Josephson current in a double ferromagnetic layer SG/F1/F2/SG graphene sandwich

The Josephson current in a double ferromagnetic layer SG/F1/F2/SG graphene junction where the SG's are graphene-based s-wave superconductors and the F1,2 are ferromagnetic layers of thicknesses d1,2 in which the exchange energies are Eex1,2, is studied. The Josephson current in this junction is composed of Cooper pairs formed by quasi particles which are massless Weyl-Dirac electrons. By switching the alignment of the two exchange fields, we find that the Josephson current in the junction can change from being in the π-state to being in the 0-state. For the case where the magnitudes of the exchange field strength are the same, it is seen that the phase difference dependence of the critical Josephson current in a parallel aligned junction indicated a cross over from a 0-state to π-state whenever the ferromagnetic barrier strength χex is equal to (n/2 + 0.25)π (with n = 1, 2, …). The AP-junction for F1 = F2 behaves as if it has no the magnetic barriers, like S/N/S junction. It is also seen that the temperature dependence of the (%) magneto-Josephson current ratio defined as the difference between the critical currents of the graphene-based P-junction and AP-junctions defined as, %PS∼(100%)x(IPc-IAPc)/IPc, is found to be oscillated under varying the exchange energies. The maximum value of %PS, (max)PS → −∞ as T → TC. The cause of these effects is the relativistic nature of the quasi particles in the graphene-based junctions.