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REVIEW 3 major objections 5 minor 53 references

Nanoscale infrared and microwave imaging of stacking faults in multilayer graphene

T0 review · 3 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read Two atomic force microscopy techniques identify graphene stacking orders at the nanoscale, including through a hexagonal boron nitride layer.

desk verdict Solid AFM-IR/sMIM toolkit for stacking screening, but 'unambiguous' overstates what the data show; strain and the inferred I4G assignment need to be addressed. read the letter →

arxiv 2504.17783 v1 pith:WO3RDYME submitted 2025-04-24 cond-mat.mes-hall cond-mat.mtrl-sci

Ludwig Holleis , Liam Cohen , Noah Samuelson , Caitlin L. Patterson , Ysun Choi , Marco Valentini , Owen Sheekey , Youngjoon Choi
show 9 more authors
Jiaxi Zhou Hari Stoyanov Takashi Taniguchi Kenji Watanabe Qichi Hu Jin Hee Kim Cassandra Phillips Peter De Wolf Andrea F. Young
This is my paper · ORCID
classification cond-mat.mes-hallcond-mat.mtrl-sci
keywords graphenestackingorderrhombohedralgraphiteBernalAFM-IRscanningmicrowaveimpedancemicroscopyvanderWaalsheterostructureshexagonalboronnitrideencapsulationdomainwalls
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

The paper argues that two atomic-force-microscopy techniques can do what far-field optics cannot: tell apart the different layer-stacking orders of multilayer graphene at the nanoscale and identify the faults between them. Photothermal infrared microscopy (AFM-IR) reads out local infrared absorption and, by recording spectra at many wavenumbers, gives contrast that can be assigned to Bernal, rhombohedral, and intermediate stacking orders. Scanning microwave impedance microscopy (sMIM) reads out the local tip-sample impedance and shows stronger relative contrast, resolving stacking faults below 20 nanometers. Both techniques work on flakes already buried under a hexagonal boron nitride dielectric, which matters because stacking order controls the electronic band structure and therefore which correlated and topological phases the material can host. The practical goal is high-throughput screening of flakes and devices so that samples with a definite, uniform interlayer registry can be made reliably.

What carries the argument

The load-bearing objects are two scanning-probe contrast mechanisms. AFM-IR (photothermal infrared microscopy) is a local version of infrared absorption spectroscopy: a pulsed infrared laser heats the sample and the AFM cantilever senses the resonant thermal expansion, so the signal tracks absorption in a volume near the 20 nm tip apex; sweeping the laser wavenumber yields a spectrum at each point. sMIM (scanning microwave impedance microscopy) sends a microwave signal down the cantilever and detects the reflected signal, whose amplitude depends on the local tip-sample impedance; in dC/dV mode an AC modulation of the tip voltage extracts the capacitance derivative and recovers contrast through a dielectric layer. The assignments are anchored by Raman 2D-peak maps, which supply the ground-truth stacking labels, and by the known band-structure differences between stacking orders that the paper cites as making infrared absorption stacking-dependent below about 0.8 eV. The domain-wall analysis then works by tracking which of the top one, two, or three layers shifts between A, B, and C registry positions, identifying transitions such as ABCA to ABAB to ACBC to ACBA as a shear-strain pattern.

What would settle it

Take a tetralayer flake with the same mixed stacking domains and determine the stacking of the central strip region directly by cross-sectional atomic-resolution imaging, for example annular dark-field scanning transmission electron microscopy. If the strip is not ABCB stacking, then the claimed identification of the intermediate order is wrong; more generally, any region where AFM-IR and sMIM contrast disagrees with the independent structural measurement would falsify the claim of unambiguous distinction.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is that AFM-IR and sMIM provide a full nanoscale picture of stacking order in few-layer graphene that Raman and far-field infrared imaging cannot. In tetralayer flakes, AFM-IR spectra acquired across 800-1800 cm-1 show contrast between Bernal (ABAB), rhombohedral (ABCA), and the intermediate ABCB stacking order, with rhombohedral identified by a peak near 1580 cm-1 and other wavenumbers separating each order from the other two; the intermediate assignment is corroborated by a region that matches Bernal in AFM-IR but rhombohedral in Raman. sMIM, calibrated by Raman maps and by AFM-IR, distinguishes the same domains with higher contrast and resolves domain walls, including narrow double walls with internal structure at the 10 nm scale. Both techniques image trilayer graphene buried under 5-10 nm of hBN, with AFM-IR contrast unchanged and sMIM requiring an AC voltage modulation (dC/dV mode). The paper also shows that certain AFM-IR wavenumbers respond to strain, revealing that micrometer-scale strain gradients and incomplete relaxation coexist with the discrete stacking domains.

Load-bearing premise

The claim of unambiguous stacking identification rests on Raman 2D-peak maps as the ground truth that labels each domain; if Raman mislabels stacking in these strained, wrinkled flakes, the inferred AFM-IR and sMIM assignments would fail.

Editorial extensions

If this is right

  • Stacking order can be mapped at the nanoscale in mixed-domain flakes, so uniform rhombohedral regions can be located and used for device fabrication instead of relying on rare large-area domains.
  • Because both techniques work on hBN-encapsulated flakes, the stacking order of finished van der Waals devices can be verified without electrical contact or disassembly.
  • sMIM's sub-20 nm resolution makes domain walls between regions of the same stacking order visible, allowing device areas to be checked for these nanoscale faults.
  • AFM-IR spectral fingerprints give an absolute, calibration-free assignment of Bernal, rhombohedral, and intermediate stacking orders in few-layer flakes.
  • The strain-sensitive infrared wavenumbers could allow simultaneous monitoring of stacking order and strain during experiments that heat, strain, or apply electric fields to the flake.

Reading between the lines

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

  • Because AFM-IR contrast appears at nearly every probed wavenumber, including energies below the lowest interband separation, the mechanism is probably not simple interband absorption; a natural extension is to record spectra to lower wavenumbers and compare with a Bernal bilayer reference to separate thermal-expansion contributions from electronic ones.
  • The strain-dependent contrast at certain wavenumbers suggests AFM-IR could be developed into a quantitative strain mapper if the response is calibrated against flakes with known uniaxial or shear strain patterns.
  • For flakes with more than four layers the number of possible stacking orders grows, and AFM-IR spectral libraries combined with an independent structural probe could classify those higher-order stackings, which the paper does not attempt.
  • For production screening, sMIM's speed and signal-to-noise make it the natural inline tool, but only when paired with AFM-IR or Raman calibration; a testable workflow would be to pre-screen entire wafers with sMIM and verify selected regions with AFM-IR.
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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 / 5 minor

Summary. The manuscript presents AFM-IR (photothermal infrared) and sMIM (scanning microwave impedance microscopy) as tools for nanoscale identification of stacking order in few-layer graphene. On exfoliated tetralayer flakes, the authors use Raman 2D-peak maps as a ground-truth label for Bernal (B4G) and rhombohedral (R4G) domains, and they assign a central strip to an intermediate stacking order (I4G, e.g. ABCB) based on partial agreement between Raman and AFM-IR contrast. They show wavenumber-dependent AFM-IR contrast, including a hyperspectral analysis where different wavenumbers highlight different stacking orders, and sMIM images with two/three contrast levels. Both techniques are applied to hBN-encapsulated trilayers and to imaging of domain walls, including a sub-20 nm-scale feature. The central claims are that AFM-IR provides 'absolute contrast' and unambiguous stacking-order identification via spectral analysis, that sMIM provides higher relative contrast and nanoscale resolution, and that both are suited for high-throughput characterization of van der Waals devices.

Significance. If the claims are established, this work offers a practical, high-throughput route to stacking-order mapping in multilayer graphene, including through an hBN capping layer, which would be valuable for fabricating rhombohedral-stacked devices. The experiments are carefully executed: Raman maps independently label the main domains, the AFM-IR and sMIM contrasts are internally consistent, and the subsurface imaging demonstrates a useful capability. The paper also shows a credible domain-wall analysis connecting the observed patterns to layer shifts and shear strain. However, the load-bearing claims of 'absolute' and 'unambiguous' identification go beyond what the evidence supports, because the I4G assignment is inferred rather than independently verified, and because the manuscript itself documents stacking-independent AFM-IR contrast attributed to strain. The strengths—independent Raman labels for the two extremal orders, consistent multispectral contrast, and sub-20 nm domain-wall resolution—deserve recognition; the overstatement needs correction rather than wholesale rejection.

major comments (3)
  1. [Photothermal infrared microscopy, Fig. 1c–1e] The assignment of the central strip to the intermediate I4G stacking order is not independently verified: it is inferred from the observation that this region has a Raman signature similar to R4G but AFM-IR contrast similar to B4G. Because the flake is acknowledged to contain considerable strain (Fig. S1), and strain is later invoked to explain AFM-IR contrast that is inconsistent with stacking order (Fig. 4f,g), the inference to a specific stacking order is not unique. The statement in the text that 'we can unambiguously assign the three different stacking orders' overstates the evidence; an independent structural probe (STM, TEM, or a separately calibrated reference sample) or a quantitative exclusion of strain-induced contrast is required to support the I4G label.
  2. [Imaging of domain wall defects, Fig. 4f,g] The manuscript explicitly states that AFM-IR at some wavenumbers shows 'additional contrast and gradients' inconsistent with the three stacking orders, 'likely an indication of strain.' This is direct evidence that AFM-IR contrast is not a function of stacking order alone. The spectral templates in Fig. 1d,e were averaged over regions of this same strained flake and are not strain-calibrated, so the claim that AFM-IR 'provides absolute contrast between stacking orders' is not established. Please either add a strain-calibration measurement (e.g., comparing spectra under controlled strain) or revise the claim to specify that AFM-IR provides relative stacking contrast that is valid in the low-strain limit.
  3. [Imaging of domain wall defects, text after Fig. 4] The paper concedes that 'domains related by translation symmetry or mirror symmetry about the center plane of the graphite are expected to show identical contrast.' This concession means that AFM-IR and sMIM cannot uniquely assign a stacking configuration among all crystallographically distinct possibilities, so the words 'absolute' and 'unambiguous' in the abstract and introduction are too strong. The claims should be restated as distinguishing the specific stacking orders probed in these samples (and, for sMIM, requiring an external calibration for absolute identification), rather than providing a complete and unique stacking-order determination.
minor comments (5)
  1. [Figure 2 caption] There is a typo in the caption: 'few layer graphehne' should be 'few layer graphene.'
  2. [Imaging of domain wall defects] In the sentence 'with the stacking order returning to the the original one over the course of 5-10 nm,' 'the the' is a typo and should be 'the original.'
  3. [Supplementary Fig. S7] The text refers to panel (c) as a cross-sectional profile, but the figure caption lists only (a), (b), and (d); the panel labeling should be made consistent.
  4. [Microscopy section] The statement that the AFM-IR contrast appears 'almost all wavenumbers' would benefit from a quantitative statement of the signal-to-noise ratio and the contrast magnitude relative to the drift-correction uncertainty, since the normalization procedure in Fig. S2 removes line-by-line background and could mask slowly varying spatial features.
  5. [Introduction] The phrase 'absolute certainty of identification' in the discussion of far-field IR imaging is not precisely defined; the authors should clarify what 'absolute' means operationally (e.g., calibration against a known reference) so that the contrast with the present sMIM result is clear.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the imaging contrasts are calibrated against external Raman/IR benchmarks, and no reported prediction reduces to its own inputs.

full rationale

The paper is an experimental characterization study rather than a derivation. AFM-IR and sMIM contrasts are calibrated against Raman 2D-peak maps (Figs. 1b and 2d), which are external structural benchmarks, and the claimed ability to distinguish Bernal, rhombohedral, and intermediate stacking is validated by comparing images at multiple wavenumbers with those independently labeled regions. The intermediate I4G assignment is an inference from the conjunction of Raman and AFM-IR contrasts (same as R4G in Raman and same as B4G in AFM-IR), not a redefinition of the contrast in terms of the label; the later spectra at other wavenumbers are a consistency check, not a prediction forced by construction. Selecting discriminating wavenumbers from the same hyperspectral map and then displaying images at those wavenumbers is calibration/demonstration rather than a fitted input being renamed a prediction. No load-bearing self-citation or imported uniqueness theorem appears: the intermediate-stacking references [33, 34] are independent groups, and the strain-related AFM-IR features in Figs. 1i and 4f-g are acknowledged as a limitation of the classification under strain, which is a correctness concern, not circularity. The paper also explicitly notes that translation- or mirror-related domains are expected to show identical contrast, so it does not overclaim uniqueness. The derivation chain is therefore self-contained with respect to its external benchmarks, and no circular step can be exhibited.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

No theoretical model is derived and no new entities are introduced. The central claim rests on standard AFM-IR and sMIM contrast mechanisms, on Raman-based stacking identification as ground truth, and on the assignment of the third tetralayer domain to an intermediate stacking order. The probe wavenumbers are empirical measurement settings, not fitted model parameters.

free parameters (1)
  • AFM-IR probe wavenumbers used for stacking contrast = Keyed at 1100, 1170, 1310, 1500, and 1576 cm^-1 from a full sweep of 800 to 1800 cm^-1
    Chosen empirically from hyperspectral maps to maximize contrast between stacking orders; they are measurement settings rather than parameters fitted to a theoretical prediction, but they are hand-selected.
assumptions (4)
  • domain assumption Raman 2D-peak position identifies stacking order in few-layer graphene
    Used as ground truth in Figs. 1b and 2d; Raman stacking identification is established for few-layer graphene but is sensitive to strain and doping, which is relevant because the flakes show wrinkles.
  • domain assumption AFM-IR contrast reflects local infrared absorption and thermal expansion
    Standard photothermal AFM-IR mechanism; the paper interprets stacking-dependent absorption spectra (Figs. 1d,e) on this basis.
  • domain assumption sMIM contrast reflects tip-sample impedance
    Standard sMIM mechanism; the paper interprets C and dC/dV contrast (Figs. 2, 3, 4) as due to local electrical properties differing by stacking.
  • domain assumption The three contrast levels in tetralayer graphene correspond to ABAB, ABCA, and ABCB stacking
    The I4G (ABCB) assignment is inferred from consistency between Raman and AFM-IR, not independently verified; the paper acknowledges related symmetries can produce identical contrast.

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Pith. "Pith review of Nanoscale infrared and microwave imaging of stacking faults in multilayer graphene." pith.science (2026). https://pith.science/paper/WO3RDYME

@misc{pith2026250417783,
  author       = {Pith},
  title        = {Pith review of: Nanoscale infrared and microwave imaging of stacking faults in multilayer graphene},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WO3RDYME}},
  note         = {Machine review of arXiv:2504.17783}
}
abstract

Graphite occurs in a range of metastable stacking orders characterized by both the number and direction of shifts between adjacent layers by the length of a single carbon-carbon bond. At the extremes are Bernal (or ``ABAB...'') stacking, where the direction of the interlayer shift alternates with each layer, and rhombohedral (or ``ABCABC...'') stacking order where the shifts are always in the same direction. However, for an N-layer system, there are in principle $N-1$ unique metastable stacking orders of this type. Recently, it has become clear that stacking order has a strong effect on the low energy electronic band structure with single-layer shifts completely altering the electronic properties. Most experimental work has focused on the extremal stacking orders in large part due to the difficulty of isolating and identifying intermediate orders. Motivated by this challenge, here we describe two atomic force microscopy (AFM) based techniques to unambiguously distinguish stacking orders and defects in graphite flakes. Photo-thermal infrared atomic force microscope (AFM-IR) is able to distinguish stacking orders across multiple IR wavelengths and readily provides absolute contrast via IR spectral analysis. Scanning microwave impedance microscopy (sMIM) can distinguish the relative contrast between Bernal, intermediate and rhombohedral domains. We show that both techniques are well suited to characterizing graphite van der Waals devices, providing high contrast determination of stacking order, subsurface imaging of graphene flakes buried under a hexagonal boron nitride (hBN) dielectric layer, and identifying nanoscale domain walls. Our results pave the way for the reliable fabrication of graphene multilayer devices of definite interlayer registry.

Figures

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Figure 1
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Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.