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arxiv: 2606.14878 · v2 · pith:44NHRM65new · submitted 2026-06-12 · ❄️ cond-mat.mes-hall · cond-mat.supr-con

Valley Valves at Domain Walls in Symmetry-Broken Rhombohedral Graphene

Vo Tien Phong , Francisco Lobo , Elsa Prada , Pablo San-Jose , Francisco Guinea , Eugene J Mele This is my paper

Pith reviewed 2026-06-27 04:19 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.supr-con
keywords rhombohedral graphenedomain wallsvalley polarizationintervalley interactionschiral superconductorJosephson junctiontransportsymmetry breaking
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The pith

Valley domain walls in rhombohedral graphene are impenetrable to transport without intervalley mixing.

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

The paper establishes that domain walls separating opposite valley polarizations in displacement-field polarized rhombohedral multilayer graphene block electron transmission in the metallic phase. Any current across these walls requires intervalley interaction terms allowed by symmetry. In the superconducting phase these terms enable supercurrent through Josephson junctions linking regions of opposite chirality. This provides a mechanism for the transport features observed in experiments on these systems. Readers would care because it identifies intervalley hybridization as the key process controlling both normal and superconducting transport at these interfaces.

Core claim

Valley domain walls are impenetrable barriers to transport in the metallic regime of symmetry-broken rhombohedral graphene. Transmission must therefore be mediated by intervalley interactions, which the authors derive from symmetry and confirm with microscopic simulations. In the superconducting phase, intervalley mixing is crucial for supporting an appreciable supercurrent through an SNS' Josephson junction connecting opposite-chirality superconducting regions.

What carries the argument

Symmetry-allowed intervalley interaction terms that mediate electron transmission across valley domain walls.

Load-bearing premise

The symmetry-broken valley-polarized phase with domain walls is realized and the microscopic Hamiltonian accurately captures the relevant intervalley processes.

What would settle it

Direct measurement showing finite transmission across a domain wall in the metallic phase even when intervalley coupling is suppressed, or zero supercurrent in an opposite-chirality Josephson junction despite the presence of intervalley mixing.

Figures

Figures reproduced from arXiv: 2606.14878 by Elsa Prada, Eugene J Mele, Francisco Guinea, Francisco Lobo, Pablo San-Jose, Vo Tien Phong.

Figure 1
Figure 1. Figure 1: Schematic illustration of a valley domain wall along the armchair direction. Energy bands on the two sides of a domain wall illustrating the spatial variation of valley polarization ετ (x) along the x direction, with µ being the chemical potential. The valley flavor is exchanged across the domain wall: K for x < 0 and K′ for x > 0. For a step-function wall, an incoming K wave is reflected off of an evanesc… view at source ↗
Figure 2
Figure 2. Figure 2: Intervalley scattering on the active sublattice. (a) Schematic hopping model realizing the intervalley mixing interac￾tions τxσ+ and τyσ+ with bond strengths distinguished by single, double, and dashed red lines connecting atoms. (b) Bulk band struc￾ture of tetralayer rhombohedral graphene along the kx (left) and ky (right) directions with ∆ = 30 meV and mz = 10 meV. The color represents valley polarizatio… view at source ↗
Figure 3
Figure 3. Figure 3: Transmission across a domain wall with intervalley cou￾pling. (a) Transmission as a function of the strength of intervalley coupling m at θ = 0◦ , ky = 0, and n = 5 × 1011 cm−2 . The in￾set shows the transmission of a wide domain wall w = 100 nm. (b) Dependence of the transmission on the angle θ of the intervalley in￾teraction at m = 3 meV, ky = 0, and n = 5 × 1011 cm−2 . Different colored curves in (a,b) … view at source ↗
Figure 4
Figure 4. Figure 4: Finite-momentum chiral p-wave superconductivity. (a) Real-space representation of the hopping processes between the elec￾tron (Ai) and hole (ai) sectors in Eq. (10). (b) Bulk band structure along the kx and ky directions color-coded by particle character (+1 for electrons and −1 for holes). (c) Spectral function for a semi￾infinite plane with an armchair termination showing the presence of a chiral Majoran… view at source ↗
Figure 5
Figure 5. Figure 5: Current-phase relation for supercurrent across an SNS’ Josephson junction. (a) CPR for different values of intervalley co￾herence m ∈ [0, 1, 2, 3, 4, 5] meV with θ = 0◦ . (b) Plot of the super￾current density amplitude Jc as a function of m at θ = 0◦ . (c) Same as (a) but for a smaller range of m ∈ [0, 0.1, 0.2, 0.3, 0.4, 0.5] meV. (d) CPR at fixed m = 3 meV for different values of θ. (e) BdG spec￾tral fun… view at source ↗
read the original abstract

Rhombohedral multilayer graphene polarized by a moderate perpendicular displacement field hosts a time-reversal-symmetry-breaking valley-and-spin-polarized metallic phase that may condense into a chiral superconductor. Recent magnetic imaging and transport measurements in this unconventional system suggest the presence of domain walls both in the metallic and superconducting phases. In this work, we show that valley domain walls are impenetrable barriers to transport in the metallic regime. Transmission through such a domain wall must therefore be mediated by intervalley interactions. We derive the symmetry-allowed terms and show via microscopic numerical simulations that they enable the transmission of electrons across the domain wall. In the superconducting phase, we find that intervalley mixing is crucial for supporting an appreciable supercurrent through a SNS' Josephson junction that connects opposite-chirality superconducting regions. Taken together, our work elucidates the nature of domain walls in these experimentally relevant multilayer systems and emphasizes the critical role of intervalley hybridization in governing their transport properties.

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 manuscript examines valley domain walls in rhombohedral multilayer graphene in a valley-and-spin-polarized metallic phase that may become a chiral superconductor. It argues that these domain walls act as impenetrable barriers to transport in the metallic regime due to valley conservation, requiring intervalley interactions for any transmission. The authors derive symmetry-allowed intervalley terms and use microscopic numerical simulations to demonstrate that these terms permit electron transmission across the walls. In the superconducting phase, they show that intervalley mixing is necessary for significant supercurrent in SNS' Josephson junctions linking superconducting regions with opposite chirality.

Significance. Should the central results be confirmed, this work would clarify the transport characteristics of domain walls in experimentally relevant rhombohedral graphene systems and underscore the importance of intervalley hybridization for both normal and superconducting transport. It connects to recent magnetic imaging and transport experiments suggesting domain walls in both phases, potentially informing models of superconductivity in these materials. The symmetry-based derivation of intervalley terms is a strength.

major comments (2)
  1. [Microscopic numerical simulations section] The claim that domain walls are impenetrable (valley conservation) and that transmission requires intervalley interactions rests on the microscopic Hamiltonian accurately capturing the relevant intervalley matrix elements without missing higher-order corrections. The manuscript does not address the sensitivity of the reported transmission or supercurrent to variations in these terms or to neglected disorder.
  2. [Superconducting phase] § on Josephson junction: the assertion that intervalley mixing is crucial for appreciable supercurrent in opposite-chirality SNS' junctions is model-dependent; the paper should quantify the supercurrent suppression in the absence of these terms to establish that the effect is not an artifact of the chosen parameters.
minor comments (2)
  1. [Introduction] Notation for the displacement field and valley polarization could be defined more explicitly at first use.
  2. [Figures] Figure captions for transmission plots should include the system size and boundary conditions used in the numerics.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments. We respond to each major comment below.

read point-by-point responses

  1. Referee: [Microscopic numerical simulations section] The claim that domain walls are impenetrable (valley conservation) and that transmission requires intervalley interactions rests on the microscopic Hamiltonian accurately capturing the relevant intervalley matrix elements without missing higher-order corrections. The manuscript does not address the sensitivity of the reported transmission or supercurrent to variations in these terms or to neglected disorder.

    Authors: Valley conservation (and thus impenetrability) follows from the symmetries of the low-energy Hamiltonian in the absence of intervalley terms; this symmetry argument is independent of higher-order corrections or the precise values of matrix elements. The intervalley terms themselves are derived from symmetry considerations that apply generally. We agree that the manuscript does not examine sensitivity to parameter variations or include disorder. In revision we will add a brief discussion noting that small changes in intervalley coupling strength do not alter the requirement for such terms, and that disorder would be expected to facilitate transmission but would not remove the need for intervalley mixing. revision: partial

  2. Referee: [Superconducting phase] § on Josephson junction: the assertion that intervalley mixing is crucial for appreciable supercurrent in opposite-chirality SNS' junctions is model-dependent; the paper should quantify the supercurrent suppression in the absence of these terms to establish that the effect is not an artifact of the chosen parameters.

    Authors: The suppression arises because opposite-chirality regions are connected by a junction that conserves valley index in the absence of intervalley mixing, leading to vanishing (or exponentially small) supercurrent. We will add explicit quantification—either numerical values or an additional panel—comparing the supercurrent with and without the intervalley terms to make this suppression quantitative and to confirm it is not an artifact of parameter choice. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation relies on independent microscopic numerics and symmetry analysis

full rationale

The paper derives symmetry-allowed intervalley terms from first principles and demonstrates transmission via explicit numerical simulations on a microscopic Hamiltonian. No step reduces a claimed prediction to a fitted parameter or self-citation by construction. The central claims (impenetrable domain walls, intervalley-mediated transmission, supercurrent in SNS' junctions) follow from the model equations without tautological redefinition. Self-citations, if present, are not load-bearing for the uniqueness or ansatz of the result. This is the expected non-finding for a model-based transport study.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities; the symmetry-allowed terms are derived but their explicit form and any fitting are not stated.

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Reference graph

Works this paper leans on

106 extracted references · 7 linked inside Pith

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    General Transformation Between Valley-Orbital Basis and Kekul ´e Basis Here, we provide a prescription to transform between the two basis sets by classifying every possible perturbation without any symmetry constraint in the valley-orbital basis. We start with a few examples. Let us write down tight-binding Hamiltonians that realizeτ 1 ⊗σ 0, τ1 ⊗σ 3, τ2 ⊗...

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    Band Structures for Example Models In this section, we study the band structures of various example models in the vicinity of Γof the Kekul ´e Brillouin zone. Let us first study the example in Eq. (S19) witha=t 1eiφ1andb=−c=t 2eiφ2 / √ 3.With this minor relabeling, we have ˆHτi⊗σj(k) = ˆH0(k)+   0t 1eiφ1 eik·δ1 0 t2eiφ2 √ 3 eik·δ2 0− t2eiφ2 √ ...

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