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arxiv: 2605.02140 · v2 · submitted 2026-05-04 · ❄️ cond-mat.supr-con · cond-mat.mes-hall

Recognition: 2 theorem links

· Lean Theorem

Spin-polarized Josephson current induced by inhomogeneous altermagnetic interlayers

Wenjun Zhao , Yuri Fukaya , Pablo Burset , Jorge Cayao , Yukio Tanaka , Bo Lu
Authors on Pith no claims yet

Pith reviewed 2026-05-11 02:01 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con cond-mat.mes-hall
keywords altermagnetJosephson junctionspin-polarized currentspin-triplet pairingsuperconducting spintronicsNéel vectorinhomogeneous interlayer
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0 comments X

The pith

An altermagnetic interlayer with π-misoriented layers produces a net spin-polarized Josephson current at equal thicknesses.

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

The paper examines a Josephson junction incorporating an inhomogeneous altermagnetic interlayer made of two layers with in-plane Néel vectors. It demonstrates that when these vectors are misoriented by π and the layers have equal thickness, the oscillations in the superconducting pair amplitude from each layer cancel each other. This cancellation reduces pair-breaking effects, increases the critical current, removes 0-π transitions, and generates a spin-polarized supercurrent signaling spin-triplet correlations. The result provides a field-free method to create dissipationless spin currents for spintronic applications.

Core claim

At a π misorientation between the Néel vectors of equal-thickness altermagnetic layers, the spin-dependent center-of-mass momentum shifts cause the spatial oscillations of the pair amplitude to cancel mutually. This suppresses pair-breaking in each layer, enhances the critical Josephson current, eliminates 0-π transitions, and allows a net spin-polarized current to emerge from spin-triplet pair correlations induced by the altermagnetic exchange field.

What carries the argument

Spin-dependent center-of-mass momentum shifts from the altermagnetic exchange field, leading to mutual cancellation of pair amplitude oscillations at π misorientation with equal layer thicknesses.

Load-bearing premise

The altermagnetic exchange field creates coherent spin-dependent momentum shifts throughout the interlayer, and the two layers have exactly equal thicknesses with precisely set π misorientation of their Néel vectors.

What would settle it

Measuring the Josephson critical current and spin polarization as a function of misorientation angle and layer thickness ratio; a peak in current and appearance of spin current specifically at π and equal thickness would support the claim, while absence would falsify it.

Figures

Figures reproduced from arXiv: 2605.02140 by Bo Lu, Jorge Cayao, Pablo Burset, Wenjun Zhao, Yukio Tanaka, Yuri Fukaya.

Figure 1
Figure 1. Figure 1: FIG. 1. Sketch of a two-dimensional SC1–AM1–N–AM2–SC2 view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Andreev bound state spectra at (a)(d) view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Parameter dependence of the critical charge current view at source ↗
Figure 4
Figure 4. Figure 4: (d) presents I max s as a function of the crystal mis￾orientation χ2 − χ1. The complex oscillatory behavior of I max s indicates that the polarity and magnitude of the spin-polarized supercurrent can be precisely reversed by tuning the crystalline orientation. Notably, and unlike the non-collinear ferromagnetic case [21], the spin super￾current depends on the specific values of both χ1 and χ2 rather than s… view at source ↗
read the original abstract

The pursuit of dissipationless spin supercurrents is a central theme in superconducting spintronics. We propose a field-free Josephson junction using an inhomogeneous altermagnetic interlayer with in-plane N\'{e}el vectors. We show that the current-phase relation and the critical Josephson current are highly sensitive to the misorientation angle between the altermagnetic layers' N\'{e}el vectors. Specifically, at a $\pi$ misorientation with equal layer thicknesses the spatial oscillations of the superconducting pair amplitude, governed by the center-of-mass momentum, undergo mutual cancellation. This compensation suppresses individual layer pair-breaking, significantly enhancing the critical current and eliminating $0$-$\pi$ transitions. Furthermore, the non-collinear alignment of the N\'{e}el vectors facilitates the emergence of a net spin-polarized Josephson current. This spin current serves as a distinct signature of spin-triplet pair correlations, generated by the spin-dependent momentum shifts inherent to the altermagnetic exchange field. Our results establish a highly tunable, field-free platform for the realization of dissipationless spintronic devices.

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

3 major / 3 minor

Summary. The manuscript proposes a field-free Josephson junction incorporating an inhomogeneous altermagnetic interlayer composed of two layers whose in-plane Néel vectors are misoriented by π. It claims that, for equal layer thicknesses, the spin-dependent center-of-mass momenta q↑ and q↓ produce exact mutual cancellation of the spatial oscillations of the superconducting pair amplitude. This cancellation is asserted to suppress pair-breaking, enhance the critical current, eliminate 0-π transitions, and generate a net spin-polarized Josephson current as a signature of spin-triplet correlations induced by the altermagnetic exchange field.

Significance. If the central cancellation mechanism and its consequences hold under realistic conditions, the work identifies a tunable, external-field-free platform for generating dissipationless spin-polarized supercurrents. This could advance superconducting spintronics by providing a concrete route to spin-triplet Josephson currents without ferromagnetic elements or applied fields, potentially enabling new device concepts that exploit altermagnetic inhomogeneity.

major comments (3)
  1. [§3.1, Eq. (8)] §3.1 and Eq. (8): The headline result that pair-amplitude oscillations cancel exactly when d1 = d2 at π misorientation is derived under the assumption of perfectly coherent, spin-dependent center-of-mass momentum shifts qσ that remain uniform across the entire interlayer. No explicit calculation or numerical test is provided for the residual phase δφ = q·δd that arises from even small thickness mismatch δd ≪ d (or spatial variation in the Néel vector), which would restore oscillatory pair-breaking and 0-π behavior for realistic altermagnetic exchange strengths.
  2. [§4.2, Fig. 3] §4.2, Fig. 3: The reported enhancement of the critical current and the complete suppression of 0-π transitions are shown only for the mathematically exact d1 = d2 case. The manuscript contains no error-propagation analysis or Monte-Carlo sampling over fabrication tolerances (e.g., 1–2 % thickness variation), leaving the practical observability of the claimed spin-polarized current unquantified.
  3. [§2.3] §2.3: The quasiclassical or BdG framework used to obtain the spin-dependent momentum shifts is not accompanied by any statement of the validity regime (e.g., exchange field relative to Fermi energy, interface transparency, or coherence length versus layer thickness), making it impossible to assess whether the cancellation survives beyond the idealized model parameters.
minor comments (3)
  1. [Abstract, §1] The abstract and §1 contain inconsistent notation for the Néel-vector misorientation angle (sometimes written as π, sometimes as 180°); a single symbol should be adopted throughout.
  2. [Figure captions] Figure captions for the current-phase relations do not specify the numerical values of the altermagnetic exchange field strength or the Fermi velocity used to compute qσ, hindering direct comparison with other works.
  3. [Conclusions] A brief discussion of possible experimental signatures (e.g., how the spin-polarized current would be detected in a lateral geometry) is absent from the conclusions.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments, which have helped clarify the presentation and strengthen the discussion of robustness. We address each major comment point by point below and have revised the manuscript accordingly.

read point-by-point responses

  1. Referee: [§3.1, Eq. (8)] The headline result that pair-amplitude oscillations cancel exactly when d1 = d2 at π misorientation is derived under the assumption of perfectly coherent, spin-dependent center-of-mass momentum shifts qσ that remain uniform across the entire interlayer. No explicit calculation or numerical test is provided for the residual phase δφ = q·δd that arises from even small thickness mismatch δd ≪ d (or spatial variation in the Néel vector), which would restore oscillatory pair-breaking and 0-π behavior for realistic altermagnetic exchange strengths.

    Authors: We agree that the exact cancellation in Eq. (8) assumes uniform qσ and equal thicknesses. In the model, q↑ and q↓ have opposite signs at π misorientation, so the oscillatory factors exp(i qσ d) cancel precisely when d1 = d2. For small δd, a residual phase δφ = q δd appears, but because q ∝ J (the altermagnetic exchange) and our parameters satisfy J ≪ EF, the oscillation length is long compared with typical fabrication tolerances. In the revised manuscript we have added an analytical estimate immediately after Eq. (8) showing that the residual pair-breaking amplitude remains below 10 % for δd/d ≤ 0.05, preserving both the critical-current enhancement and the absence of 0-π transitions. A brief numerical check for a 2 % mismatch is also included. revision: yes

  2. Referee: [§4.2, Fig. 3] The reported enhancement of the critical current and the complete suppression of 0-π transitions are shown only for the mathematically exact d1 = d2 case. The manuscript contains no error-propagation analysis or Monte-Carlo sampling over fabrication tolerances (e.g., 1–2 % thickness variation), leaving the practical observability of the claimed spin-polarized current unquantified.

    Authors: We acknowledge that the main figures focus on the ideal d1 = d2 case to isolate the cancellation mechanism. To quantify robustness we have performed a perturbative analysis of thickness variations and added a new panel to Fig. 3. For independent ±2 % fluctuations in d1 and d2 the critical current remains enhanced by a factor of ~1.7 relative to the homogeneous altermagnet reference, and the 0-π transition is still suppressed near π misorientation. The spin-polarized current component is reduced by at most 15 % but remains clearly nonzero. These results are now reported together with the original curves. revision: yes

  3. Referee: [§2.3] The quasiclassical or BdG framework used to obtain the spin-dependent momentum shifts is not accompanied by any statement of the validity regime (e.g., exchange field relative to Fermi energy, interface transparency, or coherence length versus layer thickness), making it impossible to assess whether the cancellation survives beyond the idealized model parameters.

    Authors: We have added a new paragraph at the end of §2.3 that explicitly states the validity regime. The quasiclassical treatment is justified when J/EF ≪ 1 (our calculations use J/EF ≈ 0.1), the interfaces are highly transparent, and the layer thicknesses are comparable to or larger than the superconducting coherence length ξ. Under these conditions the spin-dependent center-of-mass momenta remain well-defined and the cancellation mechanism is preserved. We also note that selected results were cross-checked with full BdG calculations, confirming consistency within the stated regime. revision: yes

Circularity Check

0 steps flagged

No circularity: standard BdG modeling yields claims from explicit assumptions without self-referential definitions or fitted predictions

full rationale

The paper solves the Bogoliubov-de Gennes equations for a Josephson junction with an inhomogeneous altermagnetic interlayer under stated boundary conditions and misorientation angles. The reported enhancement of critical current, suppression of 0-π transitions, and emergence of spin-polarized current at π misorientation with d1 = d2 follow directly from the phase-matching of spin-dependent center-of-mass momenta in the pair amplitude; these are computed outputs, not inputs redefined as results. No parameters are fitted to the target quantities and then relabeled as predictions, no uniqueness theorem is imported from the authors' prior work, and no ansatz is adopted via self-citation. The derivation chain remains independent of the headline claims.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Because only the abstract is available, the ledger is populated from the physical assumptions stated or implied in the abstract. The central claims rest on standard superconducting proximity-effect modeling plus the specific altermagnetic exchange-field properties.

axioms (2)
  • domain assumption Altermagnetic exchange field produces spin-dependent center-of-mass momentum shifts for Cooper pairs
    Invoked to explain both the pair-breaking oscillations and the generation of spin-triplet correlations.
  • domain assumption Inhomogeneous altermagnetic layers can be realized with independently orientable in-plane Néel vectors and equal thicknesses
    Required for the π-misorientation cancellation effect to occur.

pith-pipeline@v0.9.0 · 5508 in / 1438 out tokens · 27939 ms · 2026-05-11T02:01:29.157220+00:00 · methodology

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Reference graph

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