Abstract
The Josephson effect in the superconductor/ferromagnet/superconductor (SFS) graphene Josephson junction is studied using the Dirac Bogoliubov-de Gennes (DBdG) formalism. It is shown that the SFS graphene junction drives 0—π transition with the increasing of p = h0L/vFħ, which captures the effects of both the exchange field and the length of the junction; the spin-down current is dominant. The 0 state is stable for p < pc (critical value pc ≈ 0.80) and the π state is stable for p > pc, where the free energy minima are at φg = 0 and φg = π, respectively. The coexistence of the 0 and π states appears in the vicinity of pc.
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