Josephson diode effect via a non-equilibrium Rashba system

Michiyasu Mori; Sadamichi Maekawa; Wataru Koshibae

REVIEW 2 major objections 1 minor 1 cited by

Josephson diode effect via a non-equilibrium Rashba system

T0 review · 2 major / 1 minor · reviewed 2026-05-23 · grok-4.3

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Pith's one-line read Current bias in a Rashba system creates the non-equilibrium state that produces the Josephson diode effect under an in-plane magnetic field.

desk verdict The paper identifies a current-bias-induced Fermi momentum shift in a 1D Rashba wire as the source of Josephson diode asymmetry under perpendicular B, but the 1D tunneling-Hamiltonian setup is the main limitation. read the letter →

arxiv 2501.05671 v4 submitted 2025-01-10 cond-mat.supr-con cond-mat.mes-hall

Michiyasu Mori , Wataru Koshibae , Sadamichi Maekawa This is my paper · ORCID

classification cond-mat.supr-concond-mat.mes-hall

keywords JosephsondiodeeffectRashbasystemnon-equilibriumstatecurrentbiasin-planemagneticfieldspin-orbitcouplingtunnelingHamiltoniansuperconductingelectrodes

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper shows that the Josephson diode effect originates in a non-equilibrium Rashba system driven by the current bias needed to measure its current-voltage curve. This bias shifts the Fermi momentum, and when combined with an in-plane magnetic field perpendicular to the current, it makes the Josephson coupling asymmetric. Previous work missed this because it treated the system as if it remained in equilibrium. The authors model the Rashba wire as one-dimensional and calculate the coupling with a tunneling Hamiltonian to derive the asymmetry. The size and direction of the diode effect then depend on the spacing between the superconducting electrodes, the field strength, and the spin-orbit coupling.

What carries the argument

The non-equilibrium Rashba system under current bias, formulated via a tunneling Hamiltonian in one dimension, which produces asymmetric Josephson coupling when an in-plane magnetic field is perpendicular to the bias current.

What would settle it

A measurement showing that the diode effect disappears when the current bias is removed while keeping the same in-plane field and electrode spacing would falsify the claim that the non-equilibrium shift is required.

Watch

Extended reading notes

Core claim

A non-equilibrium state in a Rashba system under an in-plane magnetic field is identified as the origin of the Josephson diode effect. This state is induced by a current bias which shifts the Fermi momentum away from equilibrium. When the magnetic field is applied perpendicular to the current, the Josephson coupling becomes asymmetric, giving rise to the diode effect whose magnitude and sign depend on the distance between the superconducting electrodes, the in-plane magnetic field, and the spin-orbit coupling strength.

Load-bearing premise

The Rashba system can be treated as strictly one-dimensional and the Josephson coupling can be captured by a tunneling Hamiltonian that accounts for the current-induced Fermi-momentum shift.

Editorial extensions

If this is right

The diode effect can be tuned in magnitude and sign by changing the electrode spacing d.
The effect requires the magnetic field to be perpendicular to the current direction.
Stronger spin-orbit coupling increases the size of the asymmetry.
The diode effect is absent if the system remains in equilibrium without current bias.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Similar non-equilibrium shifts may produce diode behavior in other systems that combine spin-orbit coupling with superconductivity.
Device design could use the dependence on d to place electrodes at spacings that maximize the effect for given material parameters.
The result suggests testing whether equilibrium calculations in related Josephson structures systematically underestimate asymmetry when current is flowing.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The main thing to know is that this work traces the Josephson diode effect to a non-equilibrium state created by the bias current itself, which shifts the Fermi points in the Rashba system and produces asymmetric tunneling when the in-plane field is perpendicular to the current. Previous equilibrium treatments missed this because they did not account for the shift needed to measure the I-V curve. They model the Rashba part as strictly one-dimensional and compute the Josephson coupling with a tunneling Hamiltonian, showing that the diode magnitude and sign vary with electrode spacing d, field strength, and spin-orbit strength. That parameter dependence is the concrete output and could be checked in devices. The approach is straightforward and stays within standard methods, so the calculation itself looks internally consistent on its own terms. The soft spot is the one-dimensional restriction plus the simple momentum-shift treatment inside an equilibrium tunneling form. Real Rashba channels are quasi-1D or 2D, with transverse modes and scattering that can mix states and potentially cancel the asymmetry or restore reciprocity. The abstract gives no indication they checked whether the effect survives adding width or using a self-consistent non-equilibrium distribution. This paper is for people already working on Rashba Josephson junctions and superconducting diodes who want a microscopic handle on the bias-induced mechanism. A reader focused on device optimization will get usable trends from the d dependence. It deserves a serious referee because it flags a specific overlooked origin and makes testable statements about parameter tuning, even though the dimensionality question will need addressing in revision.

Referee Report

2 major / 1 minor

Summary. The manuscript claims that the Josephson diode effect originates from a non-equilibrium state in a Rashba system under an in-plane magnetic field. This state is induced by a current bias that shifts the Fermi momentum away from equilibrium, an effect overlooked in prior work that implicitly assumes equilibrium formulations suffice. The Josephson coupling is formulated via a tunneling Hamiltonian with the Rashba system modeled as strictly one-dimensional; asymmetry (and thus the diode effect) appears when the magnetic field is perpendicular to the current, with magnitude and sign depending on electrode separation d, magnetic field, and spin-orbit coupling strength.

Significance. If the central result holds, it supplies a concrete microscopic mechanism for the Josephson diode effect and identifies current bias as an essential ingredient, which could guide device optimization through parameter tuning (especially d). The explicit contrast with equilibrium treatments is a useful clarification for the field.

major comments (2)

[Formulation of the Josephson coupling (one-dimensional Rashba model)] The central claim rests on the strictly one-dimensional modeling of the Rashba system together with an equilibrium tunneling Hamiltonian applied to a non-equilibrium distribution via a simple momentum shift. No demonstration is given that the resulting d-dependent asymmetry survives transverse-mode mixing or scattering, which would be expected in any quasi-1D or 2D realization and could restore reciprocity.
[Introduction and model assumptions] The manuscript asserts that equilibrium-based formulations are insufficient yet provides no explicit comparison showing where those formulations fail to produce the diode asymmetry; the non-equilibrium treatment is introduced without a baseline calculation that would establish necessity.

minor comments (1)

The dependence of the diode effect on d, B, and SOC strength is stated qualitatively; quantitative plots or analytic expressions for the critical current asymmetry would strengthen the presentation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment below and indicate the corresponding revisions.

read point-by-point responses

Referee: [Formulation of the Josephson coupling (one-dimensional Rashba model)] The central claim rests on the strictly one-dimensional modeling of the Rashba system together with an equilibrium tunneling Hamiltonian applied to a non-equilibrium distribution via a simple momentum shift. No demonstration is given that the resulting d-dependent asymmetry survives transverse-mode mixing or scattering, which would be expected in any quasi-1D or 2D realization and could restore reciprocity.

Authors: Our work employs a strictly one-dimensional Rashba model as the minimal setting in which the non-equilibrium momentum shift produces a clear, analytically tractable asymmetry in the Josephson coupling. The tunneling Hamiltonian with the shifted distribution is applied precisely to isolate this mechanism. We acknowledge that transverse-mode mixing or scattering in a quasi-1D or 2D geometry could in principle modify or suppress the effect, but demonstrating robustness would require a multi-channel scattering calculation that lies outside the scope of the present study. We have added a paragraph in the discussion section explicitly stating the one-dimensional approximation and its limitations. revision: partial
Referee: [Introduction and model assumptions] The manuscript asserts that equilibrium-based formulations are insufficient yet provides no explicit comparison showing where those formulations fail to produce the diode asymmetry; the non-equilibrium treatment is introduced without a baseline calculation that would establish necessity.

Authors: We agree that an explicit baseline comparison strengthens the argument. In the revised manuscript we have added a calculation of the Josephson coupling for the equilibrium (zero-bias) case, which yields a symmetric current-phase relation with no diode effect. This is contrasted directly with the non-equilibrium result to demonstrate that the Fermi-momentum shift is required for the asymmetry. The new comparison appears in the model section and is referenced in the introduction. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: derivation introduces independent non-equilibrium tunneling formulation

full rationale

The paper's central step is the explicit construction of a tunneling-Hamiltonian Josephson coupling for a current-biased 1D Rashba wire under in-plane B, which is presented as a new formulation that was previously overlooked. No equations reduce a fitted parameter to a prediction, no self-citation chain is invoked to justify uniqueness or an ansatz, and the 1D modeling choice is stated outright rather than smuggled in. The derivation therefore remains self-contained against external benchmarks and does not collapse to its inputs by construction.

Assumptions & free parameters 0 free parameters · 2 assumptions · 0 invented entities

The central claim rests on the validity of modeling the Rashba system as one-dimensional and using a tunneling Hamiltonian for the non-equilibrium state; no explicit free parameters or invented entities are mentioned in the abstract.

assumptions (2)

domain assumption The Rashba system can be modeled as one-dimensional
Explicitly stated in the abstract as the model used for the formulation.
ad hoc to paper Equilibrium-based formulations are insufficient to describe the Josephson effect
The paper identifies this assumption as the reason the non-equilibrium mechanism was overlooked.

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Cite this review

Pith. "Pith review of Josephson diode effect via a non-equilibrium Rashba system." pith.science (2026). https://pith.science/paper/2501.05671

@misc{pith2026250105671,
  author       = {Pith},
  title        = {Pith review of: Josephson diode effect via a non-equilibrium Rashba system},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2501.05671}},
  note         = {Machine review of arXiv:2501.05671}
}

abstract

A non-equilibrium state in a Rashba system under an in-plane magnetic field is identified as the origin of the Josephson diode effect. This state is induced by a current bias--necessary for measuring the current-voltage characteristics--which shifts the Fermi momentum away from equilibrium. This essential mechanism has been overlooked in previous studies. This oversight stems from the implicit assumption that the equilibrium-based formulations are sufficient to describe Josephson effect. We formulate the Josephson coupling via the non-equilibrium Rashba system under current bias using a tunneling Hamiltonian, where the Rashba system is modeled as one-dimensional. When the magnetic field is applied perpendicular to the current, the Josephson coupling becomes asymmetric, giving rise to the diode effect. The magnitude and sign of this effect depend on the distance between the superconducting electrodes $d$, the in-plane magnetic field, and the spin-orbit coupling strength. Our results clarify the microscopic origin of the Josephson diode effect, which can be optimized by tuning $d$.

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Forward citations

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Reviewed May 23, 2026 · model on record in the stance chip above.