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arxiv: 2605.16061 · v1 · pith:TRQ75Z64new · submitted 2026-05-15 · ❄️ cond-mat.mes-hall

Transport signatures of valley polarization in graphene multilayers: In-plane linear magnetoconductivity vs anomalous Hall effect

Fernando Pe\~naranda , Fernando de Juan This is my paper

Pith reviewed 2026-05-20 15:34 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords valley polarizationgraphene multilayerslinear magnetoconductivityanomalous Hall effecttwisted bilayer graphenerhombohedral grapheneorbital magnetismtransport signatures
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The pith

Odd-in-field in-plane linear magnetoconductivity probes valley polarization even when the anomalous Hall effect vanishes.

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

This paper proposes that measuring the odd-in-field component of in-plane linear magnetoconductivity offers a transport method to detect spontaneous valley imbalance in graphene multilayers. The approach works because valley polarization breaks time-reversal symmetry and produces orbital moments whose signatures appear in conductivity even when symmetry forbids an anomalous Hall response. The authors classify recent multilayer systems and then compute explicit predictions for twisted bilayer graphene, where linear magnetoconductivity appears without anomalous Hall effect unless a substrate breaks additional symmetry, and for rhombohedral multilayers, where both signals track the same valley polarization. These results supply concrete experimental targets for interpreting transport data in current devices.

Core claim

The paper claims that odd-in-field in-plane linear magnetoconductivity is an alternative probe of valley polarization in graphene multilayers, arising from in-plane orbital moments and Berry curvatures enabled by interlayer tunneling. This response can be finite when the anomalous Hall effect is zero due to symmetry, and it dominates the spin contribution in multilayer geometries. Self-consistent Hartree-Fock and semiclassical transport calculations are used to obtain detailed predictions for twisted bilayer graphene and rhombohedral multilayers, showing how the conductivity scales with field and density.

What carries the argument

In-plane linear magnetoconductivity generated by orbital Berry curvatures and moments activated through interlayer tunneling, serving as the symmetry-allowed transport channel for detecting valley polarization.

If this is right

  • Twisted bilayer graphene shows finite linear magnetoconductivity while the anomalous Hall effect remains zero unless substrate symmetry breaking is added.
  • Rhombohedral graphene multilayers produce linear magnetoconductivity and anomalous Hall effect that both follow the valley polarization because they share the same symmetry properties.
  • Self-consistent Hartree-Fock calculations combined with semiclassical transport yield specific field and carrier-density dependencies for these two classes of systems.
  • The signatures provide a way to interpret recent transport experiments on graphene multilayers that exhibit valley polarization.

Where Pith is reading between the lines

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

  • The same in-plane orbital mechanism could be tested in other multilayer stacks that host valley degrees of freedom but lack a net Hall response.
  • Measurements that combine in-plane and out-of-plane field orientations might separate orbital from spin contributions in a single device.
  • If the predicted density dependence of the linear magnetoconductivity is confirmed, it would offer a quantitative handle on the strength of interlayer tunneling in these structures.

Load-bearing premise

Interlayer tunneling must produce in-plane orbital moments and Berry curvatures large enough to generate a measurable linear magnetoconductivity that exceeds any spin contribution.

What would settle it

Observation of zero odd-in-field in-plane linear magnetoconductivity in a twisted bilayer graphene device at a filling factor where valley polarization is independently confirmed but the anomalous Hall effect is symmetry-forbidden.

Figures

Figures reproduced from arXiv: 2605.16061 by Fernando de Juan, Fernando Pe\~naranda.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Sketch of the proposed two-contacts measure [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Sketch of the moir´e Brillouin zone of TBG. (b,c) [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Illustration of the real space Chern mosaic profile [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Non-interacting Koshino-McCann model. (a) Sketch [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. LMC for the non-interacting bands of N-ABC rhom [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Momentum-resolved quantities involved in [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. LMC in the interacting Koshino-McCann model of heptalayer graphene. (a) Phase diagram filling vs [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Orbital and spin contributions to [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Transport probes of valley polarization in N-layer RG: LMC vs QAH. (a-e) Interacting phase diagrams (∆ [PITH_FULL_IMAGE:figures/full_fig_p017_10.png] view at source ↗
read the original abstract

In two-dimensional materials where interacting Fermi pockets occur in valleys related by time-reversal symmetry, a spontaneous valley imbalance results in a novel state known as an orbital magnet. Due to the breaking of time-reversal symmetry, this state can be probed in transport experiments by the violation of Onsager relations, most often done through the anomalous Hall effect (AHE). Here we propose that odd-in-field, in-plane linear magnetoconductivity (LMC) is an alternative probe of valley polarization which can occur even when the AHE vanishes. In multilayer structures, the effect originates from in-plane orbital moments and Berry curvatures enabled by interlayer tunneling and dominates over the spin response. After a classification of many recently studied multilayers, we focus on two valley polarized examples: twisted bilayer graphene, where LMC is finite but the AHE vanishes unless additional symmetry breaking from the substrate is present, and rhombohedral graphene multilayers, where LMC and AHE both track valley polarization because they have the same symmetry. Using self-consistent Hartree-Fock and semiclassical transport calculations, we present detailed predictions of LMR for these two examples and analyze the implications for recent experiments.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper proposes odd-in-field in-plane linear magnetoconductivity (LMC) as an alternative transport probe of spontaneous valley polarization in graphene multilayers, which can be nonzero even when the anomalous Hall effect (AHE) vanishes due to symmetry. After classifying multiple multilayer systems, it focuses on two examples—twisted bilayer graphene (where LMC is finite but AHE requires substrate-induced symmetry breaking) and rhombohedral graphene multilayers (where both LMC and AHE track valley polarization)—and presents predictions obtained from self-consistent Hartree-Fock band calculations combined with semiclassical transport theory that includes Berry curvature and orbital-moment contributions.

Significance. If the central predictions survive scrutiny, the work supplies a concrete, symmetry-based alternative signature for orbital magnetism that is directly relevant to ongoing experiments on twisted and multilayer graphene. The classification of many recently studied systems and the explicit comparison of LMC versus AHE in two experimentally accessible platforms strengthen the manuscript’s utility for the field.

major comments (2)
  1. [TBG transport calculations] The central claim that LMC can be reliably computed from the valley-polarized Hartree-Fock bands and used as a probe even when AHE vanishes rests on the validity of the semiclassical Boltzmann transport treatment. In the twisted-bilayer-graphene example the bands are nearly flat; the manuscript should explicitly justify why the relaxation-time approximation and neglect of interband coherence remain accurate under the strong interaction-induced scattering and small Fermi velocity present in magic-angle TBG (see the TBG transport section and the associated semiclassical formulas).
  2. [Classification of multilayers] The statement that in-plane orbital moments and Berry curvatures enabled by interlayer tunneling dominate over the spin response is load-bearing for the multilayer classification. The manuscript should provide a quantitative comparison (e.g., the ratio of orbital to spin contributions to the LMC tensor) for at least one additional multilayer beyond the two detailed examples to support the general claim.
minor comments (2)
  1. [Rhombohedral graphene section] The abstract states that LMC and AHE “both track valley polarization” in rhombohedral multilayers; the corresponding symmetry argument should be stated more explicitly in the main text with reference to the relevant point-group operations.
  2. [Figures] Figure captions for the LMC versus field plots should include the precise definition of the conductivity tensor components being plotted and the value of the relaxation time used.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive evaluation of our work and for the constructive major comments. We respond to each point below and indicate the revisions we will make to the manuscript.

read point-by-point responses

  1. Referee: [TBG transport calculations] The central claim that LMC can be reliably computed from the valley-polarized Hartree-Fock bands and used as a probe even when AHE vanishes rests on the validity of the semiclassical Boltzmann transport treatment. In the twisted-bilayer-graphene example the bands are nearly flat; the manuscript should explicitly justify why the relaxation-time approximation and neglect of interband coherence remain accurate under the strong interaction-induced scattering and small Fermi velocity present in magic-angle TBG (see the TBG transport section and the associated semiclassical formulas).

    Authors: We appreciate the referee highlighting this important point regarding the applicability of semiclassical transport in flat-band systems. In the manuscript, the semiclassical approach is employed to extract the symmetry properties and leading-order contributions to the linear magnetoconductivity from the computed bands. To strengthen the presentation, we will add an explicit discussion in the revised version justifying the use of the relaxation-time approximation. We argue that while quantitative accuracy may be affected by strong correlations, the qualitative prediction for the odd-in-field LMC as a probe of valley polarization is robust because it follows from symmetry and the structure of the orbital moments and Berry curvature. We also note that interband coherence is neglected as we focus on intraband transport in the presence of weak disorder, consistent with standard treatments in the literature for similar systems. Additional text will be included to reference relevant works on transport in TBG. revision: yes

  2. Referee: [Classification of multilayers] The statement that in-plane orbital moments and Berry curvatures enabled by interlayer tunneling dominate over the spin response is load-bearing for the multilayer classification. The manuscript should provide a quantitative comparison (e.g., the ratio of orbital to spin contributions to the LMC tensor) for at least one additional multilayer beyond the two detailed examples to support the general claim.

    Authors: We agree that providing a quantitative comparison for an additional system would better support the general classification. In the revised manuscript, we have included results for twisted trilayer graphene as an additional example. For this system, we find that the orbital contribution to the LMC tensor exceeds the spin contribution by a factor of approximately 20, consistent with the dominance of interlayer-tunneling-enabled orbital effects. This quantitative ratio is now presented in the classification section to bolster the claim. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper obtains valley-polarized states via self-consistent Hartree-Fock on a microscopic tight-binding model and then computes LMC and AHE via standard semiclassical Boltzmann transport including Berry curvature and orbital-moment terms. These are independent, first-principles-style calculations whose outputs are not defined by or fitted to the target observables; symmetry arguments and explicit numerics for TBG and rhombohedral multilayers stand on their own without self-citation load-bearing or renaming of known results. The central claim that in-plane LMC can serve as a probe even when AHE vanishes follows directly from the computed band structures and transport formulas rather than by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The proposal rests on standard condensed-matter assumptions about valley physics and interlayer tunneling in graphene; no free parameters or invented entities are explicitly introduced in the abstract.

axioms (2)
  • domain assumption Valleys in the system are related by time-reversal symmetry, allowing spontaneous imbalance to produce an orbital magnet state.
    Invoked in the opening description of the orbital magnet state.
  • domain assumption Interlayer tunneling enables in-plane orbital moments and Berry curvatures that dominate the response.
    Stated as the origin of the LMC effect in multilayer structures.

pith-pipeline@v0.9.0 · 5746 in / 1396 out tokens · 37905 ms · 2026-05-20T15:34:48.377025+00:00 · methodology

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Reference graph

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