  Recently achieved chiral condensates open intriguing avenues for the study of
the chiral properties induced by current-density interactions. An attempt to
include these features in a spinor system is presented, which gives rise to a
nonlinear, effective spin-orbit coupling that emerges from the differential
orbital currents, along with constraints in the conserved quantities due to the
linear coupling between spin components. Chirality pervades the resulting
spectrum of stationary states and their dynamical stability, which are explored
in plane waves, dark and bright solitons, and Josephson vortices. Our
analytical and numerical results reveal the destabilizing role of polarization
and Josephson currents, and support the existence of stable nonlinear states
built of linear superpositions of plane waves.
