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arxiv: 2505.24632 · v2 · submitted 2025-05-30 · ❄️ cond-mat.mes-hall · cond-mat.mtrl-sci

Weak localization as probe of spin-orbit-induced spin-split bands in bilayer graphene proximity coupled to WSe₂

E. Icking , F. W\"ortche , A.W. Cummings , A. W\"ortche , K. Watanabe , T. Taniguchi , C. Volk , B. Beschoten
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C. Stampfer
This is my paper

Pith reviewed 2026-05-19 13:16 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.mtrl-sci
keywords bilayer graphenespin-orbit couplingweak localizationweak anti-localizationproximity effectWSe2Rashba SOCspintronics
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The pith

In bilayer graphene on WSe2, weak localization at low hole densities signals transport through one spin-split valence band.

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

The paper establishes that proximity coupling to WSe2 induces a tunable Rashba-type spin-orbit gap in bilayer graphene that splits the valence bands. In high-quality double-gated devices operating in the quasi-ballistic regime, magnetotransport shows clear weak anti-localization at higher densities but switches to weak localization once the Fermi level enters only the lower spin-split band. This density-driven crossover supplies spectroscopic evidence that the induced spin-orbit coupling has opened a gap between the two spin branches. A sympathetic reader would care because the result demonstrates a practical way to engineer spin-polarized bands in graphene while retaining its high mobility and gate control.

Core claim

In bilayer graphene proximity-coupled to WSe2, the transition from weak anti-localization to weak localization at lower hole densities demonstrates that carriers move through a single spin-split valence band, confirming the presence of a proximity-induced spin-orbit gap whose size is consistent with Rashba-model calculations.

What carries the argument

Weak localization (WL) as a density-tuned probe that distinguishes transport in one spin-split band from multi-band or anti-localization regimes.

If this is right

  • Gate voltage can select which spin-split band carries current, enabling spin-polarized transport without external magnets.
  • The same heterostructure platform supports gate-defined p-n-p cavities that preserve the spin-orbit features.
  • The induced gap size can be read out directly from the WL-WAL crossover density.
  • Bilayer graphene/TMD stacks become viable for spin-based quantum devices that keep graphene's high mobility.

Where Pith is reading between the lines

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

  • Similar WL signatures could appear in other graphene/TMD combinations if the proximity gap exceeds the Fermi energy window set by disorder.
  • The technique offers a transport-based alternative to ARPES for mapping spin-split bands in encapsulated 2D stacks.
  • Extending the density range further might reveal the point where the upper spin band begins to contribute again.

Load-bearing premise

The weak localization features arise solely from single-band spin-split transport under the Rashba model, with negligible intervalley scattering or multi-band contributions.

What would settle it

Observation of weak localization persisting at densities where both spin-split bands are occupied, or mismatch between the measured crossover density and the calculated spin-orbit gap energy.

Figures

Figures reproduced from arXiv: 2505.24632 by A.W. Cummings, A. W\"ortche, B. Beschoten, C. Stampfer, C. Volk, E. Icking, F. W\"ortche, K. Watanabe, T. Taniguchi.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: c. In this type of measurement, the appearance of a diamond-shaped region of suppressed conductance is the hallmark of the opening of a clean band gap in BLG [37, 40]. The edges of the region of suppressed con￾ductance correspond to the situation in which the electro￾chemical potential in the leads is aligned with the band edges in the double-gated region [37, 40]. For perfectly clean band gaps, the edges … view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Conductance as a function of [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
read the original abstract

Proximity coupling of bilayer graphene (BLG) to transition metal dichalcogenides (TMDs) offers a promising route to engineer gate-tunable spin-orbit coupling (SOC) while preserving BLG's exceptional electronic properties. This tunability arises from the layer-asymmetric electronic structure of gapped BLG, where SOC acts predominantly on the layer in contact with the TMD. Here, we present high-quality BLG/WSe$_2$ devices with a proximity-induced SOC gap and excellent electrostatic control. Operating in a quasi-ballistic regime, our double-gated heterostructures allow to form gate-defined p-n-p cavities and show clear weak anti-localization (WAL) features consistent with Rashba-type SOC. At lower hole densities, a transition to weak localization (WL) is observed, signaling transport through a single spin-split valence band. These findings - in agreement with calculations - provide direct spectroscopic evidence of proximity-induced spin-split band in BLG and underscore the potential of BLG/TMD heterostructures for spintronics and spin-based quantum technologies.

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

1 major / 2 minor

Summary. The manuscript reports magnetotransport measurements on double-gated BLG/WSe₂ heterostructures operating in the quasi-ballistic regime. Gate-defined p-n-p cavities exhibit clear weak anti-localization (WAL) features interpreted as consistent with Rashba-type proximity-induced SOC. At lower hole densities a crossover to weak localization (WL) is observed and attributed to transport through a single spin-split valence band, providing spectroscopic evidence for the proximity-induced spin splitting.

Significance. If the WL-to-WAL crossover can be uniquely tied to single-band occupation under the Rashba model, the work supplies a transport-based spectroscopic probe of gate-tunable spin-split bands in BLG/TMD stacks. The quasi-ballistic cavity geometry and electrostatic control are positive features that could enable future spintronic or quantum-device applications.

major comments (1)
  1. [Abstract] Abstract and implied results section: the central claim that the observed WL feature signals transport through a single spin-split valence band requires that intervalley scattering and density-dependent disorder variations are negligible. The manuscript does not appear to report quantitative bounds on the intervalley scattering time or explicit comparisons to control devices without TMD; without these, the attribution remains vulnerable to alternative explanations that can produce WL even in the absence of spin splitting.
minor comments (2)
  1. [Abstract] The abstract states agreement with calculations but does not specify which quantities (e.g., SOC gap size, crossover density) are compared or whether error bars are included in the data.
  2. Full device characterization (mobility, mean-free path, cavity dimensions) and raw magnetoconductance traces with error bars should be provided to allow independent assessment of the quasi-ballistic regime.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting the need to strengthen the attribution of the observed WL-to-WAL crossover. We address the major comment in detail below and outline the revisions we will make.

read point-by-point responses

  1. Referee: [Abstract] Abstract and implied results section: the central claim that the observed WL feature signals transport through a single spin-split valence band requires that intervalley scattering and density-dependent disorder variations are negligible. The manuscript does not appear to report quantitative bounds on the intervalley scattering time or explicit comparisons to control devices without TMD; without these, the attribution remains vulnerable to alternative explanations that can produce WL even in the absence of spin splitting.

    Authors: We agree that the manuscript would benefit from more explicit discussion of intervalley scattering and from reference to control experiments. In the quasi-ballistic p-n-p cavities the WAL amplitude at higher densities already implies that intervalley scattering is not dominant on the scale of the phase coherence length; we will add a quantitative estimate of the intervalley scattering time extracted from the WAL fits and from the density dependence of the crossover point. The observed transition occurs precisely at the hole density where our self-consistent calculations place the Fermi level at the edge of the lower spin-split valence band, and this density dependence is difficult to reproduce by disorder variations alone. While we do not include new control-device data in the present work, the WAL signature is absent in comparable BLG devices without TMD proximity (as reported in the literature), and we will expand the discussion section to include direct comparison with those results. These additions will be incorporated in the revised manuscript. revision: partial

Circularity Check

0 steps flagged

No significant circularity; experimental data interpreted via standard SOC models

full rationale

The paper reports magnetotransport measurements in double-gated BLG/WSe2 heterostructures, documenting a WAL-to-WL crossover at lower hole densities. This is compared to established Rashba SOC weak-localization theory and calculations without any self-definitional reduction, fitted-parameter-as-prediction, or load-bearing self-citation chain. The central spectroscopic claim rests on direct comparison of observed features to independent theoretical expectations rather than re-deriving or renaming inputs by construction. No equations or steps in the provided text reduce the attribution to a tautology or prior author result invoked as uniqueness theorem.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The interpretation relies on standard mesoscopic transport theory for systems with Rashba SOC and the assumption that proximity coupling acts predominantly on the contacted layer; no new free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Weak localization/anti-localization formulas for Rashba SOC remain valid in the quasi-ballistic regime of the p-n-p cavity.
    Invoked to link observed magnetoresistance features to spin splitting.

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