The Josephson effect in superfluid 3He was studied in the 1980's by Avenel and Varoquaux . More recently, the flow of superfluid 3He-B through a 65x65 array of nanometer size apertures has been measured by Backhaus et al at Berkeley [2,3]. They find in the current-phase relation a new branch, so-called π state (pi state). The π state has subsequently been observed also in a single narrow slit .
In order to explain the π state, we have made calculations in two limiting cases. The first case is one large aperture, where the 18-component order parameter is solved numerically in and around the aperture using the Ginzburg-Landau theory of 3He. We find that the calculations have to be made in three dimensions because the π state has broken symmetry (m'm2') even in a circularly symmetric orifice. The current-phase relationship (figure) shows the existence of the π state for sufficiently large apertures. The physical interpretation is that the π state corresponds to a phase slip by a half-quantum vortex. The figure correnspons to the case with equal spin-orbit rotation matrices on the two sides of the weak link, where the current-phase relation is strongly hysteretic. The hysteresis is not usually present when more general boundary conditions are used, and the π states should therefore be experimentally observable.
As the second case we have made calculations for an aperture that is small compared to the superfluid coherence length. The presence of the π state in such a "pinhole" was first demonstrated by Yip using a simplified model . We have done the pinhole calculation selfconsistently and find that the π state occurs in a single pinhole only at very low temperatures, approximately 0.2 Tc. The situation is different in an array of pinholes. There the π state can appear at higher temperatures because of anisotextural Josephson effect: the texture changes as a function of the phase difference. We find that this mechanism gives a good quantitative explanation for the π states and bistability observed in Berkeley [2,3]. For alternative theories trying to explain the π state see Refs. [5-8].
The next step is to understand the dynamics of 3He Josephson junctions.
Back to helium theory page30.8.2005, Erkki Thuneberg, Email