Description of zero field steps on the potential energy surface of a Frenkel-Kontorova model for annular Josephson junction arrays

W. Quapp,J. M. Bofill

doi:10.1140/epjb/s10051-021-00115-w

Abstract

We explain the emergence of zero field steps (ZFS) in a Frenkel-Kontorova (FK) model for a 1D annular chain being a model for an annular Josephson junction array. We demonstrate such steps for a case with a chain of 10 phase differences. We necessarily need the periodic boundary conditions. We propose a mechanism for the jump from M fluxons to M+1 in the chain.Graphic abstract

Highlights

This paper continues the former two-part series on Shapiro steps [1,2]
We explain the emergence of zero field steps (ZFS) in a Frenkel-Kontorova (FK) model for a 1D annular chain being a model for an annular Josephson junction array
Zero field steps (ZFS) [3] are reported under dc bias, they are another kind of steps in comparison to Shapiro steps which emerge with an additional frequency of an ac-excitation

Summary

Introduction

This paper continues the former two-part series on Shapiro steps [1,2]. Zero field steps (ZFS) [3] are reported under dc bias, they are another kind of steps in comparison to Shapiro steps which emerge with an additional frequency of an ac-excitation. What is quasi ‘fixed’ is the continuously alternating change of the minimum- and the SP1-structure where the single PDs run through their numbering but the chain goes on in Φ-direction. The ring condition secures, in the case M = 0, that we first get a rigid vector, Φ If we move it by a sufficiently strong extended unitary force it will overcome the top of the cosine function of the site-up potential. Both curves bifurcate at a valley-ridge inflection point (VRI), and unite after this with the global minimum or the higher SP3.

The overdamped Langevin equation

Impurities

The folding problem

Discussion

Conclusion