Lower critical field and vortices configuration in 2D superconducting junction arrays

Abstract

In order to describe properly the magnetic status of a 2D superconducting junction array, one has to consider not only the effect of the screening currents but also that of the particular experimental protocol followed to measure the physical quantities of interest like, for example, the magnetization. We show that the value of the lower critical field, f~l, of the junction array depends strongly on the intensity of the screening currents, i.e. on the strength of the junction coupling, Ej, and that reliable results can be obtained only by considering the full-inductance matrix. We also show that the magnetic configuration of the vortices may depend on the particular experimental approach followed (static or dynamic) and, even, in some cases, on the initial configuration of the phases.

Static properties of classical Josephson junction arrays: models and experimental achievements

“…Equations ( 37) and (38) show that the I -V (J -E) curve is different at different temperatures, but all the different curves coincide just on re-scaling I → I /(T 1+ν(d−1) ) or I → I/(|t| ν (d−1) ). This gives us a clue as to how to search for vestiges of a second transition and to determine critical exponents from I -V curves.…”

“…Stability analysis can be related to depinning, which occurs when a given static vortex configuration loses its stability as a result of variation of the external current, the applied magnetic field etc [37]. On the other hand, the loss of stability of the zero-vortex (w = 0) configuration as frustration is raised starting at f = 0 has been studied as a guess at the mechanism of field penetration [38]. Furthermore, remarkably the study of the stability of the static states has been recently proved to be relevant to the understanding of such an attractive dynamical phenomenon as row switching [39].…”

“…For finite values of λ ⊥ , the expected effect is the increase of the range of f -values where any vortex configuration is stable. This was explicitly checked for ladders [16] and 2D arrays [38] (for the case of a ladder, see figure 6).…”

Single-vortex dynamics in overdamped Josephson junction ladders

“…Here F F is the inductance matrix. We have obtained it by applying the Biot-Savart law so as to calculate the magnetic field induced on a link by all of the currents circulating in the array (every current is supposed to flow within a cylinder of length a and radius 0.005a) [5]. λ ⊥ is the penetration depth of the magnetic field, defined as in [6]:…”

Vortex dynamics in classical Josephson junction arrays: models and recent experimental developments

“…Further motivation for writing this article was provided by the need to review the important progress recently made in the understanding of the JJA physics related to the reformulation of the 'JJ array formalism' to include a full-screening term-a reformulation that was first implemented by Phillips et al [17] and then, in an independent way, by other groups [18,19]. Now, as a result of the introduction of the full-inductance matrix, the mutual inductance of the currents flowing in the array (the Biot-Savart law) can be worked out in a precise manner and it is no longer introduced as an ad hoc mean-field quantity [20].…”