Dirac supercurrent in an asymmetric graphene-based SG1/FB/SG2 junction

The Josephson current in an asymmetric graphene-based SG1/FB/SG2 junction where SG1,2 are graphene layers which have been induced into two superconducting states having order parameters Δ1 and Δ2 (Δ1 ≠ Δ2) on the left and right sides of a ferromagnetic barrier FB of thickness d, respectively is studied. The presence of the exchange energy Eex and the gate potential VG in the barrier FB are taken into account. For the case of k///0, we find that the Josephson current depends on the exchange energy but is independent of the gate voltage. We find that increasing Δ2 can induce the junction to become a π-junction. This does not occur in the case of similar junctions having conventional superconductors in them. The critical current at zero temperature for Δ2 → ∞ has the form IC(Δ2→∞)=2eΔ1/h=2IC(Δ2=Δ1). This behavior of the Josephson current in a graphene junction is quite different from that of the supercurrent in conventional asymmetric junctions. For those junctions, it is predicted that IC∝Δ1Δ2, leading to IC → ∞ as Δ2 → ∞. A transition from a 0-junction to a π-junction is observed as χex (χex∼2Eexd/hvF) is increased. In a 0-junction, the spin supercurrents arising from the spin dependent Andreev energy levels do not vanish. This leads to IS = I↑ + I↓ = 0 but with I↑ = -I↓ ≠ 0