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arxiv: 2606.17704 · v1 · pith:3MNPLYJInew · submitted 2026-06-16 · ❄️ cond-mat.supr-con · cond-mat.mes-hall· cond-mat.mtrl-sci

AC-flux-driven SQUID diode spectroscopy as a probe of current-phase relations

Yuriy Yerin , Iman Askerzade , Alexey Fedorchenko , Ali Gencer , Oleksandr Dobrovolskiy This is my paper

Pith reviewed 2026-06-26 22:26 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con cond-mat.mes-hallcond-mat.mtrl-sci
keywords current-phase relationJosephson junctionSQUID diodeac flux modulationBessel functionsdiode efficiencyunconventional superconductorsfractional harmonics
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The pith

Ac flux modulation in asymmetric SQUIDs dresses each CPR harmonic with a distinct Bessel function, producing unique signatures in diode efficiency.

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

The paper aims to extract higher-order and fractional harmonics from Josephson junction current-phase relations, which static interference patterns cannot reliably distinguish because different components produce similar results and are masked by asymmetries and dynamics. It shows that driving asymmetric dc SQUIDs with ac magnetic flux modulates each harmonic by a unique Bessel function, creating identifiable features in the diode efficiency as a function of ac amplitude and frequency. Two complementary analytical reductions—one Kapitza-type perturbation for conventional cases and Jacobi-Anger averaging for general CPRs—predict these signatures, which numerical solutions of the dynamical equations confirm for sinφ, sin(φ/2), and sin2φ terms. The resulting phase diagrams of diode efficiency exhibit distinct weak, sparse, dense, or intermodulated arc patterns that hold in both overdamped and underdamped regimes.

Core claim

Ac flux modulation dresses each harmonic with a distinct Bessel function, yielding characteristic signatures in the diode efficiency η(φ_ac,ω) as a function of ac flux amplitude φ_ac and frequency ω. Using Kapitza-type perturbation theory for conventional junctions and Jacobi-Anger averaging for a general CPR, the approach is verified by numerical solutions of the coupled dynamical equations, which produce robust arc patterns in η(φ_ac,ω) phase diagrams for CPRs containing sinφ, sin(φ/2), and sin2φ terms that remain distinct across damping regimes.

What carries the argument

The ac-flux-driven diode effect in asymmetric dc SQUIDs with unequal junction critical currents, where the diode efficiency η(φ_ac,ω) encodes the Bessel-modulated signatures of individual CPR harmonics.

Load-bearing premise

The Kapitza-type perturbation theory and Jacobi-Anger averaging accurately reduce the fast-driven dynamics while preserving distinct harmonic signatures without being obscured by device asymmetries or dynamical effects.

What would settle it

An experiment measuring diode efficiency versus ac flux amplitude and frequency in SQUIDs with controlled CPRs that fails to produce the predicted distinct arc patterns would falsify the claim that ac driving separates the harmonics via Bessel functions.

Figures

Figures reproduced from arXiv: 2606.17704 by Alexey Fedorchenko, Ali Gencer, Iman Askerzade, Oleksandr Dobrovolskiy, Yuriy Yerin.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic of the asymmetric dc SQUID geome [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Diode efficiency [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Static diode efficiency [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Flux-drive-amplitude dependence of the diode efficiency [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Two-dimensional phase diagrams of the diode efficiency [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Two-dimensional phase diagrams of the diode efficiency [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
read the original abstract

The current-phase relation (CPR) of a Josephson junction encodes microscopic information on superconducting states through higher-order and fractional harmonics. However, their unambiguous extraction is challenging, as different CPR components produce nearly identical static interference patterns that are further obscured by device asymmetries, damping, and dynamical effects. Here, we propose probing individual CPR harmonics via the ac magnetic-flux-driven diode effect in asymmetric dc SQUIDs with unequal junction critical currents. Using two complementary reductions of the fast-driven dynamics -- a Kapitza-type perturbation theory for the conventional junction and a Jacobi--Anger averaging for a general CPR -- we show that ac flux modulation dresses each harmonic with a distinct Bessel function, yielding characteristic signatures in the diode efficiency $\eta(\phi_{\rm ac},\omega)$ as a function of ac flux amplitude $\phi_{\rm ac}$ and frequency $\omega$. We verify and extend these predictions by numerical solutions of the coupled dynamical equations for CPRs containing $\sin\varphi$, $\sin(\varphi/2)$, and $\sin 2\varphi$ terms ($\varphi$: superconducting phase difference), and construct phase diagrams of $\eta(\phi_{\rm ac},\omega)$. Distinct CPR components are revealed to produce characteristic weak, sparse, dense, or intermodulated arc patterns that remain robust in both overdamped and underdamped regimes. This suggests ac-flux-driven SQUID diode spectroscopy as a probe of current-phase relations in topological materials, multiband systems, and other unconventional superconductors.

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

0 major / 3 minor

Summary. The manuscript proposes AC-flux-driven SQUID diode spectroscopy to extract individual current-phase relation (CPR) harmonics. Using a Kapitza-type perturbation reduction for the conventional junction and Jacobi-Anger averaging for general CPRs, it shows that AC flux dresses each harmonic with a distinct Bessel function, producing characteristic signatures in the diode efficiency η(φ_ac, ω). These predictions are verified and extended by direct numerical integration of the coupled RSJ equations for three explicit CPRs (sin φ, sin(φ/2), sin 2φ), yielding distinct weak/sparse/dense/intermodulated arc patterns in η(φ_ac, ω) phase diagrams that persist in both overdamped and underdamped regimes.

Significance. If the signatures remain distinct, the method supplies a dynamical probe capable of distinguishing higher-order and fractional CPR components that are otherwise degenerate in static interference patterns. The manuscript supplies both analytical reductions and direct numerical solutions of the RSJ equations across damping regimes; this combination of complementary derivations and explicit verification for multiple CPRs strengthens the central claim.

minor comments (3)
  1. [Abstract] Abstract: the diode efficiency η is introduced without an explicit formula; stating its definition (e.g., the normalized difference of critical currents) would clarify the central observable from the outset.
  2. [Abstract] Abstract: 'Kapitza-type perturbation theory' is invoked without a one-sentence description or citation; a brief gloss would assist readers outside the immediate subfield.
  3. The manuscript refers to 'phase diagrams of η(φ_ac,ω)' but does not specify the precise range or sampling of ω relative to the plasma frequency; adding this detail would make the robustness claims easier to assess.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary, significance assessment, and recommendation of minor revision. No major comments were raised in the report.

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The manuscript derives the diode efficiency signatures from the standard resistively shunted junction (RSJ) equations using established Kapitza-type perturbation theory and Jacobi-Anger averaging. These reductions are applied to explicit CPR forms (sin φ, sin(φ/2), sin 2φ) and the resulting predictions are cross-checked against independent numerical solutions of the dynamical equations in both overdamped and underdamped regimes. No parameters are fitted to the target η(φ_ac, ω) data, no self-citations form the load-bearing justification, and the Bessel dressing follows directly from the averaging identities rather than being defined into the result. The derivation chain is therefore self-contained against external mathematical benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard models of Josephson dynamics and new averaging approximations for the driven regime; no free parameters or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption Standard resistively shunted junction model governs the SQUID dynamics
    Invoked for the coupled dynamical equations solved numerically.
  • domain assumption Kapitza-type perturbation theory and Jacobi-Anger averaging validly reduce the fast AC-driven regime
    Central to obtaining the Bessel dressings for each harmonic.

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