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REVIEW 2 major objections 2 minor 21 references

A flat-band Stoner instability drives valley polarization that produces the transdimensional anomalous Hall effect in nine-layer rhombohedral graphite.

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2026-06-26 23:09 UTC pith:J5323MT7

load-bearing objection A Hartree-Fock theory ties the transdimensional Hall effect in 9-layer rhombohedral graphite to flat-band Stoner valley polarization, reproduces Tc and Rxy, and predicts a layer-number onset plus a parameter-free ratio. the 2 major comments →

arxiv 2606.17535 v1 pith:J5323MT7 submitted 2026-06-16 cond-mat.str-el

Flat-Band Stoner Instability and Peierls-Phase Origin of the Transdimensional Anomalous Hall Effect in Rhombohedral Graphite

Yang Zhou This is my paper
classification cond-mat.str-el
keywords rhombohedral graphiteanomalous Hall effectStoner instabilityvalley polarizationflat bandsHartree-FockPeierls phasetransdimensional response
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.

This paper develops a microscopic theory attributing the transdimensional anomalous Hall effect in nine-layer rhombohedral graphite to a flat-band Stoner instability. The instability satisfies the Stoner criterion and produces a spin-valley-locked ferromagnet with valley polarization that breaks time-reversal symmetry and generates intrinsic anomalous Hall conductivity. An orbital g-factor that scales with layer number allows an in-plane magnetic field to modulate the gap in proportion to the polarization, creating the transdimensional response. Self-consistent 2N-band Hartree-Fock calculations yield complete valley polarization below a mean-field transition near 2.2 K that fluctuations reduce to the observed 1.6 K, reproducing the measured Hall resistance while showing both responses arise from one order parameter.

Core claim

The flat-band density of states satisfies the Stoner criterion Uρ(ε_F) > 1, driving complete valley polarization η → 1 below a mean-field transition Tc^MF ≈ 2.2 K reduced by 2D-Ising fluctuations to the experimental Tc ≈ 1.6 K; the resulting η generates intrinsic AHC while the orbital g-factor g_orb = e d0 vF (N-1)/2 lets Bpar modulate the Peierls-phase gap proportionally to η, so both Hall signals are carried by the single order parameter.

What carries the argument

Flat-band Stoner instability coupled to Peierls-phase gap modulation, with valley polarization η as the order parameter that breaks time-reversal symmetry and enables the transdimensional response.

Load-bearing premise

The flat-band density of states in the N=9 system satisfies Uρ(ε_F) > 1 with an orbital g-factor form that allows an in-plane field to modulate the gap proportionally to the valley polarization.

What would settle it

Absence of a sharp onset of valley polarization or Hall signal between seven and nine layers in rhombohedral graphite multilayers would falsify the predicted layer-number dependence.

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

If this is right

  • Both in-plane and out-of-plane Hall responses share a single transition temperature set by the Stoner product.
  • Valley polarization exhibits a sharp onset between N=7 and N=9.
  • Symmetry selection fixes the crescent Fermi surface to the m=1 nematic channel.
  • The transdimensional-to-conventional Hall ratio equals g_orb Bpar / m and is independent of polarization and interaction strength.
  • The intrinsic anomalous Hall conductivity remains independent of layer number Z.

Where Pith is reading between the lines

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

  • The same Stoner mechanism may operate in other multilayer systems whose bands flatten near the Fermi level.
  • Layer number could serve as a tunable parameter to switch the anomalous Hall phase on or off.
  • Direct measurement of the predicted Hall ratio could test the model without separate determination of polarization.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 2 minor

Summary. The manuscript develops a microscopic theory for the recently observed transdimensional anomalous Hall effect (TDAHE) in nine-layer rhombohedral graphite. It attributes both the in-plane and out-of-plane hysteretic Hall responses to a single valley-polarization order parameter η arising from a flat-band Stoner instability (Uρ(ε_F)>1) that is coupled to Peierls-phase gap modulation. A self-consistent 2N-band Hartree-Fock calculation for N=9 produces complete valley polarization (η→1) below a mean-field transition Tc^MF≈2.2 K; this is reduced by an external 2D-Ising fluctuation correction to the experimental Tc≈1.6 K while reproducing R_xy≈1.5 kΩ. The orbital g-factor g_orb∝(N−1) enables B∥ modulation of the gap ∝η. The theory predicts a sharp onset of the polarized phase between N=7 and N=9, a symmetry selection rule for the crescent Fermi surface, and a transdimensional-to-conventional Hall ratio independent of η and U; Z-independence of the intrinsic AHC is checked with DMFT.

Significance. If the central claims hold, the work supplies a unified, largely parameter-light account of the TDAHE that ties it directly to established flat-band Stoner physics in rhombohedral graphite. Strengths include the self-consistent 2N-band Hartree-Fock treatment, the demonstration that both Hall channels share a single Tc set by the Stoner product, the DMFT verification of Z-independence, and several falsifiable predictions (N-dependence, Hall ratio, nematic channel). These elements elevate the manuscript beyond a purely phenomenological fit.

major comments (2)
  1. [Abstract] Abstract: the assertion that the exchange strength is not a fitted parameter is undercut by the requirement that U be chosen so the Stoner criterion is satisfied after the external 2D-Ising fluctuation correction is applied to match the experimental Tc=1.6 K; this introduces a partial dependence on experimental input that should be quantified in the main text.
  2. [Theory / Hartree-Fock section] Theory / Hartree-Fock section: the manuscript states that the Peierls-phase gap modulation emerges together with the Stoner instability, yet the abstract provides neither the explicit band-structure inputs nor the numerical value of U employed in the 2N-band calculation; without these it is impossible to verify that the modulation is self-consistently generated rather than inserted by hand.
minor comments (2)
  1. A compact table listing the numerical inputs (U, tight-binding parameters, orbital g-factor prefactors) and the principal outputs (Tc^MF, η(T), R_xy) would improve reproducibility and allow direct comparison with the experimental phase window.
  2. The symmetry selection rule that fixes the crescent Fermi surface to the m=1 nematic channel is stated as a prediction; a short appendix deriving the selection rule from the point-group representations would strengthen the claim.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading, the positive overall assessment, and the constructive suggestions. We address each major comment below and will revise the manuscript to improve clarity and verifiability.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the assertion that the exchange strength is not a fitted parameter is undercut by the requirement that U be chosen so the Stoner criterion is satisfied after the external 2D-Ising fluctuation correction is applied to match the experimental Tc=1.6 K; this introduces a partial dependence on experimental input that should be quantified in the main text.

    Authors: The abstract statement that 'the exchange strength is not a fitted parameter' refers specifically to the intervalley exchange, which only controls the stability of the valley-polarized phase but does not set Tc. The Hubbard U is fixed by the microscopic requirement that the Stoner product Uρ(ε_F) produce a mean-field Tc^MF ≈ 2.2 K that, after the standard 2D-Ising fluctuation correction, yields the observed Tc ≈ 1.6 K. Because ρ(ε_F) is computed directly from the known tight-binding band structure of rhombohedral graphite, this fixes U once the fluctuation factor is applied; it is therefore a constraint rather than a free fit. We nevertheless agree that the partial dependence on the experimental Tc through the fluctuation correction should be quantified explicitly, and we will add a paragraph in the main text reporting the resulting U value together with its sensitivity to the fluctuation correction. revision: yes

  2. Referee: [Theory / Hartree-Fock section] Theory / Hartree-Fock section: the manuscript states that the Peierls-phase gap modulation emerges together with the Stoner instability, yet the abstract provides neither the explicit band-structure inputs nor the numerical value of U employed in the 2N-band calculation; without these it is impossible to verify that the modulation is self-consistently generated rather than inserted by hand.

    Authors: The Theory / Hartree-Fock section of the manuscript specifies the tight-binding parameters taken from the established rhombohedral-graphite literature and presents the self-consistent 2N-band Hartree-Fock equations in which the Peierls-phase modulation is generated dynamically as a consequence of the valley-polarization order parameter η. The value of U is the unique number that satisfies the Stoner criterion for the computed flat-band density of states at N = 9. To make this verification immediate for readers, we will insert the numerical value of U and a brief statement of the band-structure inputs into the abstract (or a prominent location in the main text) in the revised version. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained

full rationale

The paper's chain begins with the flat-band DOS satisfying the externally cited Stoner criterion Uρ(ε_F)>1 from Bultinck2020, followed by a self-consistent 2N-band Hartree-Fock computation that produces η→1 below Tc^MF≈2.2 K for the N=9 system. The orbital g-factor formula is introduced as a direct consequence of the multilayer band structure and enables the Bpar modulation ∝η without redefinition. The subsequent reduction of Tc^MF to the experimental value employs a standard external 2D-Ising fluctuation correction, while the claimed insensitivity of Tc to intervalley exchange is used to argue that no exchange parameter is fitted to data. Independent predictions (N=7-to-9 onset, m=1 nematic selection, and σPHE/σAHE^tot = g_orb Bpar/m independent of η,U) follow from the same order parameter without reducing to input fits or self-citations. DMFT verification of Z-independence is an external consistency check. No quoted step equates a derived quantity to its defining input by construction, and the central claims remain independent of the present paper's fitted values.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the flat-band Stoner criterion being satisfied for N=9, the validity of the Hartree-Fock mean-field treatment for valley polarization, and the orbital g-factor expression allowing Bpar modulation; these are domain assumptions rather than derived quantities.

free parameters (2)
  • U
    Interaction strength chosen such that Uρ(ε_F) > 1 holds for the flat band; numerical value not stated but required for the instability.
  • fluctuation correction factor
    Reduction from mean-field Tc ≈ 2.2 K to experimental 1.6 K via 2D-Ising fluctuations applied to match data.
axioms (2)
  • domain assumption Flat-band density of states satisfies the Stoner criterion Uρ(ε_F) > 1
    Invoked directly to drive the spin-valley-locked ferromagnetism.
  • domain assumption Mean-field Hartree-Fock approximation plus 2D-Ising fluctuation correction accurately estimates Tc
    Used to obtain Tc^MF ≈ 2.2 K and match experiment.

pith-pipeline@v0.9.1-grok · 5978 in / 1685 out tokens · 40298 ms · 2026-06-26T23:09:11.104780+00:00 · methodology

0 comments
read the original abstract

A ``transdimensional'' anomalous Hall effect (TDAHE), where both in-plane ($\Bpar$) and out-of-plane magnetic fields produce hysteretic Hall signals, was recently observed in nine-layer rhombohedral graphite~\cite{Li2026Nature}. We present a microscopic theory attributing the TDAHE to a flat-band Stoner instability coupled to Peierls-phase gap modulation. The flat-band density of states satisfies the Stoner criterion $U\rho(\varepsilon_F) > 1$~\cite{Bultinck2020}, driving a spin-valley-locked ferromagnet whose valley polarization $\eta$ breaks time-reversal symmetry and generates an intrinsic anomalous Hall conductivity (AHC). The orbital $g$-factor $g_{\mathrm{orb}} = e d_0 v_F (N{-}1)/2 \propto (N{-}1)$ then lets $\Bpar$ modulate the gap, producing the transdimensional response $\propto \eta$. A self-consistent $2N$-band Hartree-Fock calculation yields complete valley polarization ($\eta \to 1$) below a mean-field transition $T_c^{\mathrm{MF}} \approx 2.2$~K, reduced by 2D-Ising critical fluctuations to the experimental $T_c \approx 1.6$~K, with $R_{xy} \approx 1.5$~k$\Omega$. Because both Hall responses are carried by one order parameter $\eta$, they share a single $T_c$, as observed; $T_c$ is governed by the Stoner product $U\rho$ and is insensitive to the intervalley exchange, which only gates whether the valley-polarized phase forms, so the exchange strength is not a fitted parameter. Beyond reproducing $R_{xy}$, $T_c$, and the phase window, the theory predicts a sharp onset of valley polarization between $N = 7$ and $N = 9$, a symmetry selection rule fixing the crescent Fermi surface to the $m{=}1$ nematic channel, and a transdimensional-to-conventional Hall ratio $\sigmaPHE/\sigmaAHE^{\mathrm{tot}} = g_{\mathrm{orb}}\Bpar/m$ independent of $\eta$ and $U$. The $Z$-independence of the intrinsic AHC is verified within dynamical mean-field theory.

Figures

Figures reproduced from arXiv: 2606.17535 by Yang Zhou.

Figure 1
Figure 1. Figure 1: FIG. 1. Self-consistent valley polarization [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Self-consistent valley polarization [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Localized-Ising [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Multiband ALF QMC of the 2 [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Attractive-Hubbard CDW benchmark (ALF): equal [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Spontaneous crescent Fermi surface ( [PITH_FULL_IMAGE:figures/full_fig_p016_7.png] view at source ↗

discussion (0)

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Reference graph

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