Vortex-antivortex crystals, fractal structures, and orbital glasses in arrays of Josephson junctions

We have found that for large varieties of one-dimensional arrangements of Josephson junctions, such as discrete Josephson transmission lines, stable vortex-anti-vortex structures may be spontaneously created. These highly complex stable, spatial configurations of Josephson vortices and anti-vortices also display fractal features in both the energy spectrum and the spatial ordering of the superconducting phase differences associated with different junctions. These vortex structures are related to an exponential number of local minima that are separated by very large barriers within the highly complex energy landscape. The novel Josephson vortex glass arises without any disorder, whilst the fractal energy spectrum involves weak interactions of Josephson vortices. The Josephson glass and its associated fractal properties may be experimentally detected by measuring the switching current distribution.

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