Theory of the pi state in 3He Josephson junctions

The flow of superfluid 3He-B through a 65 x 65 array of nanometer size apertures has been measured recently by Backhaus et al. They find in the current--phase relation a new branch, so-called pi state. We study two limiting cases which show that the pi state arises from coupling of the phase degree of freedom to the spin-orbit rotation. The pi state exists in a single large aperture, but is difficult to observe because of hysteresis. A better correspondence with experiments is obtained by assuming a thin wall, where the Josephson coupling between the two sides arises from a dense array of pin-holes.