Theory of the π State in ³He Josephson Junctions

The flow of superfluid ³He-B through a 65×65 array of nanometer-size apertures has been measured recently by Backhaus et al. They find in the current-phase relation a new branch, the so-called π state. We study two limiting cases which show that the π state arises from the coupling of the phase degree of freedom to the spin-orbit rotation. The π 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 pinholes.