Josephson vortices

Fig. 5.10. Variation of (a) the phase difference

An external field parallel to the superconducting ai>-planes penetrates into the sample in the form of so-called Josephson vortices. They differ from Abrikosov ones by the absence of a vortex core. The superconducting shielding currents are strongly confined to the ai>-planes. In fields occurring at a small angle to the ai>-plane the vortices have a step-like character (Fig. 4.2-18). They consist of a periodic sequence of parts parallel (Josephson vortices) and peipendicu-lar (Abrikosov vortices) to the a( -planes, respectively. The distance between the Abrikosov-parts depends on 0. 

Josephson junctions, 23 820, 821 Josephson string, 23 827 Josephson vortex, 23 827 Jost Report, 15 201, 202 Joule-Thompson effect, 12 374 Joule-Thomson expansion, 24 647, 648, 650-651... 

Here dm is the effective magnetic thickness of the junction, 0o the magnetic flux quantum, and My) the maximum Josephson current density. A complete oscillation of the pair current density is called a Josephson vortex and contains one magnetic flux quantum. This behavior is shown schematically in Fig. 5.10... 

Let us now consider the more interesting case > 1. The simplest realization of such a barrier comprises N 1 Josephson junctions connected in series, this gives U() = NIcsin(/N), 4>o — N. However, this system is formally metastable the vortices can traverse the junction providing phase slips A = 27r. To eliminate this, one would increase the barrier for the vortex formation, for instance, by making several parallel chains of junctions. This would further complicate the concrete function U(4>). We notice that any function U() can be approximated by a cubic parabola if the tilting of the washboard potential is close to the critical value. This is why we choose the cubic parabola form... 

Figure 5. Examples of magnetic recordings a- the schemes of different vortex systems (from top to bottom -single vortex in a flow of electrons I two vortices with opposite magnetic flux line of vortices with different number of flux quanta collective flow of a vortex system under influence of a transport current I with generation of the voltage V) b- Josephson junction c,d- DC- and HF-SQUIDs. ...

For H Hcr, the mean-squared thermal vortex fluctuation displacement u )tb in Josephson-coupled layers is given by... 

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