Visualizing orbital magnetism in electron doped rhombohedral multilayer graphene

Aaron Sharpe; Aidan Keough; Andrea F. Young; Ben Hodder Alexander; Benjamin A. Foutty; Canxun Zhang; Chenhao Jin; David Gong; Etienne Lantagne-Hurtubise; Kenji Watanabe

REVIEW 2 major objections 1 minor 1 cited by

Visualizing orbital magnetism in electron doped rhombohedral multilayer graphene

T0 review · 2 major / 1 minor · reviewed 2026-06-29 · grok-4.3

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Pith's one-line read The superconducting state in electron-doped rhombohedral tetralayer graphene carries a finite orbital magnetic moment.

desk verdict Tetralayer data shows finite orbital moment inside the zero-resistance state, but normal-state inhomogeneity undercuts the clean attribution to chiral SC. read the letter →

arxiv 2605.30316 v2 pith:INOZA4PX submitted 2026-05-28 cond-mat.mes-hall cond-mat.supr-con

Owen I. Sheekey , Trevor B. Arp , Benjamin A. Foutty , Ruoxi Zhang , Tixuan Tan , Ludwig F. W. Holleis , Yi Guo , Sandesh S. Kalantre

show 19 more authors

Canxun Zhang Mark Zakharyan David Gong Aidan Keough Youngjoon Choi Ysun Choi Siyuan Xu Tian Xie Ben Hodder Alexander Marisa Hocking Qingrui Cao Martin E. Huber Takashi Taniguchi Kenji Watanabe Chenhao Jin Etienne Lantagne-Hurtubise Aaron Sharpe Trithep Devakul Andrea F. Young

This is my paper · ORCID

classification cond-mat.mes-hallcond-mat.supr-con

keywords rhombohedralgrapheneorbitalmagnetismchiralsuperconductivityquartermetalnanoSQUIDmagnetometryBerrycurvaturefinite-momentumpairing

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 local magnetometry to map orbital magnetization in electron-doped rhombohedral graphene devices from three to thirteen layers thick. Magnetization within the quarter-metal phases reaches a peak at finite density, matching the expected concentration of Berry curvature along a ring of finite momentum. In a tetralayer device, simultaneous transport and magnetometry measurements show that the zero-resistance state itself carries a nonzero orbital moment. The same data set links stochastic resistivity jumps in the metallic regime to reversible sign changes in the valley-resolved magnetic moment and reveals extra magnetic inhomogeneity inside the apparent normal state of the superconductor.

What carries the argument

NanoSQUID-on-tip magnetometry that resolves the local orbital magnetization and correlates it with simultaneous transport measurements inside the zero-resistance regime.

What would settle it

A scan that finds zero net orbital magnetization throughout the superconducting transition while zero resistance is still observed would falsify the finite-moment claim.

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Extended reading notes

Core claim

Correlating transport and local magnetometry data in a tetralayer sample reveals that the superconducting state has a finite orbital magnetic moment, providing direct evidence of its chiral nature.

Load-bearing premise

The measured local magnetization signal inside the zero-resistance regime originates only from the orbital moment of a finite-momentum chiral Cooper-pair condensate.

Editorial extensions

If this is right

The quarter-metal magnetization peaks at finite density because Berry curvature concentrates along a ring of finite momentum.
The zero-resistance state is a chiral superconductor formed by a finite-momentum Cooper-pair condensate.
Density-tuned sign reversal of the valley magnetic moment produces metastable domains and enables gate-controlled switching of the orbital moment.
Strain-tuned competition between magnetic and non-magnetic states appears as inhomogeneity inside the apparent normal state of the superconductor.

Reading between the lines

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

The same local-magnetometry approach could be applied to other candidate chiral superconductors to test for finite orbital moments.
Gate sequences that avoid crossing the sign-change line may suppress domain formation and stabilize the superconducting state over larger areas.
The narrow layer-number window for chiral superconductivity may reflect a delicate balance between strain and the magnetic energy scale.

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Signed reviews

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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

read the letter

The main new result here is the nanoSQUID-on-tip mapping that correlates a finite local orbital magnetic moment with the zero-resistance regime in a tetralayer device. This extends earlier transport-only work on the quarter metal and the putative chiral superconductor. They also map magnetization across 3- to 13-layer samples and tie the peak at finite density to the expected ring of Berry curvature.

The transport-magnetometry correlation in the tetralayer is the cleanest part of the paper and gives a concrete experimental handle on the orbital moment. The explanation of stochastic resistivity switching via density-tuned sign changes in the valley moment, producing metastable domains, is also useful and points to practical gate control.

The soft spot is the central interpretation. The abstract itself flags magnetic inhomogeneity specifically in the apparent normal state and links it to strain-tuned competition between magnetic and non-magnetic ground states. That observation directly raises the chance that the signal inside the zero-resistance window includes contributions from persisting normal domains, trapped flux, or strain effects rather than coming purely from the finite-momentum Cooper-pair condensate. Without quantitative spatial controls or density-dependent isolation shown in the data, the "direct evidence of its chiral nature" claim rests on an assumption that needs more scrutiny.

This is experimental work aimed at groups studying flat-band graphene and unconventional pairing. The measurements are new enough that a serious referee should see it, even if the interpretation will likely require revision.

Referee Report

2 major / 1 minor

Summary. This paper uses nanoSQUID-on-tip magnetometry to map orbital magnetization in electron-doped rhombohedral multilayer graphene devices (3-13 layers). Magnetization in quarter-metal phases peaks at finite density, consistent with Berry curvature concentration in a 'ring of fire'. Correlating transport and local magnetometry in a tetralayer sample shows the superconducting state has a finite orbital magnetic moment, interpreted as direct evidence of its chiral nature with finite-momentum pairing. Stochastic resistivity switching is attributed to density-tuned sign changes in valley-resolved magnetic moments leading to metastable domains, and magnetic inhomogeneity is observed specifically in the apparent normal state of the chiral superconductor, suggestive of strain-tuned competition between magnetic and non-magnetic ground states.

Significance. If the attribution of the zero-resistance magnetization signal to the chiral superconducting condensate can be isolated from other sources, the work would provide important direct local-probe evidence linking orbital magnetism to chiral superconductivity in a flat-band system. The spatially resolved visualization of magnetization, electric-field control of orbital moments, and observations of competing orders would strengthen understanding of pairing and ground-state competition in rhombohedral graphene multilayers.

major comments (2)

[Abstract] Abstract: The central claim that the local magnetization signal correlated with zero resistance originates purely from the orbital moment of the finite-momentum chiral Cooper pair condensate (providing 'direct evidence' of chirality) is load-bearing, yet the abstract explicitly reports magnetic inhomogeneity specific to the apparent normal state. This raises the possibility of contributions from normal-state domains or strain effects, and the manuscript does not describe explicit spatial mapping, density-dependent controls, or subtraction procedures in the tetralayer data to isolate the superconducting contribution.
[Abstract] Abstract: The presentation of correlations between transport and magnetometry lacks quantitative details on signal magnitudes, error analysis, background subtraction methods, or how the local signal is distinguished from trapped flux or other artifacts, which are required to support the interpretation that the moment proves the chiral nature of the superconducting state.

minor comments (1)

The abstract would benefit from explicit reference to the specific figures or sections presenting the tetralayer transport-magnetometry correlation data.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments. We address the two major comments point by point below, with planned revisions to improve clarity and support for the central claims.

read point-by-point responses

Referee: [Abstract] Abstract: The central claim that the local magnetization signal correlated with zero resistance originates purely from the orbital moment of the finite-momentum chiral Cooper pair condensate (providing 'direct evidence' of chirality) is load-bearing, yet the abstract explicitly reports magnetic inhomogeneity specific to the apparent normal state. This raises the possibility of contributions from normal-state domains or strain effects, and the manuscript does not describe explicit spatial mapping, density-dependent controls, or subtraction procedures in the tetralayer data to isolate the superconducting contribution.

Authors: We agree that the reported normal-state inhomogeneity requires explicit isolation of any superconducting contribution to support the interpretation. The manuscript correlates the appearance of a uniform magnetization signal with the onset of zero resistance in the tetralayer device, and notes that this signal is absent or inhomogeneous above the transition. To strengthen this, the revised manuscript will add a dedicated subsection detailing the spatial maps acquired across the density-tuned transition, the density-dependent controls performed, and the precise subtraction procedures (including reference scans above Tc) used to isolate the superconducting-state moment from normal-state or strain-related backgrounds. revision: yes
Referee: [Abstract] Abstract: The presentation of correlations between transport and magnetometry lacks quantitative details on signal magnitudes, error analysis, background subtraction methods, or how the local signal is distinguished from trapped flux or other artifacts, which are required to support the interpretation that the moment proves the chiral nature of the superconducting state.

Authors: We concur that quantitative details are needed to robustly distinguish the observed moment from artifacts. The revised version will report the measured magnetization values (in units of Bohr magnetons per area) in the superconducting regime together with standard errors from repeated scans, describe the background subtraction protocol (including comparison to normal-state and high-temperature reference data to rule out trapped flux), and include an analysis showing that the signal magnitude and spatial uniformity are inconsistent with normal-state domain contributions or flux-trapping artifacts. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: purely experimental measurements with independent observables

full rationale

The paper reports nanoSQUID-on-tip magnetometry maps of orbital magnetization correlated against transport data in multilayer graphene devices. No derivations, ansatze, fitted parameters renamed as predictions, or self-citation load-bearing steps appear in the abstract or described methods. Central claims rest on direct spatial correlations between zero-resistance regimes and local magnetization signals, which are independent external benchmarks rather than reductions to the paper's own inputs. This matches the default expectation for experimental reports with no derivation chain.

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

Experimental paper; no free parameters, no invented entities, and only standard domain assumptions about orbital magnetism and Berry curvature.

assumptions (1)

domain assumption Zero-resistance state arises from a chiral superconductor with finite-momentum pairing
Explicitly stated as the attribution for the observed zero-resistance state.

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Cite this review

Pith. "Pith review of Visualizing orbital magnetism in electron doped rhombohedral multilayer graphene." pith.science (2026). https://pith.science/paper/INOZA4PX

@misc{pith2026260530316,
  author       = {Pith},
  title        = {Pith review of: Visualizing orbital magnetism in electron doped rhombohedral multilayer graphene},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/INOZA4PX}},
  note         = {Machine review of arXiv:2605.30316}
}

read the original abstract

Electron doped rhombohedral multilayer graphene at high displacement field features an exceptionally flat band minimum with near-ideal quantum geometry. Experiments in this regime observe the formation of a 'quarter metal,' in which the electron liquid condenses into a single spin- and valley flavor. Remarkably, recent experiments have found a zero resistance state in the same region of the density- and displacement-field-tuned parameter space, attributed to the formation of a chiral superconductor from an orbitally ferromagnetic normal state. Here, we use nanoSQUID-on-tip magnetometry to map the orbital magnetization of electron-doped rhombohedral graphene devices ranging in thickness between 3 and 15 layers. Magnetization within the quarter metal phases peaks at finite density, consistent with concentration of the Berry curvature in a finite-momentum 'ring of fire'. Correlating transport and local magnetometry data in a superconducting tetralayer sample reveals a finite orbital ferromagnetic moment, providing direct evidence of valley polarization in the superconducting ground state. We further show that widely observed stochastic switching of the resistivity in both metallic and superconducting regimes arises from a density-tuned sign change in the valley-resolved total magnetic moment. This leads to the formation of metastable magnetic domains under typical gate control sequences and can also be harnessed for electric-field controlled switching of the magnetization across the entire device. Finally, high resolution measurements of the magnetization across a superconducting transition allow us to put an upper bound on the 'condensation magnetization' of 0.1 Bohr magneton per carrier, placing a strong quantitative restriction on theoretical models for ferromagnetic superconductivity.

Figures

Figures reproduced from arXiv: 2605.30316 by the authors.

**Figure 2.** b and c show comparisons of the measured resistivity and local fringe field for T both above and below the superconducting Tc. Nonzero magnetic fringe field is observed over the extent of the zero resistance state both above and below Tc ≈ 400 mK. To confirm the ferromagnetic origin of this signal, we image the fringe field in real space at applied field of (B∥, B⊥) = (40 mT, 0.5 mT). Due to the moderate B∥, out-… view at source ↗

**Figure 3.** a shows transport measurements in a 13 layer device acquired by sweeping ne from low to high along the trajectory shown in Fig. 1b. The stochastic switching manifests via the clustering of resistivity traces into two classes which we color code yellow and blue, respectively. Blue curves appear to correspond to a metastable configuration which relaxes suddenly near ne ≈ 2.5×1012 cm−2 to the smoother trajectory defin… view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

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Forward citations

Cited by 1 Pith paper

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Magnetic Field Reorganization of Electronic States in Moir\'e Bilayer Graphene
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Magnetic fields reorganize the semiclassical electron orbits in moiré bilayer graphene, causing magnetic breakdown, valley-selective Lifshitz transitions, and electron-hole pocket scattering before the Hofstadter regime.

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Reviewed June 29, 2026 · model on record in the stance chip above.