Theory of the pi state in He-3 Josephson junctions

The flow of superfluid He-3-B through a 65 x 65 array of nanometer-size ape rtures has been measured recently by Backhaus et al. They find in the curre nt-phase relation a new branch, the so called pi state. We study two limiti ng cases which show that the pi state arises from the coupling of the phase degree of freedom to the spin-orbit rotation. The pi state exists in a sin gle large aperture, but is difficult to observe because of hysteresis. A be tter correspondence with experiments is obtained by assuming a thin wall, w here the Josephson coupling between the two sides arises from a dense array of pinholes.