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REVIEW 3 major objections 4 minor 65 references

Observation of Yu-Shiba-Rusinov-like states at the edge of CrBr3/NbSe2 heterostructure

T0 review · 3 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read The edge states in CrBr3/NbSe2 that were called Majorana modes are conventional Yu-Shiba-Rusinov bound states.

desk verdict A credible, data-rich case that CrBr3/NbSe2 edge states are YSR rather than Majorana, weakened only by the 'conclusive' claim and an assumed—not measured—J tuning mechanism. read the letter →

arxiv 2411.18227 v1 pith:SBI7TRI3 submitted 2024-11-27 cond-mat.supr-con

Yuanji Li , Ruotong Yin , Mingzhe Li , Jiashuo Gong , Ziyuan Chen , Jiakang Zhang , Ya-Jun Yan , Dong-Lai Feng This is my paper · ORCID
classification cond-mat.supr-con
keywords Yu-Shiba-RusinovstatesMajoranaedgemodesCrBr3/NbSe2heterostructurescanningtunnelingmicroscopy/spectroscopyquantumphasetransitionin-gapboundvanderWaalstopologicalsuperconductivity
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 re-examines the CrBr3/NbSe2 heterostructure with an ultralow-temperature scanning tunneling microscope and argues that the zero-energy conductance peaks previously seen at the edges of CrBr3 islands are not Majorana edge modes. The authors find the CrBr3 monolayer is insulating and behaves as a vacuum barrier, so the superconductivity underneath is essentially unchanged. At reconstructed edge segments they resolve two kinds of in-gap states, a zero-energy peak and a pair of particle-hole symmetric bound states, whose spatial positions track the edge lattice reconstruction. As the tip is moved closer, increasing tunneling transmissivity, the zero-energy peak splits and the pair first merges then splits again; the paper reads this as the energy-versus-exchange-coupling curve of Yu-Shiba-Rusinov states crossing a quantum phase transition. If correct, this removes CrBr3/NbSe2 as a candidate Majorana platform and gives a concrete experimental way to tell trivial in-gap peaks from protected topological ones.

What carries the argument

The carrying object is the Yu-Shiba-Rusinov (YSR) energy formula $\varepsilon = \Delta\,(1-a^2)/(1+a^2)$, where $a = J S_{\mathrm{imp}} \pi \rho_s$, which relates the in-gap bound-state energy to the exchange coupling $J$ between a localized magnetic moment and the superconductor. The paper uses the STM tip's approach as a knob: lowering the tip increases tunneling transmissivity $G_N$ and, through tip-sample forces, is assumed to increase $J$ monotonically, so the measured evolution of peak positions traces the YSR curve across the quantum phase transition at $J_{\mathrm{crit}}$. The lattice reconstruction at CrBr3 edges supplies the localized spins, and the formula's prediction of merging at zero energy and re-splitting with reversed weights is the signature that distinguishes YSR states from Majorana modes.

What would settle it

Measure the local magnetic moment of the reconstructed edge sites with spin-polarized scanning tunneling microscopy: if the bright edge sites show no localized spin, or if a zero-energy peak stays pinned at zero energy over the same range of tip approach instead of splitting, the YSR interpretation would lose its support.

Watch

Extended reading notes

Core claim

The paper's central claim is that the discrete in-gap edge states of CrBr3/NbSe2 are topologically trivial Yu-Shiba-Rusinov (YSR) states, not chiral Majorana edge modes. Using the YSR relation $\varepsilon = \Delta (1-a^2)/(1+a^2)$ with $a = J S_{\mathrm{imp}} \pi \rho_s$, the authors argue that increasing the exchange coupling $J$ between a localized edge spin and the NbSe2 superconductor moves the bound states toward zero energy, produces a zero-energy peak at the quantum phase transition $J = J_{\mathrm{crit}}$, and then splits them again with reversed electron-hole weight. They reproduce this entire sequence by increasing the tunneling transmissivity with the STM tip, which they take to tune $J$. The same spectral evolution is seen on CrBr3 clusters, and the edge states appear only where the CrBr3 lattice reconstructs, which the paper identifies as the source of localized spins. The authors conclude that the previously reported zero-energy peaks are YSR states sitting coincidentally at the quantum phase transition.

Load-bearing premise

The load-bearing assumption is that bringing the STM tip closer increases the exchange coupling between a localized edge spin and the superconductor in a smooth, monotonic way, so the measured spectral changes trace the Yu-Shiba-Rusinov energy curve rather than some other tip-induced effect.

Editorial extensions

If this is right

  • The discrete zero-energy peaks at CrBr3/NbSe2 edges should be regarded as YSR states at the quantum phase transition, so they do not provide evidence for topological Majorana edge modes.
  • CrBr3/NbSe2 in its present form does not realize the proposed chiral topological superconductor; the insulating CrBr3 layer and weak magnetic proximity suppress Shiba bands.
  • Transmissivity-dependent STS becomes a usable test: a genuine Majorana zero mode should stay at zero energy when tip-sample coupling changes, while YSR peaks split or merge according to the YSR curve.
  • Edge lattice reconstruction is the microscopic origin of the localized spins, so engineering the reconstruction would control where and at what energy in-gap states appear.

Reading between the lines

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

  • We infer that the same tip-tuning protocol could be applied to other magnet/superconductor interfaces that show discrete zero-energy peaks, providing a quick spectroscopic screen for trivial versus topological origin.
  • If the YSR assignment is right, spin-polarized tunneling spectroscopy across the transition should reveal the predicted reversal of electron- and hole-like spectral weight at a given edge site, a prediction the paper does not test.
  • The mechanism implies that local exchange couplings at reconstructed edges could be deliberately varied by tip-induced strain or voltage, mapping YSR phase diagrams of individual edge spins.
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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 / 4 minor

Summary. The manuscript reports a reinvestigation of the CrBr3/NbSe2 heterostructure using ultralow-temperature STM/STS at 40 mK with improved energy and spatial resolution. The authors find that monolayer CrBr3 acts as an insulating barrier, so that the superconducting gap and vortex states measured on the CrBr3 film are nearly identical to those on bare NbSe2. At the edges of CrBr3 islands, they observe two types of in-gap states: zero-energy conductance peaks (ZECPs) and particle-hole symmetric pairs of in-gap conductance peaks. These states are spatially discrete and correlate with lattice reconstruction at the edge. Tunneling transmissivity-dependent measurements show that the ZECP splits with increasing GN, while the pair of in-gap peaks first approach each other, merge into a ZECP, and then split again, with the process being reversible. The authors interpret these behaviors as conventional Yu-Shiba-Rusinov (YSR) states undergoing a quantum phase transition, and argue that their results constitute conclusive evidence for the topologically trivial origin of the edge states, contradicting earlier claims of Majorana edge modes in this heterostructure.

Significance. If the YSR interpretation of the edge states holds, the paper makes an important contribution by resolving a high-profile controversy: it provides a concrete, reproducible counterexample to the claim of topological Majorana edge modes in CrBr3/NbSe2. The study benefits from the higher resolution of the measurements, a direct comparison with bare NbSe2, and the observation of reversible, GN-dependent spectral evolution that is difficult to reconcile with protected Majorana modes. The spatial correlation of the edge states with lattice reconstruction is a useful structural insight. However, the paper's central evidence is qualitative: the YSR assignment is not supported by a quantitative fit of the data to the YSR formula, no spin-sensitive measurement is presented, and the key assumption that tip approach tunes the exchange coupling J is not independently verified. Nevertheless, the work is significant as a systematic experimental study that raises strong caveats against the earlier Majorana interpretation.

major comments (3)
  1. [Tunneling transmissivity-dependent dI/dV spectrum measurements (Fig. 4)] The central interpretation rests on the assumption that increasing GN by reducing tip-sample distance monotonically tunes the exchange coupling J between edge spins and NbSe2. The paper states that the electrostatic force from the approaching tip will affect the coupling, but no quantitative estimate or direct measurement of J is provided. Without establishing this monotonic relationship, the observed 'approach-merge-split-again' evolution is not uniquely tied to the YSR energy-versus-J curve. A non-magnetic resonant level whose energy is shifted by tip-induced electrostatic gating could, in principle, produce similar qualitative behavior as it crosses the Fermi energy. Please provide a quantitative model of the tip-induced coupling change, a control experiment on a non-magnetic impurity or defect, or an explicit argument ruling out electrostatic gating as the origin of the spectral evolution. This is a load-bearing point for the main conclusion.
  2. [Introduction and Discussion] The manuscript twice states that the results provide 'conclusive experimental evidence for the topologically trivial origin' of the edge states. This is an overstatement given that the identification is qualitative: no quantitative fit to the YSR formula ε = Δ(1−a²)/(1+a²) is performed, no spin-resolved STS data are presented, and about 13% of the edge spectra are left unclassified (Supplementary Fig. 6). The data are consistent with a YSR interpretation, but they do not conclusively exclude all alternatives, such as non-magnetic in-gap states or tip-induced artifacts. Please soften the claim to 'strong evidence' or 'consistent with', unless a quantitative analysis that tests the YSR model against the measured spectra is added.
  3. [Discussion (edge states and lattice reconstruction)] The paper infers the existence of localized magnetic moments at the reconstructed CrBr3 edges solely from the observation of in-gap states and the structural reconstruction. The YSR interpretation requires a local spin, yet the magnetic character of these edge sites is not directly demonstrated. A magnetic-field-dependent study would provide a concrete test: YSR states are expected to split linearly with applied magnetic field, whereas non-magnetic bound states would behave differently. Including such data, or at least explicitly discussing the absence of a spin-sensitive probe, would substantially strengthen the central claim.
minor comments (4)
  1. [Discussion] The statement about 'higher spatial resolution (~4.25 pixel/nm)' is misleading because pixel density is a data acquisition grid density, not a physical measure of spatial resolution. Please rephrase to describe the actual sampling density or the physical resolution determined by the tip condition.
  2. [Introduction] The YSR formula is garbled in the text: '𝜀 = Δଵି௔మ / ଵା௔మ' should be typeset as ε = Δ(1−a²)/(1+a²). Please ensure proper mathematical typesetting in the final version.
  3. [Fig. 4] The sketched phase diagram in Fig. 4h would be more convincing if the experimentally extracted peak positions from Figs. 4a-g were overlaid on the theoretical YSR energy curve. A quantitative comparison of the measured peak energies as a function of GN with the YSR formula would provide stronger support for the interpretation.
  4. [Structural and electronic properties of CrBr3/NbSe2 heterostructure] The paper states that CrBr3 acts as a vacuum barrier with little influence on NbSe2, but also reports a ~30 meV energy shift and weak charge transfer. These statements appear somewhat contradictory and should be reconciled, for example by clarifying that the barrier behavior holds for the low-energy electronic structure while a weak interfacial charge transfer is still present.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the YSR assignment is an empirical interpretation against a standard external model, with only minor non-load-bearing self-citations.

full rationale

The paper does not fit any parameter to its own data and then relabel it as a prediction. The YSR energy formula ε = Δ(1−a²)/(1+a²) with a = J S_imp π ρ_s is introduced as standard external theory (refs 11–15), and the observed approach-merge-split-again evolution of the in-gap peaks is compared qualitatively to this known curve (Fig. 4h), not derived from a fit. The identification of the zero-energy conductance peak as the YSR quantum-phase-transition point is an interpretation of the data within that standard model, not a circular reduction. The only self-citations are refs 19 and 20, used respectively as examples of YSR spectroscopy and for the effective electron temperature (~170 mK) in Methods; neither supports the central claim. The assumption that tip approach tunes J via electrostatic force (Sec. 'Tunneling transmissivity-dependent dI/dV spectrum measurements') is an unverified physical premise, which is a correctness or evidence-strength concern, but it is not circular because J is not measured from the same spectra and then used to predict those spectra. The conclusion that the edge states are topologically trivial YSR states is therefore a genuine empirical interpretation, not a self-justifying chain. Score 1 reflects only the presence of minor, non-load-bearing self-citations.

Assumptions & free parameters 0 free parameters · 3 assumptions · 1 invented entities

The central interpretation rests on standard YSR theory, a specific assumption about how tip approach tunes J, an assumed vacuum-barrier role of CrBr3, and inferred localized spins at edges. No free parameters are fitted to data; the critical GN values are measured outputs rather than model inputs.

assumptions (3)
  • domain assumption YSR energy formula epsilon = Delta*(1-a^2)/(1+a^2) with a = J*S_imp*pi*rho_s.
    Used to interpret the evolution of edge states; standard theory from refs 15-20, but the paper does not derive it and does not independently verify the parameters for this system.
  • ad hoc to paper Increasing GN = It/Vb monotonically increases the exchange coupling J between the CrBr3 edge and NbSe2.
    Central to mapping the observed spectral evolution onto the YSR quantum phase transition; the paper argues tip approach changes J via electrostatic force (Supplementary Fig. 8) but does not measure J.
  • domain assumption The monolayer CrBr3 film has no electronic states near EF and acts as a vacuum barrier.
    Used to interpret the nearly identical superconducting gap and vortex states on CrBr3 and NbSe2; supported by the large-gap spectrum in Fig. 2a but not by a direct barrier-height measurement.
invented entities (1)
  • Localized magnetic moments at reconstructed CrBr3 step edges.
    purpose: To explain the YSR-like in-gap bound states observed at the edges.
    The moments are inferred from the spectra and the correlation with lattice reconstruction; no spin-polarized STM or other direct magnetic probe is provided. The Discussion speculates that reconstruction 'may alter the arrangement patterns of CrBr3 molecules, thus resulting in localized spins at the step edges.'

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Cite this review

Pith. "Pith review of Observation of Yu-Shiba-Rusinov-like states at the edge of CrBr3/NbSe2 heterostructure." pith.science (2026). https://pith.science/paper/SBI7TRI3

@misc{pith2026241118227,
  author       = {Pith},
  title        = {Pith review of: Observation of Yu-Shiba-Rusinov-like states at the edge of CrBr3/NbSe2 heterostructure},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SBI7TRI3}},
  note         = {Machine review of arXiv:2411.18227}
}
read the original abstract

The hybrid ferromagnet-superconductor heterostructures have attracted extensive attention as they potentially host topological superconductivity. Relevant experimental signatures have recently been reported in CrBr3/NbSe2 ferromagnet-superconductor heterostructure, but controversies remain. Here, we reinvestigate CrBr3/NbSe2 by an ultralow temperature scanning tunneling microscope with higher spatial and energy resolutions. We find that the single-layer CrBr3 film is insulating and acts likely as a vacuum barrier, the measured superconducting gap and vortex state on it are nearly the same as those of NbSe2 substrate. Meanwhile, in-gap features are observed at the edges of CrBr3 island, which display either a zero-energy conductance peak or a pair of particle-hole symmetric bound states. They are discretely distributed at the edges of CrBr3 film, and their appearance is found closely related to the atomic lattice reconstruction near the edges. By increasing tunneling transmissivity, the zero-energy conductance peak quickly splits, while the pair of nonzero in-gap bound states first approach each other, merge, and then split again. These behaviors are unexpected for Majorana edge modes, but in consistent with the conventional Yu-Shiba-Rusinov states. Our results provide critical information for further understanding the interfacial coupling in CrBr3/NbSe2 heterostructure.

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Pith tools

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