results. A normal-state control or field-dependent gap closing is necessary before the superconducting assignment can support the topological conclusions.
  2. [Section VI, Eq. (3) and Eq. (5)] The chiral order parameter Δ = Δ0 cos(θ)e^{iθ} is an input, not an output, of the model. The Dynes density of states in Eq. (3) depends only on |Δ|, so the chiral phase enters the simulated spectra exclusively through the assumed ABS transmission function in Eq. (5) and the empirical IΓ term. The agreement in Fig. 4 therefore demonstrates consistency with the chosen model, not that the gap is superconducting or that the order parameter is chiral. The manuscript should provide a quantitative comparison with phase-less anisotropic models and other non-chiral alternatives, for example by fitting the same spectra with the phase-less version shown in Extended Data Fig. E6e,f.
  3. [Section X, Eqs. (1)–(8)] The model contains at least eight free parameters (Δ0, γ, Z, α, β, δ, the IΓ amplitude, and D plus const in Eq. (8)), yet no parameter values, no goodness-of-fit measures, and no statistical model comparison are reported. Without these, the statement in Section VI that the close agreement provides 'strong evidence for an anisotropic chiral pairing symmetry' is disproportionate to what the fitting procedure actually demonstrates.
  4. [Sections IV and V] The in-gap states appear only when the tip–sample distance is reduced via higher setpoint current. Reversibility rules out some permanent tip changes, but a reversible tip-induced electronic or mechanical effect is not excluded. The interpretation of these states as Andreev bound states, and especially as topological ABSs, would require additional evidence such as their evolution with magnetic field or temperature or a direct relation to the surface-band dispersion, rather than only their spatial extension across the surface.
minor comments (5)
  1. [Section VI] The phrase 'paring symmetry' should be 'pairing symmetry'.
  2. [Methods] The term 'quasi-partical lifetime' should be 'quasiparticle lifetime'.
  3. [Figure 2b caption] The black arrows in Fig. 2b are said to indicate the range of spectral variation, but the text does not explain what the arrows point to; please clarify.
  4. [Section III] The text refers to in-gap states as 'presumably of bulk origin' in Section III but later assigns them to surface ABSs; the terminology should be made consistent.
  5. [Figure 4 and Extended Data Fig. E6] No explicit parameter sets are given for the simulations shown in Fig. 4 and Extended Data Fig. E6; please include the numerical values used so that the fits are reproducible.

Circularity Check

2 steps flagged · score 6.0 of 10

The chiral order parameter is an assumed model input, and the 'revealed' anisotropic chiral pairing is a goodness-of-fit conclusion; the surface-SC premise is carried by self-citations without temperature/field controls.

  1. fitted input called prediction [Methods, Eq. (3); Section VI]
    "with γ being a phenomenological broadening parameter accounting for finite quasi-partical lifetime, and an anisotropic chiral order parameter of the form ∆ = ∆0 cos(θ)eiθ [42]. ... The close agreement between experiment and theory provides strong evidence for an anisotropic chiral paring symmetry in the SC state of PtBi2."

    The order parameter whose symmetry the paper claims to 'reveal' is inserted as the model input. The Dynes DOS in Eq. (3) depends only on |Δ|, so the chiral phase e^{iθ} affects the simulated conductance only through the ABS model in Eq. (5), which is itself part of the assumed chiral framework. After tuning the phenomenological parameters α, β, Z, d and adding an empirical IΓ term, the spectra are fitted; the fit's success is then presented as 'strong evidence' for the input symmetry. This is a self-consistency check, not an independent determination of Δ(k). The hierarchy in Extended Data Fig. E6 can exclude a phase-less model, but it cannot derive the chiral phase from the data.

  2. self citation load bearing [Introduction, second paragraph; Methods, STM/STS measurements]
    "Recent ARPES studies have identified trigonal PtBi2 as a 3D Weyl semimetal, with a SC gap opening exclusively on the Fermi arc surface states at temperatures around 10 K [4]."

    The paper's central premise—that the 10–16 meV STS gaps in Fig. 1d–g and Fig. 2 are superconducting—is imported from refs [4,5]. Ref. [5] is the authors' own prior STM/STS study (Schimmel et al., including co-authors of this paper) and ref. [4] also shares a co-author. All spectra are taken at the single temperature T = 5.1 K; no temperature sweep through the reported ~10 K surface transition and no magnetic-field sweep are shown. The contested null results [32,33] are acknowledged but never addressed. Thus a load-bearing premise rests on self-citation rather than on controls in this work.

full rationale

The paper's main inference is the pairing symmetry of PtBi2. That inference is not a prediction from a fixed first-principles model; it is an inverse problem. The model (Eqs. 1–8) is built with the claim's conclusion already inside: Δ = Δ0 cosθ e^{iθ} is placed in the Dynes DOS and the ABS conductance, and the phenomenological parameters α, β, Z, d plus an extra empirical IΓ term are adjusted to reproduce the setpoint-dependent dI/dV curves. Agreement between the simulated and measured spectra is therefore a check of internal consistency of the chiral ansatz, not independent evidence for chiral pairing. The model hierarchy does give some discriminative power—an isotropic gap gives a U-shaped DOS, an anisotropic gap a V-shaped DOS, and a phase-less ABS model produces a central peak inconsistent with the data—so the paper is not completely tautological. However, the 'anisotropic chiral' conclusion is effectively the assumed input, and the surface-SC premise itself is carried by refs [4,5] (which overlap with the present authors) rather than by temperature/field controls, while refs [32,33] question it. Hence partial circularity: score 6 rather than 8–10, because the data can at least reject some alternative forms within the modeled family.

Assumptions & free parameters 8 free parameters · 7 assumptions · 0 invented entities

The central claim rests on a heavily parameterized phenomenological model. Eight groups of fitted or freely adjusted quantities (Delta0, gamma, Z, alpha, beta, delta, IGamma scale, D/const) are used to reproduce spectra, and the chiral order parameter is an input, not a derived output. The experimental interpretation additionally assumes surface superconductivity is real despite competing references, and that the in-gap states are intrinsic ABSs. No new physical entities are postulated.

free parameters (8)
  • Delta0 (pair potential amplitude) = ~10-16 meV
    Scale of the Dynes gap in Eq. 3, set by coherence peak positions in Figs. 1d-g and E1.
  • gamma (Dynes broadening) = not reported
    Phenomenological lifetime broadening in Eq. 3, adjusted per spectrum.
  • Z (junction barrier strength) = not reported (alpha=beta=0.4Z in E6)
    Dimensionless barrier parameter in Eq. 6 controlling transmissivity and the ABS gap delta; treated as distance-dependent.
  • alpha (IT weight exponent) = not reported
    Exponential weighting between conventional and ABS currents in Eq. 1, governed by tip-sample distance.
  • beta (ABS vs IGamma weight) = not reported
    Phenomenological weight in Eq. 1, stated to be inversely dependent on tip-sample distance.
  • delta (ABS subgap) = not reported
    Z-dependent ABS gap in Eq. 7; the functional form is not specified.
  • IGamma empirical term = proportional to Gamma_ABS * eV_bias
    Introduced ad hoc in Methods to reproduce negative differential conductance; no microscopic derivation.
  • D and const = not reported
    Overall scale and offset in Eq. 8, adjusted to match measured conductance.
assumptions (7)
  • domain assumption Surface superconductivity in PtBi2 is established by prior ARPES and STM reports [4,5].
    Used as the starting point; competing refs [32,33] question surface superconductivity, and no new bulk or transition characterization is presented here.
  • standard math Dynes formula describes the superconducting density of states.
    Used in Eq. 3; a standard phenomenological model for broadened superconducting DOS.
  • standard math Kashiwaya-Yamakage tunneling formalism describes ABS conductance.
    Used for IABS in Eqs. 4-7, taken from prior literature [41,44].
  • domain assumption Each Fermi arc hosts a node at its center with a +/- pi chiral phase change.
    Invoked in Methods to justify the theta projection of the order parameter; based on prior ARPES/theory [31] but not independently verified in this work.
  • domain assumption In-gap zero-bias conductance arises from ungapped bulk states.
    Assumed from refs [4,5]; no bulk spectroscopic measurement is presented here.
  • domain assumption Observed in-gap states are intrinsic surface ABSs, not tip artifacts.
    Argued from reversibility and multiple tips (Fig. 2d, E3), but no independent probe is provided.
  • standard math Standard Fermi-function-based tunneling current integrals are valid.
    Used in Eqs. 2 and 4; standard tunneling theory.

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Pith. "Pith review of Sizable superconducting gap and anisotropic chiral topological superconductivity in the Weyl semimetal PtBi$_2$." pith.science (2026). https://pith.science/paper/SFRCWG5T

@misc{pith2026250713843,
  author       = {Pith},
  title        = {Pith review of: Sizable superconducting gap and anisotropic chiral topological superconductivity in the Weyl semimetal PtBi$_2$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SFRCWG5T}},
  note         = {Machine review of arXiv:2507.13843}
}
abstract

Topological superconductors offer a fertile ground for realizing Majorana zero modes -- topologically protected, zero-energy quasiparticles that are resilient to local perturbations and hold great promise for fault-tolerant quantum computing. Recent studies have presented encouraging evidence for intrinsic topological superconductivity in the Weyl semimetal trigonal PtBi$_2$, hinting at a robust surface phase potentially stable beyond the McMillan limit. However, due to substantial spatial variations in the observed superconducting (SC) gap $\Delta$ the nature of the underlying order parameter $\Delta$($k$) remained under debate. Here we report the realization of sizable surface SC gaps ($\Delta > 10\,\mathrm{meV}$) in PtBi$_2$, exhibiting remarkable spatial uniformity from hundreds of nanometers down to the atomic level, as revealed by scanning tunneling microscopy and spectroscopy. Building on this spatial homogeneity -- indicative of long-range phase coherence -- we uncover previously unobserved low-energy Andreev bound states (ABSs) that ubiquitously emerge within the SC gap across the surface. Theoretical simulations that closely reproduce the experimental spectra, reveal an anisotropic chiral pairing symmetry of $\Delta$($k$), and further suggest that the observed ABSs are of topological origin. The combination of a large, nontrivial pairing gap and accessible surface states establishes PtBi$_2$ as a compelling platform for investigating topological superconductivity and its associated Majorana modes.

Figures

Figures reproduced from arXiv: 2507.13843 by the authors.

Figure 1
Figure 1. b shows a large-scale STM image of the freshly cleaved surface of a PtBi2 single crystal. An atomic￾resolution STM image (Fig. 1c) reveals a triangular sur￾face lattice, consistent with the decorated honeycomb termination. To establish whether PtBi2 hosts surface superconductivity with a sizable gap, we conducted dif￾ferential conductance (dI/dV ) spectroscopy. As shown in Fig. 1d-g, pronounced SC gaps with well￾def… view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. and as overlaid spectra in Extended Data Fig. E4. At Istab = 500 pA (Fig. 3a and Extended Data Fig. E4a), the spectra remain highly consistent across all positions, exhibiting a well-defined, symmetric profile about the EF, aside from minor variations near zero bias. A representative spectrum (highlighted in bold) fea￾tures a conductance minimum at EF, followed by a steep increase in spectral weight toward the gap e… view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

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Forward citations

Cited by 4 Pith papers

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