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Andreev modes in ballistic planar Josephson junctions eject into a normal region at a phase-controlled angle that scales as √(Δ/μ), larger than ordinary Cooper-pair momentum.

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2026-07-13 06:17 UTC pith:DMODCJAE

load-bearing objection Clean theory paper: phase-steered quasiparticle ejection from planar JJs at √(Δ/μ), larger than the usual Doppler scale, with analytics, numerics, and open code. the 2 major comments →

arxiv 2607.08845 v1 pith:DMODCJAE submitted 2026-07-09 cond-mat.mes-hall cond-mat.supr-con

Probing Cooper pair momentum by quasiparticle steering with planar Josephson junctions

Isidora Araya Day , Anton R. Akhmerov , Antonio R. L. Manesco This is my paper
classification cond-mat.mes-hall cond-mat.supr-con
keywords Cooper pair momentumAndreev bound statesplanar Josephson junctionquasiparticle ejectionDoppler shiftballistic transportelectron opticsphase control
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Cooper-pair momentum is usually tiny next to the Fermi momentum, so it is hard to see in the direction quasiparticles move. This paper shows that Andreev bound states traveling along a short, clean planar Josephson junction leave the junction into an adjacent normal metal at a finite angle set by the superconducting phase difference. That angle grows as the square root of the gap over the chemical potential, so it is parametrically larger than the usual Doppler scale Δ/μ and remains measurable even deep in the Andreev regime. The effect arises because repeated Andreev reflections from a phase-biased condensate give the bound state a transverse momentum that pure electrons then inherit at a transparent interface. If confirmed, phase-controlled ejection becomes a kinematic, momentum-space probe of condensate motion rather than an energy-shift measurement.

Core claim

Subgap Andreev bound states that propagate along a short ballistic planar Josephson junction are transmitted into pure electron modes in an adjacent normal region at a phase- and energy-dependent average angle Θ that scales as √(Δ/μ). This scale exceeds the conventional Cooper-pair momentum ratio Δ/μ because the bound state accumulates transverse momentum through repeated Andreev reflections, and that momentum is inherited by the ejected electron current.

What carries the argument

Phase-controlled quasiparticle ejection: the next-to-leading-order transverse ABS momentum ⟨ky⟩_ABS ∼ √(Δ/a) obtained from a two-state Andreev-approximation basis, which is then matched at a transparent SNS–normal interface so that the transmitted electron current carries the same angular scale.

Load-bearing premise

The junction must be fully ballistic and the SNS–normal interface fully transparent, so Andreev modes convert into pure electron modes without ordinary band-mismatch reflection that would scramble the angle.

What would settle it

In a short epitaxial planar SNS device with a transparent normal lead, measure the transmission-weighted average emission angle of subgap quasiparticles versus phase and bias (via quantum point contacts or scanning gate microscopy). If the angle fails to track the predicted √(Δ/μ) phase and energy dependence, or remains finite at time-reversal-symmetric phase, the claim is false.

Watch this falsifier — get emailed when new claim-graph text bears on it.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The manuscript shows that Andreev bound states propagating along a short ballistic planar Josephson junction eject into an adjacent normal region at a phase- and bias-controlled angle that scales as Θ ∼ √(Δ/μ). This is parametrically larger than the conventional Cooper-pair momentum scale Δ/μ. The result is obtained from a controlled expansion of the linearized BdG Hamiltonian beyond the Andreev approximation (Eqs. 2–10), a continuum scattering solution that matches the SNS half-plane modes to pure electron modes in the normal lead (Appendix B), and supporting tight-binding Kwant simulations at Δ/μ up to 0.1–0.2 (Fig. 2). The authors propose detection via quantum point contacts or scanning gate microscopy and estimate material parameters for InAs–Al and graphene platforms.

Significance. If the result holds, the work supplies a kinematic probe of condensate momentum transfer that is complementary to existing Doppler-shift spectroscopies: the signal is a momentum-space deflection of emitted quasiparticles rather than an energy shift. The √(Δ/μ) enhancement makes the effect sizeable even deep in the Andreev regime, which is a genuine conceptual advance over single-reflection Doppler estimates. Strengths that raise confidence include a parameter-free scaling argument from Hamiltonian rescaling, an explicit continuum interface solution, quantitative agreement with open tight-binding code (Zenodo), and concrete experimental geometries with material estimates. The paper is a natural extension of recent work on ballistic Andreev-mode transport and is of clear interest to the mesoscopic superconductivity community.

major comments (2)
  1. The central theoretical claim is well supported inside the stated regime (ballistic junction, transparent SNS–normal interface, short junction). The only load-bearing experimental caveat is that the inheritance of the ABS transverse-momentum scale by the ejected electron current relies on the absence of ordinary band-mismatch reflection and on clean conversion of Andreev modes into pure electron modes (Sec. 2, interface paragraphs; Appendix B matching conditions ψ_h(0,y)=0 and continuous wavefunction). A short quantitative estimate of how weak interface mismatch or residual normal reflection would degrade ⟨Θ⟩ would strengthen the experimental section without changing the theory result.
  2. Near the gap edge the perturbative transverse momentum (Eq. 10) has a slow fourth-root divergence that is cut off by the finite normal-state bandwidth. Figure 2(c) shows good continuum–tight-binding agreement away from this cutoff, but the experimental proposals (Sec. 3) do not specify how close to the minigap or gap edge the bias should be kept for the √(Δ/μ) scaling to remain reliable. A brief statement of the usable energy window for the quoted material parameters would make the detection claims more falsifiable.
minor comments (5)
  1. Eq. (1) writes k = |k| while later using separate kx, ky components; a short clarification that the kinetic term is (ℏ²/2m)(kx² + ky²) would avoid momentary confusion.
  2. Figure 2(c) collapses data using a nontrivial combination of E and ϕ. Adding one sentence in the caption that states the expected collapse variable from Eq. (10) would help readers interpret the plot without flipping back to the text.
  3. In Appendix B the residual minimization for Ae(k), Be(k) is described at a high level; a pointer to the specific grid sizes and regularization used in the Zenodo code (already cited) would improve reproducibility of the continuum curves.
  4. The self-field estimate in Sec. 3 is useful; stating the assumed junction length and number of modes more explicitly would make the <10⁻⁴ rad bound easier to recompute.
  5. A few recent arXiv references (e.g. 2025–2026) are cited as published Phys. Rev. entries; verify final bibliographic details before production.

Circularity Check

0 steps flagged

No significant circularity: ejection angle follows from BdG rescaling, perturbation, and independent interface matching.

full rationale

The claimed scaling Θ∼√(Δ/μ) is obtained from dimensional analysis of the linearized, rescaled BdG Hamiltonian (Eqs. 2–4), a next-to-leading-order perturbative evaluation of the ABS transverse momentum (Eq. 10), and a self-contained continuum scattering construction at the SNS–normal interface (Appendix B) that enforces wavefunction continuity and ψ_h(0,y)=0. These steps are checked against tight-binding scattering (Fig. 2c) with open code. Self-citations (notably [11]) supply background on Andreev-mode transport and the standard Andreev-approximation basis states used as a starting point for the perturbation; they are not used as a uniqueness theorem, fitted input, or definitional stand-in for the ejection angle. No prediction reduces by construction to its inputs, and the central kinematic claim is independently derived within the paper.

Axiom & Free-Parameter Ledger

0 free parameters · 5 axioms · 0 invented entities

The claim rests on standard BdG modeling of a short planar Josephson junction, the Andreev approximation regime, ballistic propagation, and a transparent SNS–normal interface. No free parameters are fitted to data; numerical values of Δ/μ are illustrative. No new particles or forces are introduced.

axioms (5)
  • domain assumption Bogoliubov–de Gennes description of a short planar SNS junction with step-like phase profile (Eq. 1).
    Standard continuum model for proximity-induced planar junctions; invoked throughout Sec. 2 and Appendix B.
  • domain assumption Andreev approximation Δ/μ ≪ 1 with controlled next-to-leading corrections for transverse momentum.
    Used to linearize longitudinal dispersion and obtain the √(Δ/a) transverse scale (Eqs. 2–10).
  • domain assumption Ballistic Andreev-mode transport along the junction with suppressed backscattering.
    Taken from Tam–Kane and prior author work; required for a well-defined propagating ABS that reaches the normal interface.
  • domain assumption Transparent SNS–normal interface: no ordinary band-mismatch reflection; Andreev modes convert to pure electron modes.
    Stated in Sec. 2; matching conditions in Appendix B set hole component to zero at the interface.
  • domain assumption Parabolic normal-state dispersion used to convert transverse momentum into ejection angle Θ ≈ ⟨ky⟩/k_F.
    Enters the scaling Θ ∼ √(Δ/μ) and the continuum angle extraction; graphene warping is noted as a possible correction.

pith-pipeline@v1.1.0-grok45 · 21104 in / 2353 out tokens · 23440 ms · 2026-07-13T06:17:50.352241+00:00 · methodology

0 comments
read the original abstract

The Cooper pair momentum in a superconductor is associated with a phase gradient of the superconducting order parameter. In general, this momentum is small compared to the Fermi momentum, which makes it challenging to measure. Josephson junctions, however, enable the creation of large phase gradients and transfer of the Cooper pair momentum to quasiparticles via Andreev reflection. In this work we demonstrate that Andreev bound states propagating along ballistic planar Josephson junctions eject into an adjacent normal region at a phase-controlled angle that scales as $\Theta \sim \sqrt{\Delta/ \mu}$, where $\Delta$ is the superconducting gap and $\mu$ is the chemical potential. This angle parametrically exceeds the conventional Cooper pair momentum scale $\Delta/ \mu$, and thus this phenomenon is sizeable even within the Andreev approximation regime $\Delta / \mu \ll 1$. Our results establish phase-controlled quasiparticle ejection as a kinematic probe of condensate momentum transfer: unlike existing probes that detect the Doppler energy shift, the signal appears as a momentum-space deflection of emitted quasiparticles.

Figures

Figures reproduced from arXiv: 2607.08845 by Antonio R. L. Manesco, Anton R. Akhmerov, Isidora Araya Day.

Figure 1
Figure 1. Figure 1: Electron current density ejected from a planar Josephson junction into [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Current angle distribution of the ejected electron current density and [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Proposed experimental setup to detect the ejection angle of quasiparticles [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Root structure of the bounded subgap solutions of Eq. [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Real-space profiles of the bounded subgap solution families shown in [PITH_FULL_IMAGE:figures/full_fig_p018_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Transmitted intensity profiles |t(y)| 2 at the SNS–normal interface, obtained from the dense linear-k solve of the half-line integral equations. Each panel corresponds to a different phase difference ϕ, and each curve corresponds to one of five evenly spaced energies between the local minigap ∆ cos(ϕ/2) and the gap edge ∆. In every panel, the plotted intensity is normalized by maxy |t(y)| 2 . 20 [PITH_FUL… view at source ↗

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