Josephson vortices at tricrystal boundaries

Josephson vortices at tricrystal boundaries with and without a $\ensuremath{\pi}$ junction in zero applied field are considered. It is shown that if the three tricrystal arms are conventional junctions, a one-flux-quantum ${\ensuremath{\varphi}}_{0}$ vortex at or near the intersection has lower energy than one far from the intersection. If the largest Josephson length exceeds the sum of the other two, the tricrystal ceases to be a pinning site. If one of the tricrystal arms is a $\ensuremath{\pi}$ junction, a ${\ensuremath{\varphi}}_{0}/2$ vortex at the intersection is the ground state of the system, and an even number of ${\ensuremath{\varphi}}_{0}/2$ vortices is forbidden, whereas $3{\ensuremath{\varphi}}_{0}/2$ and $5{\ensuremath{\varphi}}_{0}/2$ correspond to possible but, in general, metastable states. For certain combinations of Josephson lengths, the $3{\ensuremath{\varphi}}_{0}/2$ state has lower energy than the combined energy of the ${\ensuremath{\varphi}}_{0}/2$ vortex at the tricrystal joint and a ${\ensuremath{\varphi}}_{0}$ vortex far from the joint. Conditions are discussed under which the $3{\ensuremath{\varphi}}_{0}/2$ vortex can be observed.

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