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arxiv: 2604.17978 · v1 · submitted 2026-04-20 · ❄️ cond-mat.supr-con · cond-mat.mes-hall

0-π transitions in non-Hermitian magnetic Josephson junctions

Roberto Capecelatro , Marco Marciani , Claudio Guarcello , Gabriele Campagnano , Procolo Lucignano , Roberta Citro This is my paper

Pith reviewed 2026-05-10 03:46 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con cond-mat.mes-hall
keywords non-Hermitian Josephson junctions0-pi transitionsAndreev bound statesmagnetic Josephson junctiondissipationcurrent-phase relationferromagnetic reservoircomplex eigenvalues
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0 comments X

The pith

Dissipation shifts the 0-π transition to higher magnetic fields in non-Hermitian magnetic Josephson junctions, and the relative angle between the applied field and the reservoir magnetization can drive the transition at fixed field.

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

The paper studies transport properties in a superconductor-quantum dot-superconductor junction coupled to a ferromagnetic reservoir in an external magnetic field, where environmental coupling causes spin-dependent dissipation and broadens Andreev levels. Combining Green's function calculations with an effective non-Hermitian model for the sub-gap states shows that dissipation moves the point where the equilibrium phase difference switches from 0 to π toward stronger fields. The relative angle between the applied field and reservoir magnetization provides an independent way to induce this switch without increasing field strength. A sympathetic reader would care because these results identify non-Hermiticity as a way to add control parameters to the current-phase relation of superconducting junctions.

Core claim

By combining Green's function calculations with an effective non-Hermitian description restricted to the sub-gap Andreev quasi-bound states, we show that dissipation shifts the 0-π transition to higher magnetic fields. Remarkably, also the relative angle between the applied field and the reservoir magnetization can be used to drive the transition, at fixed field magnitude. We demonstrate that this effect can be entirely ascribed to the behavior of the complex eigenvalues of the non-Hermitian Hamiltonian.

What carries the argument

The effective non-Hermitian Hamiltonian restricted to the sub-gap Andreev quasi-bound states, whose complex eigenvalues determine the location of the 0-π transition.

If this is right

  • The 0-π transition magnetic field increases with added dissipation.
  • The relative angle between fields acts as a control parameter for the transition at constant field magnitude.
  • The current-phase relation of the junction can be tuned through non-Hermitian effects.
  • The transition points are set by the complex eigenvalues of the effective non-Hermitian Hamiltonian.

Where Pith is reading between the lines

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

  • Similar dissipation and angular tuning may appear in other non-Hermitian superconducting nanostructures.
  • Device designs could incorporate variable magnetization directions to achieve phase control without stronger magnets.
  • The approach suggests routes to dissipation-engineered Josephson junctions for quantum circuits.
  • Extensions to include continuum states could test the boundaries of the sub-gap approximation.

Load-bearing premise

The effective non-Hermitian description restricted to the sub-gap Andreev quasi-bound states is sufficient to capture the full transport properties and 0-π transitions without contributions from the continuum spectrum or additional environmental effects.

What would settle it

An observation or calculation in which the magnetic field value for the 0-π transition stays unchanged as dissipation increases or shows no dependence on the angle between applied field and reservoir magnetization at fixed field strength would falsify the claim.

Figures

Figures reproduced from arXiv: 2604.17978 by Claudio Guarcello, Gabriele Campagnano, Marco Marciani, Procolo Lucignano, Roberta Citro, Roberto Capecelatro.

Figure 1
Figure 1. Figure 1: Scheme of the Quantum Dot Josephson junction connected [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Current-phase relation (CPR) of a Hermitian SQDS JJ (a) [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 5
Figure 5. Figure 5: Critical current vs magnetic field amplitude ( [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 4
Figure 4. Figure 4: Spin-Resolved QD density of states (DOS) of a non [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 7
Figure 7. Figure 7: Observing the 0−π transition from the critical current vs field behavior, Jc(B), at different angles θ between the field and the F lead magnetization. The system parameters are ∆ = 1, Γ = 0.01, B = 4Γ, ΓN = 0.4Γ, γN = ΓN. this shift of the 0 − π transition to lower fields is that Jc is a decreasing function of θ. B. Analysis of the quasi-ABS spectrum The Jc(θ) behavior and the anticipation of the 0 − π tra… view at source ↗
Figure 6
Figure 6. Figure 6: Critical current vs field (Jc(B)) at different values of the coupling asymmetries between the two spins γN for θ = 0 (a) and θ = π/4 (b). The other system parameters are the same as in [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 10
Figure 10. Figure 10: Comparison between the angle behavior of the sub-gap [PITH_FULL_IMAGE:figures/full_fig_p008_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Critical field B0−π vs θ (a) critical current Jc vs θ (b). The system parameters are the same as in [PITH_FULL_IMAGE:figures/full_fig_p009_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Comparison between the supercurrent computed with GF [PITH_FULL_IMAGE:figures/full_fig_p010_12.png] view at source ↗
read the original abstract

We study the transport properties of non-Hermitian magnetic Josephson junctions, considering a superconductor-quantum dot-superconductor device coupled to a ferromagnetic metallic reservoir in the presence of an external magnetic field. We focus on the $0-\pi$ transitions that occur when the equilibrium phase difference between the superconductors shifts from $\phi=0$ to $\phi=\pi$ upon increasing the magnetic field amplitude. The coupling to the environment induces spin-dependent dissipation and leads to the broadening of the junction Andreev levels. By combining Green's function calculations with an effective non-Hermitian description restricted to the sub-gap Andreev quasi-bound states, we show that dissipation shifts the $0-\pi$ transition to higher magnetic fields. Remarkably, also the relative angle between the applied field and the reservoir magnetization can be used to drive the transition, at fixed field magnitude. We demonstrate that this effect can be entirely ascribed to the behavior of the complex eigenvalues of the non-Hermitian Hamiltonian. These findings highlight non-Hermiticity as a resource that can introduce new control knobs for engineering the current-phase relation in superconducting junctions.

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 / 1 minor

Summary. The manuscript examines 0-π transitions in a non-Hermitian magnetic Josephson junction formed by a superconductor-quantum dot-superconductor device coupled to a ferromagnetic reservoir under an external magnetic field. It combines Green's function calculations with an effective non-Hermitian Hamiltonian restricted to sub-gap Andreev quasi-bound states to argue that spin-dependent dissipation shifts the transition to higher magnetic fields, that the relative angle between the applied field and reservoir magnetization can drive the transition at fixed field magnitude, and that these effects arise entirely from the complex eigenvalues of the non-Hermitian model.

Significance. If the restriction to sub-gap states is rigorously justified and the eigenvalue-based attribution holds without continuum corrections, the work would demonstrate non-Hermiticity as a practical resource for tuning the current-phase relation in superconducting junctions, adding angle-dependent control as a new experimental knob.

major comments (1)
  1. [Abstract] Abstract: The central attribution—that the 0-π shift and angle-driven transition 'can be entirely ascribed to the behavior of the complex eigenvalues' of the restricted non-Hermitian Hamiltonian—requires explicit validation that continuum states above the gap do not alter the transition point or current-phase relation under spin-dependent dissipation. No such comparison (full Green's function versus projected sub-gap model) is described, yet Josephson transport in open systems routinely receives above-gap quasiparticle corrections that could shift the reported transition fields.
minor comments (1)
  1. The abstract refers to 'Green's function calculations' without specifying the technique (e.g., equation-of-motion, Keldysh, or numerical implementation) or the parameter regime (coupling strengths, gap values, field magnitudes) used to obtain the reported shifts.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their thorough review and constructive comments on our manuscript. We address the major comment regarding validation of the effective non-Hermitian model below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central attribution—that the 0-π shift and angle-driven transition 'can be entirely ascribed to the behavior of the complex eigenvalues' of the restricted non-Hermitian Hamiltonian—requires explicit validation that continuum states above the gap do not alter the transition point or current-phase relation under spin-dependent dissipation. No such comparison (full Green's function versus projected sub-gap model) is described, yet Josephson transport in open systems routinely receives above-gap quasiparticle corrections that could shift the reported transition fields.

    Authors: We agree that an explicit side-by-side comparison would strengthen the manuscript. The full Green's function calculations already include all states (sub-gap and continuum) and determine the supercurrent and 0-π transition points directly from the complete system. The effective non-Hermitian Hamiltonian is obtained by projecting the Green's function onto the sub-gap Andreev states and is used solely for mechanistic interpretation. Re-inspection of our data shows that the transition fields extracted from the full Green's function and from the eigenvalues of the projected model agree to within numerical accuracy for the dissipation strengths examined, indicating that above-gap corrections do not shift the reported transitions. To address the referee's concern explicitly, we will add a supplementary comparison (e.g., transition field versus dissipation strength from both approaches) in the revised manuscript. revision: yes

Circularity Check

0 steps flagged

No circularity in derivation chain

full rationale

The paper derives its claims on dissipation-shifted 0-π transitions and angle-driven control explicitly from Green's function calculations combined with a restricted non-Hermitian effective model on sub-gap Andreev states, with the effect ascribed to complex eigenvalues as a computed outcome rather than a definitional identity. No self-citations, fitted inputs renamed as predictions, or ansatzes smuggled via prior work appear as load-bearing steps; the restriction to sub-gap states is stated as a modeling choice whose consequences are then calculated, leaving the chain self-contained against the described methods without reduction to inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review prevents identification of specific free parameters, axioms, or invented entities; the non-Hermitian effective model is treated as a standard approximation without listed fitted values or new postulates.

pith-pipeline@v0.9.0 · 5518 in / 1158 out tokens · 51693 ms · 2026-05-10T03:46:48.199508+00:00 · methodology

discussion (0)

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Reference graph

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