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    Equidistant resonance jumps in superconducting coplanar resonators driven by Abrikosov vortices

    Dmitrii S. Kalashnikov1,*, Denis Yu. Vodolazov1,2, Ruslan I. Kinzibaev1,3, Andrei G. Shishkin1,3, and Vasily S. Stolyarov1,3,†

    • *Contact author: kalashnikov.ds@phystech.edu
    • †Contact author: stolyarov.vs@phystech.edu

    Phys. Rev. B 114, 024502 – Published 1 July, 2026

    DOI: https://doi.org/10.1103/d3wg-6ls3

    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 S21 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, staircaselike jumps as a function of magnetic field. Upon reversal of the field sweep, these jumps form an almost equidistant series with spacing ΔH≃1.7–1.8Oe, which, in agreement with theoretical estimates, we interpret as signatures of multiple-vortex entry and exit events. Additionally, we observe the nonproportional responses of the resonant frequency and the internal quality factor that indicate a complex contribution of vortex and antivortex configurations. We expect that our results will stimulate further studies of large vortex-antivortex systems, explicitly accounting for their discrete nature.

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