Visualization of Defect Electronic States in Layered Semiconductor CrSBr

Adina Luican-Mayer; Aljoscha Soll; Jonathan Brunette; Joost Aretz; Kiyoung Jo; Malte R\"osner; Nathan Guisinger; Zden\v{e}k Sofer

REVIEW 3 major objections 5 minor 11 references

Scanning tunneling microscopy identifies the type-2 defect in CrSBr as a b-axis-aligned double sulfur vacancy that creates spin-polarized in-gap states near the valence band edge.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-08-01 07:50 UTC pith:XDWFCBVQ

load-bearing objection Fresh STM data on CrSBr defects, but the V2S identification is a plausible hypothesis rather than a proven result. the 3 major comments →

arxiv 2607.21301 v1 pith:XDWFCBVQ submitted 2026-07-23 cond-mat.mes-hall cond-mat.mtrl-sci

Visualization of Defect Electronic States in Layered Semiconductor CrSBr

Jonathan Brunette , Joost Aretz , Kiyoung Jo , Aljoscha Soll , Zden\v{e}k Sofer , Malte R\"osner , Nathan Guisinger , Adina Luican-Mayer This is my paper

classification cond-mat.mes-hall cond-mat.mtrl-sci

keywords CrSBrscanning tunneling microscopyscanning tunneling spectroscopydouble sulfur vacancydefect electronic statesDFT+Uin-gap stateslayered magnetic semiconductor

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper uses scanning tunneling microscopy and spectroscopy on bulk CrSBr to resolve two dominant atomic-scale defects, both of which produce localized electronic states near the valence band edge. By comparing atomically resolved topographic images and differential conductance maps with DFT+U simulated STM images, the authors identify the more structured 'type 2' defect as a double sulfur vacancy aligned along the crystal's b-axis. If correct, this is a direct experimental visualization of the electronic structure of this specific intrinsic defect complex in CrSBr. The finding matters because CrSBr's magnetism, excitons, and transport are sensitive to defects, and identifying a concrete defect configuration is a step toward deliberately engineering those properties.

Core claim

The central claim is that the type 2 defect observed in STM topographs and dI/dV maps is a b-axis-aligned double sulfur vacancy (V2S). The evidence is a qualitative match between the measured bias-dependent STM images and Tersoff-Hamann simulated STM maps computed with DFT+U for a bilayer CrSBr supercell containing one such vacancy. The calculations show that this defect introduces spin-polarized in-gap bands with anisotropic dispersion, and the experimental images show the same energy-dependent two-point structure that elongates along the b-axis as the valence band edge is approached. The paper concludes that V2S imprints occupied and unoccupied states of the same spin species into the CrSB

What carries the argument

The load-bearing tool is the comparison between experimental constant-current STM topographs and simulated STM images. The simulations use the Tersoff-Hamann approximation, which treats the tip as a point probe and weights the local density of states in an energy window below the Fermi level, applied to DFT+U relaxed 4x3x2 supercells of bilayer CrSBr. Within that machinery, the decisive object is the b-axis-aligned double sulfur vacancy (V2S), one of several candidate defect complexes tested; only V2S reproduces the observed two central bright points that merge and elongate along the b-axis near the valence band edge.

Load-bearing premise

The identification rests on the assumption that DFT+U simulated STM images at constant height are a faithful proxy for the experimental constant-current topographs, including an unstated alignment between calculated and applied voltages; if that proxy fails, the V2S assignment is unsupported.

What would settle it

A direct falsifier would be an atomic-resolution experiment that resolves the exact missing atoms at the type 2 defect site, such as cross-sectional STEM or STM with a functionalized tip. If the site does not show a pair of missing sulfurs along the b-axis, the V2S assignment collapses. Alternatively, if DFT+U simulated STM images of another defect complex (for example, a Br vacancy) were found to match the type 2 images equally well, the claim would be undermined.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

If V2S is the type 2 defect, sulfur-rich growth conditions known to suppress sulfur vacancies should also suppress the corresponding in-gap electronic states in CrSBr.
The predicted spin-polarized in-gap bands could be probed directly with spin-resolved scanning tunneling spectroscopy or by measuring how the STS signal changes under an applied magnetic field.
The paper's observation that scanning at higher negative bias creates new defects near the original one suggests local bias-induced defect migration or formation, which could be used to modify defect configurations in a controlled way.
Quantitative limitations of DFT+U mean the absolute energies of the in-gap states are uncertain; angle-resolved photoemission on defective samples could help pin down those energies experimentally.
If the V2S assignment holds, defect-engineering strategies in CrSBr can target this specific complex, potentially tuning excitonic responses and magnetic coupling near single defects.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

A direct extension of this work would be to look for optical signatures of the V2S defect, such as defect-bound exciton lines or low-energy photoluminescence, since the paper argues the defect imprints close-lying occupied and unoccupied states of the same spin species.
The permanent change in the defect's appearance after scanning to -1.15 V (described in the supplement) suggests that STM bias can irreversibly rearrange vacancies; a systematic study of bias-induced defect migration could turn STM into a local defect-writing tool.
Because the type 1 defect shows only a local reduction of density of states without resolvable internal structure, it may be a different complex (for instance, a Br vacancy or a single sulfur vacancy); correlating STM with an atomic-scale probe that is chemically sensitive could identify it.
If the V2S identification is correct, CrSBr becomes a model system for studying how a single, well-defined vacancy pair modifies a magnetic semiconductor's band structure, and the b-axis alignment of the defect may be a consequence of the material's quasi-1D electronic character.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

Fresh STM data on CrSBr defects, but the V2S identification is a plausible hypothesis rather than a proven result.

read the letter

Johanna — quick read of arXiv:2607.21301. The experimental core is good: first atomically resolved STM/STS of individual defects in CrSBr, with two defect types, densities, band gap, and bias-dependent evolution. The images are clean, the lattice parameters and gap match literature, and the authors do a sensible job of characterizing how the defects' appearance changes as the bias approaches the valence band edge. That alone is a solid contribution for the CrSBr community.

The interpretation step — assigning the type 2 defect to a b-axis-aligned double sulfur vacancy — is suggestive but not yet supported to the level the paper implicitly claims. The comparison between the DFT+U simulated Tersoff-Hamann maps and the experimental constant-current topographs is visual, and the paper offers no quantitative metric. There's also no stated energy alignment between the calculated eigenstates and the experimental bias voltages; the simulations use a bilayer slab with a 4x3x2 cell where the single defect sits at ~5e13 cm^-2, two orders above the measured density, and the authors themselves concede both exaggerated dispersion and the 'partially poor' quality of DFT+U for quantitative band positions. So the match could be coincidental, especially since several candidate defects were screened and only V2S looked right — that selection process is a real strength, but it doesn't turn a qualitative resemblance into proof. The authors are appropriately hedged in the abstract and conclusion ('consistent with'), so this reads as a plausible hypothesis rather than an overreach.

The type 1 defect is left unidentified, which is fine, but the supplemental note about a bias-induced permanent change at type 2 defects deserves more than a sentence. No data/code deposit either, which is a minor annoyance for an STM paper.

Net: worth a serious referee. The raw experiment is valuable and the V2S assignment is testable — a quantitative image-similarity score, a smaller-defect-concentration calculation, or an STS line cut across the defect would strengthen it considerably. I'd send it to review and ask for those additions. For a reading group, it's a maybe: the defect-physics discussion is useful, but the central conclusion should be taken with a grain of salt.

Referee Report

3 major / 5 minor

Summary. The manuscript reports an STM/STS study of bulk CrSBr at 211 K, resolving two types of native defects. Type 1 appears as a dark, spatially extended depression, and type 2 shows a more structured, bias-dependent pattern that evolves from two central bright points at low bias into b-axis-elongated features near the valence band. The authors also measure lattice parameters, defect densities, and a 1.7 eV band gap. DFT+U calculations for a set of candidate defect configurations are used to generate simulated Tersoff–Hamann STM images; by visual comparison with the type 2 defect, the authors infer that the defect is a b-axis-aligned double sulfur vacancy (V2S). The paper explicitly acknowledges limitations in the DFT+U description, the high effective defect concentration in the supercell, and the qualitative nature of the match.

Significance. If the assignment is correct, the paper provides a concrete atomistic identification of a common intrinsic defect in CrSBr, linking STM-visible electronic structure to a specific vacancy complex that is also favored by a recent growth study. The experimental data set — atomically resolved topographs, bias-dependent imaging, and dI/dV maps of individual defects — is a valuable contribution to the defect physics of CrSBr, a material of current interest for magnetism and excitonics. The identification is plausible and the paper is careful to limit its claim to "consistent with" in the conclusion, but the central inference rests entirely on a qualitative image comparison whose energy calibration and uniqueness are not established. The work therefore represents a useful step, but the defect assignment needs substantially stronger support before it can be taken as established.

major comments (3)

[Figure 4 and Theoretical details] Energy alignment between the DFT+U simulations and the experimental bias voltages is not established. The simulations are presented at -1.2, -1.0, -0.4 and -0.2 eV, while the experimental topographs are acquired at biases from -0.55 V to -1.15 V. The DFT Fermi level lies near the conduction-band edge, whereas the experimental Fermi level is near midgap, and the authors note this is a supercell-size artifact. No rigid shift, valence-band-onset matching, or other alignment procedure is reported. Without this alignment, the claimed energy-dependent correspondence between Fig. 4c and Fig. 4d is not a controlled fingerprint. This is load-bearing because the identification rests on the sequence of morphological changes with energy.
[Figure 4c and 4d; Methods] The comparison is between constant-height Tersoff–Hamann simulated LDOS maps at fixed energies and constant-current experimental topographs acquired at 211 K. Constant-current and constant-height images can differ in apparent corrugation, feature positions, and contrast, especially for strongly localized defect states. The dI/dV maps, which are also used in the experimental description, are not simulated. The criterion "good qualitative agreement" is applied after visually selecting V2S from only five candidate configurations in Fig. S2; no quantitative metric (e.g., cross-correlation, feature-position residuals, or symmetry score) is provided, and the candidate set does not include Cr-related defects or other complexes known from prior microscopy. The assignment is therefore not uniquely tested. A quantitative comparison or at least an explicit test against more candidates is needed to
[Page 10, supercell discussion] The authors acknowledge that the 4x3x2 supercell with one V2S corresponds to an effective defect concentration of approximately 5e13 cm^-2, about two orders of magnitude higher than the measured ~2.3e11 cm^-2, and that this "leads to an exaggerated dispersion of the in-gap defect states" and that DFT(+U) "quantitative predictions of bandwidths, -energies, and -gaps" are partially poor. These limitations directly affect the simulated STM maps: the energy positions, spatial extent, and dispersion of the defect states used for matching are all plausibly distorted. The manuscript does not report convergence checks in larger supercells or with different U/J values. For the central assignment to be robust, the authors should show that the relevant simulated features — especially the two central bright points and their b-axis elongation — are stable against these controlled approximations.

minor comments (5)

[Methods] The method name "DFT-3 method of Grimme" should be "DFT-D3".
[Throughout] "Tersoff-Haman" should be "Tersoff-Hamann".
[Supplemental Figure S2 caption] The caption contains a typo: "( ( a)" should be "(a)".
[Page 11, conclusion] The statement "identifying it as consistent with" is appropriately cautious, but the abstract's "we infer that a common defect corresponds to" is stronger than the evidence presented. The wording should be harmonized.
[Figure 3b] The text describes D2 appearing near -750/-800 meV and "formation of additional pairs of bright points" at lower bias, but the connection to Fig. 3b panels and to the irreversible change described in Fig. S1 could be clarified; the dI/dV maps for the newly formed defects are not separately labeled.

Circularity Check

0 steps flagged

No significant circularity: the V2S assignment is based on ab initio simulated STM images compared with independent experimental STM data, not on a fitted input or a self-citation loop.

full rationale

The derivation chain is self-contained. The paper reports STM/STS observations of two defect types and then compares them against ab initio DFT+U calculations of several explicit defect configurations: b-axis and a-axis double sulfur vacancies, single sulfur vacancy, and sulfur–bromine vacancies in the top and bottom layers (Supplementary Fig. S2). The simulated STM images are generated in the Tersoff-Hamann approximation at fixed energies with a point-like tip at constant height; no parameter is fitted to the experimental topographs. The Hubbard parameters U=2.5 eV and J=0.4 eV are literature values from ref. 36, not adjusted to reproduce the measured defect contrast. The experimental images are constant-current topographs at 211 K and the comparison is qualitative, but qualitative agreement is an evidentiary limitation, not a definitional reduction. The paper explicitly acknowledges the main weaknesses of the proxy: the 4x3x2 supercell corresponds to a defect concentration about two orders of magnitude above the measured one, this exaggerates in-gap dispersion, and DFT(+U) gives only 'partially poor' quantitative bandwidths, energies, and gaps. These caveats reduce confidence in the V2S identification but do not make the conclusion equivalent to the input. The only overlapping-author citation (Tulchinsky et al., ref. 25) is used to motivate focusing on sulfur-related defects, but the identification itself is argued from the simulated STM maps and from ruling out other candidates; the conclusion does not reduce to that citation being true. No fitted quantity is relabeled as a prediction, and no uniqueness theorem is imported from the authors' prior work. Therefore the paper contains no circular step; the central claim is underdetermined or uncertain at most, which is a correctness concern, not circularity.

Axiom & Free-Parameter Ledger

3 free parameters · 4 axioms · 0 invented entities

The central claim depends on modeling choices (U, J, supercell size, Tersoff-Hamann approximation, energy offsets) and on a qualitative visual match. None of these are independently anchored beyond prior literature, and the paper itself flags several of them as limitations.

free parameters (3)

DFT+U parameters U and J = U = 2.5 eV, J = 0.4 eV
Chosen for the DFT+U calculation; they affect band gap and defect-state energies that determine the simulated STM maps.
Simulated STM energy offsets = -1.2, -1.0, -0.4, -0.2 eV
Displayed simulated energies are compared against experimental biases from -0.55 V to -1.15 V without a stated rigid-shift or alignment procedure; the choice of energies influences which features are matched.
Supercell defect concentration = 1 V2S in 4x3x2 supercell (~5x10^13 cm^-2)
Computational cell is about 100x the experimental defect density, acknowledged in the text to exaggerate dispersion of in-gap states; it may also affect the simulated STM spatial pattern.

axioms (4)

domain assumption Tersoff-Hamann constant-height simulation at 3 Å approximates experimental constant-current STM topographs.
Invoked in the Methods and Figure 4 comparison without addressing constant-height vs constant-current imaging differences or tip-state effects.
domain assumption DFT+U with U=2.5 eV and J=0.4 eV positions V2S in-gap states reliably enough for identification.
Used throughout the theoretical section; the paper explicitly cautions that DFT(+U) gives partially poor quantitative predictions for weakly screened semiconductors.
domain assumption The 4x3x2 supercell defect density does not qualitatively alter the defect's STM signature.
The text notes the concentration is ~100x experimental and exaggerates dispersion, but still treats the simulated maps as representative.
ad hoc to paper Visual 'good qualitative agreement' in Figure 4 is sufficient evidence to identify the defect type.
The paper uses visual resemblance between simulated and experimental STM maps as the acceptance criterion; no quantitative metric is provided.

pith-pipeline@v1.3.0-alltime-deepseek · 10692 in / 13107 out tokens · 138543 ms · 2026-08-01T07:50:51.721365+00:00 · methodology

0 comments

read the original abstract

Chromium sulfur bromide (CrSBr) is a layered magnetic semiconducting material combining a rich magnetic phase diagram with axis-dependent electronic and optical properties. While defects in CrSBr have been shown to affect magnetic order and excitonic responses, their microscopic nature, atomic structure, and electronic properties are not yet fully understood. In this work, we use scanning tunneling microscopy/spectroscopy (STM/STS) to explore the structure and electronic signatures of two prominent defects in bulk CrSBr. Their structure reflects the symmetries of the underlying lattice, with electronic features near the valence band edge. By comparing experimental data with ab initio simulated STM images, we infer that a common defect corresponds to a b-axis-aligned double sulfur vacancy, in line with findings from a recent growth analysis study. This result advances our understanding of the role of intrinsic defects in shaping the electronic structure of CrSBr.

Figures

Figures reproduced from arXiv: 2607.21301 by Adina Luican-Mayer, Aljoscha Soll, Jonathan Brunette, Joost Aretz, Kiyoung Jo, Malte R\"osner, Nathan Guisinger, Zden\v{e}k Sofer.

**Figure 2.** Figure 2: a) Typical STM topographic map (VB = -0.55 V, IS = -50 pA). Two primary defect types are observed, outlined in purple and blue dashed squares respectively. b) Higher magnification STM topographic maps of the two defect types (VB = -0.55 V, IS = -50 pA). All measurements were taken at 211K. labeled as type 1 and type 2. From this map, we can extract defect densities of ~2.4*1011 and ~2.3*1011 cm-2 for the r… view at source ↗

discussion (0)

Reference graph

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