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Fiske steps and Abrikosov vortices in Josephson tunnel junctions

M. P. Lisitskiy and M. V. Fistul
Phys. Rev. B 81, 184505 – Published 10 May 2010
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  • INTRODUCTION
  • MODEL OF A JOSEPHSON JUNCTION WITH…
  • FISKE RESONANCES IN INHOMOGENEOUS…
  • CRITICAL CURRENT AND FISKE RESONANCES…
  • JOSEPHSON JUNCTIONS WITH MISALIGNED…
  • EXPERIMENTAL RESULTS AND DISCUSSION
  • CONCLUSIONS
  • ACKNOWLEDGEMENTS
    • References

    Abstract

    We present a theoretical and experimental study of the Fiske resonances in the current-voltage characteristics of “small” Josephson junctions with randomly distributed misaligned Abrikosov vortices. We obtained that in the presence of Abrikosov vortices, the resonant interaction of electromagnetic waves, excited inside a junction, with the ac Josephson current manifests itself by Fiske steps in a current-voltage characteristics even in the absence of external magnetic field. We found that the voltage positions of the Fiske steps are determined by a junction size but the Fiske-step magnitudes depend both on the density of trapped Abrikosov vortices and on their misalignment parameter. We measured the magnetic field dependence of both the amplitude of the first Fiske step and the Josephson critical current of low-dissipative small Nb-based Josephson tunnel junctions with artificially introduced Abrikosov vortices. A strong decay of the Josephson critical current and a weak nonmonotonic decrease in the first Fiske-step amplitude on the Abrikosov vortex density were observed. The experimentally observed dependencies are well described by the developed theory.

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    • Received 18 February 2010

    DOI:https://doi.org/10.1103/PhysRevB.81.184505

    ©2010 American Physical Society

    Authors & Affiliations

    M. P. Lisitskiy*

    • Istituto di Cibernetica “E.Caianiello” del CNR, Via Campi Flegrei 34, 80078 Pozzuoli, Naples, Italy

    M. V. Fistul

    • Theoretische Physik III, Ruhr-Universität Bochum, D-44801 Bochum, Germany

    • *m.lisitskiy@cib.na.cnr.it

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    Vol. 81, Iss. 18 — 1 May 2010

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    • Figure 1
      Figure 1
      Schematic cross section of a Josephson tunnel junction with a misaligned Abrikosov vortex. δ is the misalignment length. λL1 and λL2 are the London penetration depths of the superconductors S1 and S2 separated by insulating layer I forming the tunnel barrier. The orientation of the two magnetic field, B⊥ and B∥, is provided.Reuse & Permissions
    • Figure 2
      Figure 2
      I−V curves recorded at B∥=2.2 G when the first Fiske step is maximized (open circles) and at B∥=12.7 G when the Fiske step is suppressed (closed circles). The method allowing to extract both the amplitude of the first Fiske step, IF(1), and its voltage position, V1, is shown. The experimental first Fiske-step branch is fitted by a linear function in the current interval between IcF/2 and IcF (dashed line). The experimental quasiparticle branch is fitted by a polynomial function (solid line). The voltage position V1 is obtained from the point of the intersection of the dashed line with the solid line. The amplitude of the first Fiske step is IF(1)=IcF−Iq, where Iq is the quasiparticle current at voltage V1. VIc is the threshold voltage to define the Josephson critical current.Reuse & Permissions
    • Figure 3
      Figure 3
      The experimental Ic(B∥) curve (open circles) and theoretical fit by Eq. (10) (solid line). The trapped Abrikosov vortices are absent.Reuse & Permissions
    • Figure 4
      Figure 4
      Experimental IF(1)(B∥) curve for the junction without trapped Abrikosov (open circles). Solid line represents the theoretical dependence calculated by Eqs. (4, 5) for γ=1.1×1010 s−1. Dashed line is the result of calculation without J12(a2) term at γ=4.3×109 s−1 according to the original theoretical analysis of Ref. 27.Reuse & Permissions
    • Figure 5
      Figure 5
      Ic(B∥) curves measured after cooling of the junction in perpendicular magnetic field B⊥ of various values.Reuse & Permissions
    • Figure 6
      Figure 6
      IF(1)(B∥) curves measured after the junction was cooled in perpendicular magnetic field B⊥ of various values.Reuse & Permissions
    • Figure 7
      Figure 7
      Open squares: experimental dependence of the maximum Josephson critical current Icmax on the density of trapped Abrikosov vortices nA; open circles: experimental dependence of the maximum amplitude of the first Fiske step IF(1),max on the density of trapped Abrikosov vortices nA. Solid line is the theoretical IF(1),max(nA) curve, calculated by Eqs. (7, 11). The values of γ=2.2×1010 s−1 and a mean misalignment parameter over all vortex densities δ¯=0.8 μm were used; full circles represent the theoretical IF(1),max(nA) dependence obtained by Eqs. (8, 11).Reuse & Permissions
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