Josephson π states in superfluid ³He B-phase/A-phase/B-phase junctions

The l̂ texture in the A phase of superfluid ³He B-phase/A-phase/B-phase hybrid junction was a key to form the π state with higher critical current observed in Berkeley. Here we investigate the effect of n̂ texture in the B phase on current-phase relations for the BAB junction with a fixed l̂ texture. We show that the n̂ texture greatly changes the current-phase relation just like l̂ texture does. The change is due to the n̂-texture-induced modification of the spin structure in the A phase of the BAB junction via the AB boundary condition. As a result, current-phase relations in BAB junctions are determined by the d̂ vector in the A phase depending on both n̂ and l̂ textures.