Abstract We study a graphene Josephson junction where the inner graphene layer is subjected to spin–orbit coupling by proximity effect. This could be achieved, for example, by growing the graphene layer on top of a transition-metal dichalcogenide, such as WS ₂ 2. Here, we focus on the ballistic, wide, and short junction limits and study the effects of the spin–orbit interaction on the supercurrent. In particular, we analyze the current-phase relation using an analytical approach based on the continuum model. We find combinations of types of spin–orbit coupling that significantly suppress the supercurrent by opening a gap in the graphene band structure. At the same time, other combinations enhance it, acting as an effective spin–valley resolved chemical potential. Moreover, we find that a strong Rashba spin–orbit coupling leads to a junction with a highly voltage tunable harmonic content.
Bonasera et al. (Mon,) studied this question.
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