Critical current of a long Josephson junction in the presence of a perturbing Abrikosov vortex

We investigate theoretically how the proximity of an Abrikosov vortex influences the physical properties of a long Josephson junction. We find that delta(Ic), the contribution to the critical current associated with the presence of the vortex, is generally positive (he critical current is increased) and is crucially dependent on the specific boundary conditions satisfied by the transport current. In the case in which the latter has a bulk component in the vicinity of the vortex, delta(Ic) is proportional to the coupling psi between the vortex and the junction. The situation is however more complex when the transport current is purely a surface phenomenon. In this case delta(Ic) strongly depends on the distance between the vortex and the edges of the junction, and is in general much smaller than that of the bulk current case unless a special commensurability condition is met. In particular we show that a contribution to delta(Ic) proportional to psi is obtained in this case only when an integer number of Josephson vortices can be accommodated between the location of the vortex and one of the edges of the junction. [S0163-1829(98)10137-6].