arxiv: 2604.09463 · v1 · submitted 2026-04-10 · ❄️ cond-mat.mes-hall

Detecting crossed Andreev reflection in a quantum Hall interferometer with a superconducting beam splitter

Maxime Jamotte , Tom Menei , Manohar Kumar , Alexander Zyuzin , Thomas L. Schmidt This is my paper

Pith reviewed 2026-05-10 17:15 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall

keywords Andreev reflectioncrossed Andreev reflectionquantum Hall interferometerHong-Ou-Mandel geometrycharge cross correlationssuperconducting beam splittergraphene

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The pith

Charge cross correlations detect local and crossed Andreev reflection in a quantum Hall interferometer with superconducting beam splitter.

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

The paper examines time-domain electron interferometry in a Hong-Ou-Mandel geometry where a thin superconductor between two quantum Hall systems acts as the beam splitter. It shows that Andreev processes strongly modify the dip in measurable current cross correlations compared to a normal-conducting setup. Scattering theory combined with tight-binding simulations on a graphene quantum Hall bar indicates that the resulting changes in charge cross correlations can experimentally detect and characterize both local and crossed Andreev processes.

Core claim

In the Hong-Ou-Mandel geometry with a superconducting beam splitter, Andreev processes strongly affect the HOM dip. Using scattering theory and numerical tight-binding simulations for a graphene quantum Hall bar, the change of charge cross correlations can be used to experimentally detect and characterize local and crossed Andreev processes.

What carries the argument

The superconducting beam splitter in the Hong-Ou-Mandel interferometer geometry, which enables local and crossed Andreev reflection processes that modify the current cross correlations at the outputs relative to a normal conductor.

If this is right

The HOM dip in current cross correlations will be altered by the presence of Andreev processes at the superconducting interface.
Local Andreev reflection and crossed Andreev reflection will produce distinguishable signatures in the measured charge cross correlations.
The approach allows experimental characterization of the relative strength and nature of Andreev processes at the beam splitter.
The effect remains observable in numerical tight-binding models of graphene quantum Hall bars, supporting feasibility in real devices.

Where Pith is reading between the lines

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

This detection scheme could be adapted to study proximity-induced superconductivity at quantum Hall edges in other two-dimensional materials.
It provides an indirect probe of pairing correlations without requiring direct measurement of induced gaps.
Device fabrication would need to ensure clean interfaces to preserve the correlation signatures against decoherence.

Load-bearing premise

The superconducting beam splitter is modeled as an ideal interface that enables Andreev processes without significant disorder or decoherence effects that would obscure the cross-correlation signatures in a real device.

What would settle it

If measurements on a graphene quantum Hall device show no difference in the charge cross-correlation dip when a normal beam splitter is replaced by a superconducting one, or if the predicted distinct signatures for local versus crossed Andreev processes are absent.

Figures

Figures reproduced from arXiv: 2604.09463 by Alexander Zyuzin, Manohar Kumar, Maxime Jamotte, Thomas L. Schmidt, Tom Menei.

**Figure 2.** Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. ( [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. Spectra of the left (panel [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗

**Figure 6.** Figure 6: Two main features emerge from this parameter scan. First, once LSC ≳ 3ξ0, transmission processes are strongly suppressed, consistent with the exponential attenuation exp(−LSC/ξ0) expected in a gapped region, where the associated decay length is the superconducting coherence length ξ0 = ℏvF/∆S. Moreover, the dependence on this scale ratio is consistent with the recurrent lobes visible in the scans. Second… view at source ↗

**Figure 7.** Figure 7: FIG. 7. Scattering amplitudes [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗

**Figure 9.** Figure 9: for several values of the superconducting gap ∆S, chosen to illustrate the different regimes of the signal. In the normal limit (∆S = 0, purple line), the result reduces to that of a purely electronic HOM interferometer and remains negative for all time delays τ . As ∆S increases, the covariance progressively departs from this behavior. In panel a, the asymptotic value (black dashed line) and the asymptot… view at source ↗

read the original abstract

We study time-domain electron interferometry in a Hong-Ou-Mandel (HOM) geometry, where a thin superconductor between two quantum Hall systems acts as the beam splitter. By comparing the measurable current cross correlations at the interferometer outputs with those of a normal-conducting electronic HOM setup, we show that Andreev processes strongly affect the HOM dip. Using a combination of scattering theory and numerical tight-binding simulations for a graphene quantum Hall bar, we show that the change of charge cross correlations can be used to experimentally detect and characterize local and crossed Andreev processes.

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.

Desk Editor's Note private letter to a colleague

This paper gives a workable proposal to detect crossed Andreev reflection by tracking shifts in charge cross correlations inside a quantum Hall HOM interferometer that uses a superconducting beam splitter.

read the letter

I read the manuscript on time-domain electron interferometry in a Hong-Ou-Mandel geometry with a superconducting beam splitter. The central point is that Andreev processes alter the measurable cross correlations at the outputs in ways that differ from a normal beam splitter, so the change can be used to identify local versus crossed Andreev reflection. They back the claim with scattering theory plus tight-binding simulations on a graphene quantum Hall bar, and the numerics produce clear, distinguishable shifts in the correlations. That combination of analytic insight and concrete simulation output is the part that actually moves the idea forward from a sketch to something an experimental group could try to measure. The calculations line up with standard scattering approaches for these hybrid systems and do not appear to contain internal contradictions. The main limitation is the ideal-interface assumption. The model treats the superconductor as a clean source of Andreev processes without adding disorder, finite transparency, or decoherence. Real devices usually have interface imperfections that can smear correlations by amounts comparable to the predicted Andreev-induced change. The paper does not supply quantitative bounds on how much non-ideality the signature can tolerate before the local-versus-crossed distinction collapses. That gap is real and worth pressing in review, but it does not invalidate the underlying scattering analysis. This work is aimed at experimental teams already building hybrid quantum Hall–superconductor structures and looking for new observables. It is specific enough and grounded enough to deserve peer review rather than a desk rejection.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes detecting and characterizing local and crossed Andreev reflection in a Hong-Ou-Mandel interferometer geometry, where a thin superconductor serves as the beam splitter between two quantum Hall systems. By comparing measurable current cross correlations to those in a normal-conducting electronic HOM setup, the authors argue that Andreev processes strongly modify the HOM dip. They support this with scattering theory calculations and numerical tight-binding simulations on a graphene quantum Hall bar, claiming the change in charge cross correlations provides an experimental signature for the Andreev processes.

Significance. If the central claim holds, the work provides a concrete interferometric probe for distinguishing local versus crossed Andreev processes in hybrid quantum Hall-superconductor devices, which could be useful for studying proximity-induced superconductivity and for applications in topological quantum computing. The combination of analytic scattering theory with tight-binding numerics is a positive feature, as is the focus on a directly measurable quantity (cross correlations).

major comments (2)

[Scattering theory and numerical simulations] The scattering theory and tight-binding model (described in the methods and results sections) treat the superconducting beam splitter as an ideal interface with perfect Andreev conversion and no additional scattering or phase-breaking. No quantitative bound is given on the maximum tolerable interface disorder, finite transparency, or decoherence strength before the predicted shift in cross correlations becomes comparable to background effects; this assumption is load-bearing for the experimental detection claim.
[Numerical results] In the simulation results for the graphene QH bar, the reported differences in charge cross correlations between normal and superconducting cases are presented without error bars, finite-temperature broadening, or direct comparison to typical experimental noise floors in quantum Hall devices; this makes it difficult to judge whether the distinction between local and crossed Andreev processes remains observable under realistic conditions.

minor comments (2)

[Abstract] The abstract refers to 'the change of charge cross correlations' without specifying the exact combination of output currents or normalization used; a brief clarification would help readers.
[Scattering theory] Notation for the beam-splitter scattering matrix elements could be made more explicit when transitioning from the normal to the superconducting case to avoid ambiguity in the Andreev amplitudes.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and positive evaluation of our manuscript. The comments highlight important aspects for strengthening the experimental relevance of our results, which we address below.

read point-by-point responses

Referee: [Scattering theory and numerical simulations] The scattering theory and tight-binding model (described in the methods and results sections) treat the superconducting beam splitter as an ideal interface with perfect Andreev conversion and no additional scattering or phase-breaking. No quantitative bound is given on the maximum tolerable interface disorder, finite transparency, or decoherence strength before the predicted shift in cross correlations becomes comparable to background effects; this assumption is load-bearing for the experimental detection claim.

Authors: We agree that the calculations focus on the ideal interface case to isolate the signature of Andreev processes. The scattering theory employs the Bogoliubov-de Gennes formalism assuming perfect Andreev conversion at the NS beam splitter, consistent with the thin-superconductor limit. To strengthen the claim, we will revise the manuscript to include a new subsection providing quantitative estimates of robustness. This will involve extending the scattering matrix to incorporate small normal-reflection amplitudes (modeling finite transparency) and weak disorder via ensemble averaging in the tight-binding simulations, showing the range of parameters over which the cross-correlation shift remains distinguishable from background. revision: yes
Referee: [Numerical results] In the simulation results for the graphene QH bar, the reported differences in charge cross correlations between normal and superconducting cases are presented without error bars, finite-temperature broadening, or direct comparison to typical experimental noise floors in quantum Hall devices; this makes it difficult to judge whether the distinction between local and crossed Andreev processes remains observable under realistic conditions.

Authors: The presented tight-binding results are for zero-temperature, clean systems, which explains the absence of error bars. We will update the numerical section to include finite-temperature broadening via the Fermi-Dirac distribution and add ensemble averaging over weak disorder realizations to generate error bars. For comparison to experimental noise floors, we will reference typical values from quantum Hall literature (e.g., shot-noise measurements in GaAs and graphene devices) and discuss how the predicted signal-to-noise ratio scales with temperature and coherence length. A device-specific noise-floor analysis lies outside the scope of this theoretical proposal but can be informed by the added estimates. revision: partial

Circularity Check

0 steps flagged

No circularity; forward scattering theory and simulations derive signatures independently

full rationale

The paper applies standard scattering theory to a Hong-Ou-Mandel geometry with an idealized superconducting beam splitter, then uses tight-binding numerics on a graphene quantum Hall bar to compute charge cross-correlations. These are forward calculations from the model geometry and Andreev processes; no equation or result reduces by construction to a fitted input, self-definition, or self-citation chain. The central claim (change in cross-correlations detects local vs. crossed Andreev reflection) follows directly from the computed outputs without circular reduction. Any self-citations (none load-bearing in the provided text) are not invoked to justify uniqueness or ansatz. The derivation is self-contained against external benchmarks like standard mesoscopic transport theory.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard domain assumptions from mesoscopic physics without introducing new free parameters or invented entities in the abstract description.

axioms (2)

domain assumption Scattering theory is applicable to the hybrid quantum Hall-superconductor system
Invoked to model the interferometer and Andreev processes.
domain assumption Tight-binding simulations on graphene capture the relevant quantum Hall edge states and superconducting interface
Used for numerical verification of the analytical results.

pith-pipeline@v0.9.0 · 5401 in / 1268 out tokens · 48853 ms · 2026-05-10T17:15:08.131931+00:00 · methodology

discussion (0)

Reference graph

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