Zero-Bias Shapiro Steps in Asymmetric Pinning Nanolandscapes

  • O. V. Dobrovolskiy
  • V. V. Sosedkin
  • R. Sachser
  • V. A. Shklovskij
  • R. V. Vovk
  • M. Huth
Original Paper


The coherent nonlinear dynamics of Abrikosov vortices in asymmetric pinning nanolandscapes is studied by theoretical modeling and combined microwave and dc electrical resistance measurements. The problem is considered on the basis of a single-vortex Langevin equation within the framework of a stochastic model of anisotropic pinning. When the distance over which Abrikosov vortices are driven during one half ac cycle coincides with one or a multiple of the nanostructure period, Shapiro steps appear in the current-voltage curves (CVCs) as a general feature of systems whose evolution in time can be described in terms of a particle moving in a periodic potential under combined dc and ac stimuli. While a dc voltage appears in response to the ac drive, the addition of a dc bias allows one to diminish the rectified voltage and eventually to change its sign when the extrinsic dc bias-induced asymmetry of the pinning potential starts to dominate the intrinsic one. This rectified negative voltage in the CVCs becomes apparent as zero-bias Shapiro steps, which are theoretically predicted and experimentally observed for the first time.


Shapiro steps Nonlinear vortex dynamics Washboard pinning potential Ratchet reversal Combined microwave and dc electrical resistance measurements 



This work was financially supported by the German Research Foundation (DFG) through grant DO 1511 and conducted within the framework of the NanoSC-COST Action MP1201 of the European Cooperation in Science and Technology. This research has received funding from the European Unions Horizon 2020 research and innovation program under Marie Sklodowska-Curie Grant Agreement No. 644348 (MagIC).


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Goethe UniversityFrankfurt am MainGermany
  2. 2.V. Karazin National UniversityKharkivUkraine

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