Josephson effect of massive pseudospin-1 fermions in the ferromagnetic dice lattice

We theoretically study the Josephson effect of massive pseudospin-1 fermions in a superconductor/ferromagnet/superconductor (S/F/S) junction based on the dice lattice, including Sz- and +U-type mass terms with the magnitude m. For the Sz-type fermions, it is found that, in the absence of ferromagnetic exchange field h, the supercurrent is effectively inhibited by m or the junction length L. In the presence of h, 0−π state transition can be realized by modulating h, m, or L. The m-induced state transition occurs more frequently for a larger h or L. Particularly, the inhibition of supercurrent caused by m still remains for a large m. In the doping case, corresponding to a nonzero EF, the m-induced state transition may disappear for a large h or L. With EF increased, the inhibition caused by m diminishes for a small h whereas intensifies for a large h. In addition, the supercurrent features for the +U-type fermions distinct from those for the Sz-type fermions are demonstrated.