Current phase relation in a planar graphene Josephson junction with spin–orbit coupling

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 $$_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>2</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> . 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.