  We investigate the Josephson effect in one triple-terminal junction with
embedded parallel-coupled double quantum dots. It is found that the
inter-superconductor supercurrent has opportunities to oscillate in $4\pi$
period, with the adjustment of the phase differences among the superconductors.
What is notable is that such a result is robust and independent of fermion
parities, intradot Coulomb strength, and the dot-superconductor coupling
manner. By introducing the concept of spinful many-particle Majorana modes, we
present the analytical definition of the Majorana operator via superposing
electron and hole operators. It can be believed that this work provide a simple
but feasible proposal for the realization of Majorana modes in a nonmagnetic
system.
