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arxiv: 2605.15751 · v2 · pith:SZ2SXWRS · submitted 2026-05-15 · cond-mat.supr-con

Equidistant resonance jumps in superconducting coplanar resonators driven by Abrikosov vortices

Dmitrii S. Kalashnikov , Denis Yu. Vodolazov , Ruslan I. Kinzibaev , Andrei G. Shishkin , Vasily S. Stolyarov This is my paper

Reviewed by Pith2026-07-02 23:34 UTCgrok-4.3pith:SZ2SXWRSopen to challenge →

classification cond-mat.supr-con
keywords superconducting resonatorsAbrikosov vorticesmagnetic field dependenceresonance jumpscoplanar waveguideniobiumvortex entry
0
0 comments X

The pith

Abrikosov vortex entry and exit events produce equidistant jumps in the resonance of superconducting coplanar resonators.

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

This paper examines how perpendicular magnetic fields affect the transmission parameter S21 of niobium quarter-wave coplanar resonators at temperatures from 18 mK to 5 K. Beyond the reversible Meissner regime the entire resonance peak shows abrupt staircase-like jumps with increasing field. When the field sweep direction reverses, the jumps form an almost equidistant series spaced 1.7-1.8 Oe apart. The authors interpret this spacing, which matches their theoretical estimates, as signatures of multiple Abrikosov vortex entry and exit events. They additionally report non-proportional shifts in resonant frequency and internal quality factor that point to complex vortex-antivortex configurations.

Core claim

In niobium coplanar resonators the resonance parameter S21 exhibits staircase-like jumps as a function of perpendicular magnetic field beyond the reversible Meissner regime. Upon field reversal these jumps form an almost equidistant series with spacing 1.7-1.8 Oe, which the authors interpret as signatures of multiple Abrikosov vortex entry and exit events. The resonant frequency and internal quality factor exhibit non-proportional responses indicating a complex contribution from vortex and antivortex configurations.

What carries the argument

The staircase-like jumps in S21 versus perpendicular magnetic field, interpreted as multiple-vortex entry and exit events.

If this is right

  • Resonator performance in magnetic fields is governed by discrete vortex events rather than smooth continuous effects.
  • Non-proportional frequency and quality-factor shifts arise from vortex-antivortex configurations.
  • Large vortex-antivortex systems must be modeled with explicit account of their discrete nature.

Where Pith is reading between the lines

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

  • Device geometry or film pinning could be engineered to suppress or control the size of these jumps for improved field tolerance.
  • Similar discrete jumps may limit the stability of other superconducting microwave circuits operating near small perpendicular fields.
  • The regular spacing offers a potential experimental handle for measuring effective vortex density or pinning energy in thin films.

Load-bearing premise

That the observed 1.7-1.8 Oe jump spacing matches theoretical estimates for multiple-vortex events.

What would settle it

Measuring whether the jump spacing remains 1.7-1.8 Oe in a resonator film with deliberately altered pinning strength or at a field strength where single-vortex entry is independently confirmed.

Figures

Figures reproduced from arXiv: 2605.15751 by Andrei G. Shishkin, Denis Yu. Vodolazov, Dmitrii S. Kalashnikov, Ruslan I. Kinzibaev, Vasily S. Stolyarov.

Figure 1
Figure 1. Figure 1: FIG. 1. Sample A. (a) Design of the chip layout with six [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Magnetic-field dependence of resonator #3. (a,b) Color maps of the transmission amplitude [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Equidistant jumps in the resonance frequency. Panels (a) and (b) show the dependence of the resonant frequency [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (a) Field-dependent kinetic inductance of a vortex [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Color maps of the transmission amplitude, [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
read the original abstract

Superconducting coplanar resonators are key building blocks of cryogenic microwave circuits, yet their performance in perpendicular magnetic fields is ultimately limited by Abrikosov vortices. In this work we investigate the dependence of the transmission parameter $S_{21}$ of niobium quarter-wave coplanar resonators on perpendicular magnetic fields up to 40 Oe and at temperatures between 18 mK and 5 K. Beyond the reversible Meissner regime, the entire resonance peak exhibits abrupt, staircase-like jumps as a function of magnetic field. Upon reversal of the field sweep, these jumps form an almost equidistant series with spacing 1.7-1.8 Oe, which, in agreement with theoretical estimates, we interpret as signatures of multiple-vortex entry and exit events. Additionally, we observe the non-proportional responses of the resonant frequency and the internal quality factor that indicate a complex contribution of vortex and antivortex configurations. We believe that our results will stimulate further studies of large vortex-antivortex systems, explicitly accounting for their discrete nature.

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 / 0 minor

Summary. The manuscript reports experimental measurements of the transmission parameter S21 in niobium quarter-wave coplanar resonators under perpendicular magnetic fields up to 40 Oe and temperatures from 18 mK to 5 K. Beyond the reversible Meissner regime, the resonance peak exhibits abrupt staircase-like jumps; upon field reversal these form an almost equidistant series with spacing 1.7-1.8 Oe, which the authors interpret as signatures of multiple Abrikosov vortex entry and exit events in agreement with theoretical estimates. Non-proportional responses of resonant frequency and internal quality factor are also noted, suggesting complex vortex-antivortex configurations.

Significance. If the quantitative match between observed spacing and first-principles vortex-entry estimates is demonstrated with explicit parameters and device geometry, the work would provide direct evidence for discrete multi-vortex dynamics in superconducting resonators at millikelvin temperatures. This could inform design of field-tolerant microwave circuits and motivate studies of large vortex-antivortex systems, though the current text supplies only the observational claim without the supporting calculation.

major comments (1)
  1. [Discussion / interpretation of results] The central interpretation—that the 1.7-1.8 Oe spacing matches theoretical estimates for multiple-vortex entry/exit—requires an explicit derivation or parameter set (e.g., Φ₀/(w·d), Nb film λ, ξ, or pinning assumptions) to be load-bearing. The manuscript states agreement with 'theoretical estimates' but provides neither the formula, numerical inputs from the resonator dimensions, nor the vortex-density calculation, leaving the numerical agreement unverifiable and alternative explanations (geometric resonances, flux avalanches, or sweep artifacts) unaddressed.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback. The point raised about strengthening the interpretation is well taken, and we will revise the manuscript accordingly to address it directly.

read point-by-point responses

  1. Referee: [Discussion / interpretation of results] The central interpretation—that the 1.7-1.8 Oe spacing matches theoretical estimates for multiple-vortex entry/exit—requires an explicit derivation or parameter set (e.g., Φ₀/(w·d), Nb film λ, ξ, or pinning assumptions) to be load-bearing. The manuscript states agreement with 'theoretical estimates' but provides neither the formula, numerical inputs from the resonator dimensions, nor the vortex-density calculation, leaving the numerical agreement unverifiable and alternative explanations (geometric resonances, flux avalanches, or sweep artifacts) unaddressed.

    Authors: We agree that the current manuscript would be strengthened by an explicit derivation. In the revised version we will add a dedicated paragraph (or short appendix) that derives the expected field spacing using the resonator geometry, Nb film thickness d and width w, the flux quantum Φ₀, and the London penetration depth λ together with coherence length ξ appropriate for the Nb film. The calculation will be compared directly to the measured 1.7–1.8 Oe interval. We will also insert a concise discussion of why geometric resonances, flux avalanches and sweep-rate artifacts are inconsistent with the data, citing the observed temperature dependence, the near-perfect reversibility upon field reversal, and the narrow field window. These additions will be made without changing any experimental results or figures. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental data interpreted via external theory

full rationale

The paper reports direct experimental observations of abrupt staircase jumps in the resonance peak (S21) versus perpendicular magnetic field, with measured spacing 1.7-1.8 Oe on field reversal. The interpretation as multiple-vortex entry/exit is stated to agree with 'theoretical estimates' but the abstract supplies no internal derivation, fitting procedure, or self-citation that reduces the spacing claim to the data by construction. No equations, ansatzes, or uniqueness theorems are invoked that would make the result tautological. The central claim therefore rests on independent observation plus external benchmarks rather than any of the enumerated circular patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No mathematical derivation or model appears in the abstract; the central claim is an experimental observation with an interpretive link to vortex events.

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