Josephson effect of massive pseudospin-1 fermions in the ferromagnetic α-T3model.

We theoretically investigate the Josephson effect of massive pseudospin-1 fermions in the ferromagnetic α-T<sub>3</sub> model, which includes the Sz-and U-type fermions, via the modulation of parameter α. Our results first reveal that the non-ferromagnetic junction is invariably in the 0 state, with the supercurrent vanishing when the mass magnitude m or the junction length L is sufficiently large. In the ferromagnetic junction, the 0 -π state transition can be induced by varying the value of α, with this transition strongly influenced by m and the Fermi energy EF. Particularly, a large m is shown to cause the disappearance of both the 0 -π state transition and the supercurrent itself. Furthermore, we demonstrate the distinctive supercurrent properties that characterize the Sz- and U-type fermions. These results may provide valuable insights for developing quantum electronic devices based on the superconducting properties of α-T3materials with massive pseudospin-1 fermions.