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Transdimensional anomalous Hall effect in rhombohedral thin graphite

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Nine-layer rhombohedral graphene shows a Hall effect driven by in-plane orbital magnetization, breaking the rule that Hall fields require magnetization perpendicular to current.

desk verdict A bold in-plane magnetization claim in rhombohedral graphene that lacks the field-alignment calibration needed to rule out a tilt-induced artifact. read the letter →

arxiv 2505.03891 v1 pith:TFTID6BW submitted 2025-05-06 cond-mat.mes-hall cond-mat.str-el

Qingxin Li , Hua Fan , Min Li , Yinghai Xu , Junwei Song , Kenji Watanabe , Takashi Taniguchi , Hua Jiang
show 6 more authors
X. C. Xie James Hone Cory Dean Yue Zhao Jianpeng Liu Lei Wang
This is my paper · ORCID
classification cond-mat.mes-hallcond-mat.str-el
keywords transdimensionalanomalousHalleffectrhombohedralgraphenein-planeorbitalmagnetizationferromagnetismspontaneoussymmetrybreakingHartree-FockcalculationvanHovesingularitycorrelatedmetal
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 the first observation of a transdimensional anomalous Hall effect in electrostatically gated rhombohedral ennealayer graphene, a nine-layer stack about three nanometres thick. The central claim is that a correlated metallic phase near the van Hove singularity breaks time-reversal, mirror, and rotational symmetries on its own, allowing electrons to sustain coherent orbital motion both in the plane and across the thickness. The result is a coexistence of out-of-plane and in-plane orbital magnetizations, seen as magnetic hysteresis in the Hall resistance for magnetic fields along both directions. If the interpretation holds, the standard rule that the Hall field must be perpendicular to both current and magnetization, $\mathbf{E}_H \propto \mathbf{J} \times \mathbf{M}$, is violated by a genuinely new class of anomalous Hall effect that needs no spin-orbit coupling.

What carries the argument

The load-bearing object is the transdimensional orbital loop: the sample is thick enough ($d\approx 3$ nm) to host out-of-plane electron motion, yet thin enough that the vertical mean free path $\ell_z$ is not interrupted by scattering, so current loops can close both in the plane and through the thickness. In the correlated phase, the machinery that produces the effect is spontaneous symmetry breaking driven by long-range electron-electron interactions, treated by unrestricted Hartree-Fock theory. The calculation finds that the system breaks time-reversal, threefold rotation $C_3$, and vertical mirror $M_y$ symmetries, turning a ring-shaped Fermi surface into a crescent-shaped one whose Bloch states carry orbital magnetization parallel to the current. That in-plane orbital magnetization couples directly to an in-plane magnetic field and yields the parallel Hall hysteresis, while the coexisting out-of-plane orbital magnetization gives the perpendicular hysteresis.

What would settle it

Run the same hysteresis sweeps with the field direction calibrated in situ (for example, rotating the sample in a vector magnet to better than 0.1 degrees): if the parallel hysteresis weakens or vanishes as residual perpendicular field is removed, or tracks the perpendicular component at all tilt angles, the transdimensional claim is falsified. A second check is to measure the vertical mean free path directly, through a thickness series or magnetotransport analysis, to verify the premise that $\ell_z$ exceeds the 3 nm thickness.

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Extended reading notes

Core claim

On the paper's own terms, the discovery is that in a narrow region of density and displacement field -- the phase labelled V, flanked by quarter-metal and partial-isospin-polarized phases -- the device shows robust magnetic hysteresis in both the perpendicular and the parallel field directions. The perpendicular hysteresis has a coercive field near 3 mT and is assigned to Stoner-type isospin ferromagnetism; the parallel hysteresis, with coercive fields between 160 and 500 mT, is assigned to the switching of an in-plane orbital magnetization arising from coherent out-of-plane electron loops. Because the measurement current lies in the plane, an in-plane orbital magnetization parallel to the current makes the observed Hall field incompatible with the conventional orthogonality relation. Unrestricted Hartree-Fock calculations support this assignment: interactions spontaneously break the threefold rotation and vertical mirror symmetries, producing a crescent-shaped, fully spin- and valley-polarized Fermi surface with an in-plane orbital magnetization of order $2.2\,\mu_B$ per electron, and no spin-orbit coupling in the model.

Load-bearing premise

The central claim collapses if the parallel-field hysteresis is a misalignment artifact -- the paper gives no in-situ alignment calibration, and a one-degree tilt at 160 mT produces a perpendicular component equal to the measured out-of-plane coercive field -- and it also depends on the vertical mean free path exceeding the three-nanometre sample thickness, a quantity the paper does not measure.

Editorial extensions

If this is right

  • The anomalous Hall effect can no longer be classified only by out-of-plane orbital magnetization: a material with in-plane orbital magnetization can produce a Hall voltage even when the magnetization is parallel to the current.
  • The TDAHE phase resists Landau quantization up to at least 13 T, so it represents a strongly correlated metallic ground state rather than a quantum Hall or Chern insulator.
  • The effect survives to temperatures near 1.5 K and vanishes sharply by 1.6 K, implying an interaction energy scale that is substantial for a purely orbital, SOC-free state.
  • Magnetization reversal with doping at the quarter-metal boundary offers a route to electrically switch the sign of the in-plane orbital magnetization within a metallic phase, without an insulating topological gap.

Reading between the lines

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

  • Editorial extension: if the alignment issue is resolved and the in-plane hysteresis is real, the same transdimensional mechanism should appear in other rhombohedral multilayer stacks whose thickness lies between one monolayer and the vertical mean free path, with the phase boundary set by the displacement field.
  • Editorial extension: the spontaneous symmetry breaking is purely orbital and needs no spin-orbit coupling, so placing a moiré superlattice on such a transdimensional state is a plausible route to quantized transdimensional anomalous Hall phases; the paper only mentions this as a future direction.
  • Editorial extension: the sharp collapse above 1.6 K could be dominated by the vertical mean free path shortening rather than thermal domain-wall dynamics; a thickness series of devices would separate the two mechanisms.
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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 reports the observation of a 'transdimensional anomalous Hall effect' (TDAHE) in electrostatically gated rhombohedral ennealayer graphene. The authors identify a correlated metallic phase (phase V) at low carrier density and large displacement field that shows no Shubnikov-de Haas oscillations up to 13 T. In this phase, Hall resistance hysteresis loops are observed for both out-of-plane and in-plane magnetic field sweeps (Fig. 3b, d). The in-plane hysteresis, with a coercive field of about 160 mT, is attributed to an in-plane orbital magnetization My arising from coherent out-of-plane electron motion in the 'transdimensional' regime where the sample thickness (~3 nm) is within the vertical mean free path. Unrestricted Hartree-Fock calculations predict a symmetry-broken metallic state with a crescent-shaped Fermi surface, spontaneous breaking of time-reversal, C3, and mirror symmetries, and an in-plane orbital magnetization of about 2.2 mu_B per electron. The authors argue that this constitutes a fundamentally new class of anomalous Hall effect that violates the conventional orthogonality rule E_H ∝ J x M.

Significance. If the claims are correct, the work is significant: it would introduce a new type of anomalous Hall effect driven by in-plane orbital magnetization, expanding the classification of Hall effects and opening a new direction in correlated-electron physics in rhombohedral graphene multilayers. The paper includes two devices, comprehensive density-displacement-field phase diagrams, quantum oscillation analysis, and a concrete theoretical mechanism. The experimental data are reproducible across devices (Extended Data Fig. 9). However, the central experimental evidence—the B-parallel hysteresis—is not convincingly separated from a likely artifact of field misalignment, and the 'transdimensional' interpretation lacks direct support for the assumed vertical mean free path. The Hartree-Fock theory provides a plausible but post-hoc and parameter-dependent scenario.

major comments (3)
  1. [Transdimensional anomalous Hall state (Fig. 3b, 3d) and Methods] The claim that the B-parallel hysteresis evidences in-plane orbital magnetization rests on the assumption that the applied field is essentially in the sample plane. The paper does not report any calibration of the sample angle relative to the magnetic field, nor does it state whether the magnets are vector magnets or have in-situ rotation capability. At the quoted in-plane coercive field of about 160 mT, a misalignment of only about 1 degree produces a perpendicular component of about 2.8 mT, which is essentially the same as the out-of-plane coercive field of about 3 mT shown in Fig. 3d. Since phase V also exhibits out-of-plane Stoner-type hysteresis, a tilt-induced perpendicular component would generate a hysteresis loop in the B-parallel sweep that mimics the claimed in-plane magnetization. The antisymmetrization procedure described in the Methods does not remove this artifact, because the tilt-induced perpendicular component reverses sign when the nominally in-plane field reverses, and the hysteresis is odd under that reversal. The authors should provide a control measurement (e.g., a phase with out-of-plane magnetization but no in-plane magnetization, or a measurement with active compensation of the perpendicular component) and a quantitative angular calibration. Without this, the central observation is not established.
  2. [Discussion and Extended Data Fig. 1d] The term 'transdimensional' and the interpretation of the in-plane orbital magnetization require that the vertical mean free path lz be comparable to or larger than the sample thickness d ~ 3 nm. The paper asserts that d falls in the transdimensional range ('providentially within the transdimensional range') but no measurement or estimate of lz is given. Without evidence that coherent out-of-plane orbital motion survives across the thickness, the connection between the observed hysteresis and out-of-plane orbital currents is unjustified. The authors should provide an estimate of lz from the quantum oscillation lifetime or from a thickness-dependence study, or clearly state that the 'transdimensional' interpretation is one of several possibilities.
  3. [Supplementary Section III (Hartree-Fock treatment) and Fig. 4d] The theoretical prediction of the crescent-shaped Fermi surface and the in-plane orbital magnetization relies on parameter renormalization that involves several free inputs (epsilon_BN ~ 4, ds = 40 nm, E*_C ~ 0.3 eV, Lc = 2.25 nm). The paper does not discuss the sensitivity of the predicted orbital magnetization and the stability of the symmetry-broken state to these parameters. Additionally, the theory is presented as a post-hoc explanation (with a separate manuscript in preparation, ref. 37), so it cannot by itself disambiguate the experimental artifact discussed above. I recommend that the authors report the parameter region in which the crescent state is stable and compare the predicted anomalous Hall conductivity with the measured Rxy.
minor comments (5)
  1. [Methods] The sentence 'using a anodic-oxidation-assisted atomic force microscope cutting' contains an article error; it should read 'using anodic-oxidation-assisted atomic force microscope cutting'.
  2. [Extended Data Fig. 9 caption] The caption lists labels 'c' and 'd' twice; the figure appears to show B-parallel hysteresis (b), B-perpendicular hysteresis (c), and maps (d, e), so the labels should be corrected.
  3. [Fig. 3g] The list of densities 'n = 0.8, 1.1, 1.4, 17, 1.9' likely contains a typo: '17' should probably be '1.7'.
  4. [Introduction] The compound formula 'EuCd 2Sd2' appears to be a typo; it should be 'EuCd2As2' or another correct chemical formula.
  5. [General] Abbreviations such as SdH, PIP, and LPI are used without definitions at first appearance; please define them in the main text.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the TDAHE observation is independently measured and the Hartree-Fock state is a self-contained postdiction; self-citations are not load-bearing.

full rationale

The paper's central claim is experimental: phase V of 9-layer rhombohedral graphene shows antisymmetrized Hall resistance hysteresis under both B_perp and B_parallel sweeps (Fig. 3b,d; Extended Data Fig. 9b). This observation does not depend on the theory in Fig. 4d, so the interpretation is not constructed from the fitted inputs. The Hartree-Fock calculation is a self-consistent postdiction with stated inputs (Slater-Koster continuum model, double-gate screened Coulomb interaction, 32 initial symmetry-breaking seeds) and outputs a crescent Fermi surface with in-plane orbital magnetization; no parameter is fitted to the measured hysteresis. The only self-references are (i) SI Eq. S7, which 'adopt[s] the established expressions for renormalized low-energy parameters ... following the comprehensive analysis presented in Refs. 43' (same-group PRB paper), and (ii) the pointer 'More detailed mechanism and properties of transdimensional orbital magnetism will be reported in a separate theoretical work[37]'. Neither is load-bearing in a circular sense: the RG formulas are standard perturbative results with stated assumptions and are not tuned to the target state, and Ref. [37] is explicitly deferred rather than used as evidence. The absence of an in-situ B_parallel alignment calibration is a real experimental-control concern (a ~1-degree tilt would create a B_perp comparable to the 3 mT coercive field), but that is a validity risk, not a derivation that reduces to its own inputs. No step satisfies the quote-and-reduce standard for circularity.

Assumptions & free parameters 4 free parameters · 5 assumptions · 2 invented entities

The theoretical model rests on several modeling choices (dielectric constant, hBN thickness, energy windows, momentum cutoff) and on assumed physics (Coulomb-dominated interactions, RG renormalization from Ref [43], neglect of intervalley terms). The physical interpretation additionally assumes a long vertical mean free path and perfect in-plane field alignment. None of these are fitted to the TDAHE data, but the phase boundaries and the existence of the crescent Fermi surface are sensitive to them, and the strongest claim relies on the unverified alignment assumption.

free parameters (4)
  • relative dielectric constant of hBN, epsilon_BN = 4
    Used in the screened Coulomb interaction in the supplementary Hartree-Fock calculation. Chosen from literature, not fitted to this experiment, but affects the phase boundaries and orbital magnetization magnitude.
  • hBN thickness ds = 40 nm
    Set throughout the double-gate screened Coulomb potential V_dg(q). No sensitivity analysis is provided.
  • low-energy window E*_C = 0.3 eV
    Defines the energy window for the Hartree-Fock projection and the renormalization of single-particle parameters. This choice affects interaction strength and phase boundaries.
  • momentum space cutoff Lc = 2.25 nm
    Sets the momentum cutoff pi/Lc in the continuum model, corresponding to an energy cutoff of about 1 eV. Alters the non-interacting band structure and interaction matrix elements.
assumptions (5)
  • domain assumption The vertical mean free path lz exceeds the 3 nm thickness of the 9-layer flake in the TDAHE phase.
    The transdimensional scenario requires coherent out-of-plane orbital motion across the full thickness. The paper never measures lz or provides evidence for weak interlayer scattering (Introduction, Fig. 1a).
  • domain assumption The nominally parallel magnetic field B_parallel has a negligible out-of-plane component during the parallel-field sweeps.
    The B_parallel-induced hysteresis is interpreted as in-plane magnetization switching, but a misalignment of order 1 degree would generate a perpendicular component comparable to the out-of-plane coercive field at B_parallel = 160 mT (Fig. 3b-e, Methods).
  • domain assumption Long-range intravalley Coulomb interactions dominate the low-energy physics; on-site Hubbard and intervalley terms are negligible.
    Supplementary Section III estimates these terms are small at n ~ 10^12 cm^-2, but this assumption defines the model and excludes other possible interaction channels.
  • domain assumption The renormalization group formulas for vF and t_perp from Ref [43] apply to 9-layer rhombohedral graphene.
    Equations S7a-S7c are adopted from a paper by the same theory group; no independent experimental benchmark for 9-layer RG is given in this work.
  • domain assumption The 32 order-parameter ansatz in the unrestricted Hartree-Fock calculation spans the relevant broken-symmetry ground states.
    Supplementary Section III restricts to trial states of the form tau^a sigma^b s^{0,z}; other symmetry breakings such as intervalley coherence are not explored.
invented entities (2)
  • Transdimensional orbital ferromagnetic state
    purpose: Explains phase V as a metallic state with a crescent Fermi surface and coexisting in-plane and out-of-plane orbital magnetizations.
    Predicted by Hartree-Fock in this paper; the only experimental evidence is the same transport hysteresis used to infer it, and the detailed theory is in an unpublished same-group manuscript [37].
  • In-plane orbital magnetization My
    purpose: The proposed new type of orbital magnetization parallel to the current that produces a Hall signal in the transdimensional regime.
    No direct magnetization measurement is reported; it is inferred from B_parallel hysteresis, which could also arise from a perpendicular field component due to magnet misalignment.

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Cite this review

Pith. "Pith review of Transdimensional anomalous Hall effect in rhombohedral thin graphite." pith.science (2026). https://pith.science/paper/TFTID6BW

@misc{pith2026250503891,
  author       = {Pith},
  title        = {Pith review of: Transdimensional anomalous Hall effect in rhombohedral thin graphite},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TFTID6BW}},
  note         = {Machine review of arXiv:2505.03891}
}
read the original abstract

Anomalous Hall effect (AHE), occurring in materials with broken time-reversal symmetry, epitomizes the intricate interplay between magnetic order and orbital motions of electrons[1-4]. In two dimensional (2D) systems, AHE is always coupled with out-of-plane orbital magnetization associated in-plane chiral orbital motions. In three dimensional (3D) systems, carriers can tunnel or scatter along the third dimension within the vertical mean free path lz. When sample thickness far exceeds lz, scattering disrupts coherent out-of-plane motion, making 3D AHE effectively a thickness-averaged 2D counterpart[4] -- still governed by out-of-plane orbital magnetization arising from in-plane orbital motions. Here, we explore an uncharted regime where the sample thickness is much larger than the atomic layer thickness yet smaller than or comparable to lz. In such "transdimensional" regime, carriers can sustain coherent orbital motions both within and out of the 2D plane, leading to a fundamentally new type of AHE that couples both out-of-plane and in-plane orbital magnetizations. We report the first observation of such phenomenon -- transdimensional AHE (TDAHE) -- in electrostatically gated rhombohedral ennealayer graphene. This state emerges from a peculiar metallic phase that spontaneously breaks time-reversal, mirror and rotational symmetries driven by electron-electron interactions. Such TDAHE manifests as concurrent out-of-plane and in-plane Hall resistance hysteresis, controlled by external magnetic fields along either direction. Our findings unveils a new class of AHE, opening an unexplored paradigm for correlated and topological physics in transdimensional systems.

Figures

Figures reproduced from arXiv: 2505.03891 by the authors.

Figure 9
Figure 9. We note that finite couplings between longitudinal and transverse directions would mix Rxx and Rxy signals. According to that Rxy is antisymmetric with respect to magnetic field B, whereas Rxx is symmetric, we can separate the two components using standard symmetrization and anti￾symmetrization procedures during the data processing. The symmetrization procedure for Rxx is as follows: R sym xx (B, ↑) = ((Rxx(B, ↑)+Rx… view at source ↗

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  1. Fermi lune and transdimensional orbital magnetism in rhombohedral multilayer graphene

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    Electron-electron interactions in slightly doped rhombohedral multilayer graphene are predicted to create a time-reversal-breaking Fermi surface shaped like a crescent (the Fermi lune), giving large non-reciprocal res...

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Reviewed August 15, 2026 · model on record in the stance chip above.