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6
Stacked Josephson Junctions
. Pedersen
1 Introduction
The topic of fluxons in Josephson junctions appears often and in many con-
texts within superconductivity. The potential applications and the appear-
ance of high-Tc superconductivity are some of the reasons for this recently
increased interest. prehensive reviews of fluxons (solitons) in
long Josephson junctions [8], [2], [10], [9] exist, of which particularly the
most recent [9] gives an excellent overview of the state of the art for low-
Tc niobium-type long Josephson junctions. In recent years the properties
of long Josephson junctions stacked on top of each other has been studied
quite intensively. This is because such systems model existing low-Tc super-
conducting multilayers. In addition these models have revealed surprising
dynamical properties. The appearance of high-Tc ceramic superconductors
has also had quite an impact on the topic of fluxons in superconductors,
in particular stacked long Josephson junctions. Here the fluxons play a
very important role, for example, in the O type of material with a
layered structure and big anisotropy. Dynamic properties of fluxons are
also relevant for the material properties such as the bulk current density
and the behaviour near the transition temperature. Some of these high-Tc
phenomena we will try to include in our description below.
2 Short summary of fluxon properties
An excellent mathematical description of fluxons in long Josephson junc-
tions may be found, for example, in Ref. [9]. We will thus only summa-
rize the most important properties here, and rely on Ref. [8], [2], [10], [9]
for details. Fluxon propagation in a long quasi-one-dimensional Josephson
junction is assumed to be described by the perturbed sine-Gordon equation
[8], [2], [10], [9] for the quantum mechanical phase difference, φ(x, t),
−φxx + φtt + αφt + sin φ= γ. ()
Here, subscripts x and t denote differentiation with re