Abstract
The Josephson currents through real vector potential (RVP) and pseudo vector potential (PVP) barriers in graphene are investigated. In graphene, the pseudo vector potential may be caused by a local strain. The comparison of supercurrents induced by the two type-barriers is focused. As a result, we find that not only will the RVP induce a transition Josephson current from the 0 → π state but also causes the difference in the phases of the order parameters of the two superconducting graphene layers to shift from φ → φ. The critical current is PVP-independent around the neutrality point while it strongly depends on the RVP. The vector potential dependence of critical current is found to be perfectly linear for both PVP and RVP barriers.
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