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arxiv: 2605.18411 · v1 · pith:Y3U6KHLMnew · submitted 2026-05-18 · ❄️ cond-mat.mes-hall · cond-mat.supr-con

Spin and orbital mixing of edge states in a quantum Hall system proximitized by a superconductor

S. Maji , M. P. Nowak This is my paper

Pith reviewed 2026-05-19 23:57 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.supr-con
keywords quantum HallAndreev reflectionedge statessuperconductor proximityspin-orbit couplingZeeman interactionchiral Andreev modesBogoliubov-de Gennes
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The pith

Andreev reflection mixes quantum Hall edge modes at higher filling factors in a proximitized system.

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

The paper examines how a superconductor next to a two-dimensional quantum Hall system creates chiral Andreev edge states. Numerical modeling with Bogoliubov-de Gennes equations shows that Andreev reflection causes mixing of edge modes at higher filling factors, something not possible in clean electronic systems alone. Incorporating Zeeman interaction keeps spin species separate, but adding Rashba spin-orbit coupling with an in-plane field leads to complex spin mixing across all bands. The work also finds robust degeneracies in electron transmission probabilities arising from unitarity and particle-hole symmetry.

Core claim

In a quantum Hall system proximitized by a superconductor, the Andreev reflection process induces a mixing of the quantum Hall edge modes at higher filling factors, a phenomenon strictly prohibited in clean, purely electronic systems. When incorporating the Zeeman interaction, the Andreev edge states split into uncoupled spin species maintaining spin orthogonality. The combination of Rashba spin-orbit coupling with an in-plane magnetic field drives complex spin mixing among all chiral Andreev bands, altering conductance oscillations, while electron transmission probabilities exhibit robust degeneracies due to unitarity constraints and particle-hole symmetry.

What carries the argument

Chiral Andreev edge states analyzed through the Bogoliubov-de Gennes equations and the scattering matrix symmetries under magnetic field and spin-orbit interaction.

Load-bearing premise

The numerical model assumes an ideal clean interface and perfect proximitization without disorder or interface scattering.

What would settle it

Measuring the non-local conductance or transmission probabilities in a real device at higher filling factors to check for the predicted mode mixing and spin mixing effects under applied fields.

Figures

Figures reproduced from arXiv: 2605.18411 by M. P. Nowak, S. Maji.

Figure 1
Figure 1. Figure 1: The scheme of the considered system. A semi [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (a) Conductance of normal-superconductor system [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: (a) Conductance cross-section versus chemical po [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: (a) Conductance versus perpendicular magnetic [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: (a) Conductance of a QH-superconductor system [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: (a) Occupation probability of different CAES states [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: (a) Conductance of a QH-superconductor system [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: (a) Conductance of a QH-superconductor system [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗
read the original abstract

We investigate the formation and transport properties of chiral Andreev edge states in a two-dimensional quantum Hall system proximitized by a superconductor. By numerically modeling the system using the Bogoliubov-de Gennes equations, we analyze the non-local conductance and transmission probabilities of multimode and spinful systems. We demonstrate that the Andreev reflection process induces a mixing of the quantum Hall edge modes at higher filling factors, a phenomenon strictly prohibited in clean, purely electronic systems. When incorporating the Zeeman interaction, we show that the Andreev edge states split into uncoupled spin species, maintaining spin orthogonality that prevents mixing between opposite spin sectors. Furthermore, we explore the impact of Rashba spin-orbit coupling. While the spin-orbit interaction alone causes slight spin depolarization, its combination with an in-plane magnetic field drives complex spin mixing among all chiral Andreev bands, fundamentally altering the conductance oscillations. Finally, we reveal that the electron transmission probabilities exhibit robust degeneracies, which emerge as a direct consequence of the unitarity constraints and the particle-hole symmetry of the system's scattering matrix in a magnetic field and the presence of spin-orbit interaction.

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 numerically studies chiral Andreev edge states in a two-dimensional quantum Hall system proximitized by a superconductor via solutions of the Bogoliubov-de Gennes equations. It claims that Andreev reflection induces mixing of quantum Hall edge modes at higher filling factors (strictly forbidden in clean, purely electronic systems), examines the splitting into spin-orthogonal species under Zeeman interaction, shows complex spin mixing when Rashba SOC is combined with an in-plane magnetic field, and identifies robust degeneracies in electron transmission probabilities arising from unitarity and particle-hole symmetry of the scattering matrix.

Significance. If the numerical trends hold, the work provides a direct demonstration of Andreev-enabled orbital mixing in multimode, spinful quantum Hall edge states and a symmetry-based explanation for transmission degeneracies. The use of explicit BdG diagonalization and scattering calculations (rather than fitting) is a strength, as are the parameter-free symmetry arguments for the degeneracies.

major comments (1)
  1. [Numerical modeling / BdG setup] Model and numerical setup: the proximitization is implemented via a uniform pairing gap with an ideal, disorder-free interface and no interface barrier. This assumption is load-bearing for the central claim that Andreev reflection alone produces inter-mode mixing at higher filling factors; without a test or discussion of robustness against weak disorder or finite interface scattering, it remains unclear whether the reported mixing is generic or specific to the idealized Hamiltonian.
minor comments (2)
  1. [Abstract] Abstract: the range of filling factors at which the mode mixing is observed should be stated explicitly for precision.
  2. [Results on Rashba SOC] Rashba SOC + in-plane field results: the phrase 'complex spin mixing' would benefit from a quantitative metric (e.g., spin polarization or overlap integrals) tied to a specific figure or equation.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive assessment and constructive comment on our manuscript. We address the concern regarding the numerical modeling and BdG setup below, providing the strongest honest defense of our approach while agreeing to incorporate a clarifying discussion.

read point-by-point responses

  1. Referee: [Numerical modeling / BdG setup] Model and numerical setup: the proximitization is implemented via a uniform pairing gap with an ideal, disorder-free interface and no interface barrier. This assumption is load-bearing for the central claim that Andreev reflection alone produces inter-mode mixing at higher filling factors; without a test or discussion of robustness against weak disorder or finite interface scattering, it remains unclear whether the reported mixing is generic or specific to the idealized Hamiltonian.

    Authors: We agree that the idealized interface and uniform pairing gap are central to our demonstration. This setup is chosen specifically to isolate the role of Andreev reflection in enabling inter-mode mixing of quantum Hall edge states at higher filling factors, which is strictly prohibited in clean, purely electronic systems by chirality and orthogonality. Our BdG simulations provide a direct, parameter-free illustration of this mechanism. We acknowledge that weak disorder or finite interface scattering could quantitatively modify the results and that explicit tests of robustness would be valuable. However, such extensions lie beyond the scope of the current work, which focuses on establishing the fundamental effect in the clean limit. We will add a concise discussion in the revised manuscript noting the assumptions of the model and explaining why the reported mixing is expected to be relevant for high-mobility samples with transparent superconductor interfaces. revision: partial

Circularity Check

0 steps flagged

No significant circularity; results from direct BdG numerics

full rationale

The paper computes transmission probabilities, non-local conductance, and edge-state mixing via direct numerical diagonalization of the Bogoliubov-de Gennes Hamiltonian on a lattice model with uniform proximity-induced pairing and no disorder. These quantities are obtained as outputs of the scattering matrix under the model's stated assumptions rather than being fitted to target data or presupposed by self-citation. No load-bearing step reduces by construction to the inputs, and the central demonstration of Andreev-induced mixing at higher filling factors follows from the explicit solution of the equations without renaming known results or importing uniqueness theorems from prior self-work.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claims rest on the standard applicability of the Bogoliubov-de Gennes formalism to proximitized quantum Hall edges and on the assumption of a clean, translationally invariant interface geometry; no new entities are postulated.

free parameters (2)
  • filling factor
    Higher filling factors are chosen to observe the reported mixing; specific values are model inputs.
  • Rashba SOC strength
    Parameter controlling the strength of spin-orbit mixing in the simulations.
axioms (2)
  • domain assumption Bogoliubov-de Gennes equations accurately capture the superconducting proximity effect in the quantum Hall regime
    Invoked as the basis for all numerical modeling of Andreev edge states.
  • domain assumption The interface is clean and disorder-free
    Required for the claim that mixing is strictly prohibited in purely electronic systems but appears with Andreev reflection.

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Reference graph

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