Self-Organization in a Long Josephson Junction
The discovery of the Josephson effect stimulated the development of superconductor microelectronics with a huge number of both theoretical and experimental papers devoted to it. Such interest is caused by its great technological potential and the value of
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3.1 Introduction and Motivation The discovery of the Josephson effect stimulated the development of superconductor microelectronics with a huge number of both theoretical and experimental papers devoted to it. Such interest is caused by its great technological potential and the value of the Josephson effect in information processing, generation of ultra-high frequency oscillators, fast switching devices, mixers, detectors, amplifiers and so on (see, e.g., [3.1–3,3.7]). In its simplest form the Josephson junction is a sandwich system of two superconducting films separated by a thin (about 10−7 cm) layer of insulator (Fig. 3.1). The Josephson effect is a quantum tunneling effect where two superconductors sufficiently close to each overcome the insulator barrier and current goes through. When the superconductors are located sufficiently close to each other, their wave functions overlap in the insulator region. Therefore, the supercurrent appearing in the system depends on the phase difference ϕ of the wave functions at the two sides of the insulating layer. There is a significant difference between short (or small) and long Josephson junctions. The distinguishing measure of this classification is the socalled Josephson penetration depth, λJ , connected with the phase difference, ϕ ∼ exp (−xλJ ), where x is the spatial coordinate. If the geometric sizes of the junction is less than λJ , then the contact is called small (in practical terms a point), otherwise it is long. We shall study a long Josephson junction z Superconductor
x y
Insulator Superconductor
Fig. 3.1. Schematic of a long Josephson junction V. I. Nekorkin et al., Synergetic Phenomena in Active Lattices © Springer-Verlag Berlin Heidelberg 2002
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3. Self-Organization in a Long Josephson Junction
(or transmission line). Let us summarize the physical processes occurring in such a junction. Figure 3.1 shows circulating Josephson supercurrents (the so-called Josephson vortices) and the corresponding distribution of magnetic field oriented along the y-axis and localized within the insulating layer. The magnitude of this field is Φ0 ϕx , with Φ0 = /2l = 2.07 × 10−15 W b being the quantized magnetic flux. The electric field is oriented along the z-axis and its value is ϕt . If the phase difference ϕ is varying from 0 to 2π then a pulse or soliton (for ϕx ) appears in the contact (Fig. 3.1). It can move along the contact, transferring a magnetic flux quantum. Accordingly, the soliton in a long Josephson junction is often called a “fluxon”. Besides such one-soliton states, long Josephson junctions allow more complex multisoliton states or multihump solitons which are a form of soliton bound state. Such solitons may be characterized by topological charge n = (2π)−1 [ϕ(t, +∞)−ϕ(t, −∞)]. This quantity takes only integer values. In particular, an isolated soliton has n = +1, while a two-soliton state has n = +2 and so on. In this chapter we consider the self-organization occurring in dissipative long Josephson junctions (LJJ). In particular, we consider the dynamics of kinks and soli
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