Ground states of one and two fractional vortices in long Josephson 0-κ junctions

Half-integer Josephson vortices in 0-π junctions, discussed theoretically and observed experimentally, spontaneously appear at the point where the Josephson phase is π discontinuous. The creation of arbitrary discontinuities of the Josephson phase has been demonstrated recently. Here we study fractional vortices formed at an arbitrary κ discontinuity and discuss their stability and possible ground states. The two stable states are not mirror symmetric. Furthermore, the possible ground states formed at two κ discontinuities separated by a distance a are investigated, and the energy and regions of stability of each ground state are calculated. We also show that the ground states may strongly depend on the distance a between the discontinuities. There is a crossover distance a_c such that for a<a_c and for a>a_c the ground states may be qualitatively different.