Order parameters and current-phase relations in 3He-B Josephson junctions through a porous layer

Abstract

Recent discoveries of the π states in 3He-B Josephson junctions through an array of apertures and a single aperture have aroused much theoretical interest on the mechanism of π states. Both tunneling junction and single orifice junction models were successfully applied to explain the occurrence of π states and their relationship with the texture orientations of n̂ vectors in two 3He-B reservoirs. In this paper, we study a model 3He-B Josephson junction through a porous layer. The order parameters and current-phase relations are calculated self-consistently using the quasiclassical theory. In agreement with previous theories, the π state is also observed when the n̂'s are aligned antiparallel and normal to the porous layer. In this model, however, the π state exists only when the coupling between two 3He-B reservoirs is strong, and the usual 0 state is present when the coupling diminishes. Being contrary to the single aperture case, the π state in our model is robust only when the magnetic field is aligned either nearly normal to or within the porous layer.