Spin orbit interaction fingerprints of a ballistic graphene Josephson junction

In this study, we establish the universal characteristics of the contributions of the Rashba spin orbit interaction (RSOI) and the Dresselhaus spin orbit interaction (DSOI) to the supercurrent in a graphene Josephson junction. The most striking property of the skewness and the critical supercurrent, so far not unequivocally revealed, is the presence of a maximum value or a single singularity at the key point (the DSOI equates to half of the RSOI) in pristine case. This is in sharp contrast to that in conventional Josephson junction (the π junction) and its counterpart in heavily doped graphene case (monotonically decay). Using a general delta potential model, we determine the barrier effect on the quasilocalized Andreev level (π periodic) and the propagating Andreev mode (π/2 periodic). Moreover, we trace the pronounced critical supercurrent Fabry-Pérot oscillations patterns as a function of the doping level, and find that it shows a good qualitative agreement with the recent experiment of M. Ben Shalom et al. [Nat. Phys. 12, 318 (2016)]. Our results show that definitive signatures of specular Andreev reflection can be observed in the graphene material and suggest that the graphene Josephson junction can lead to a new possible application in quantum computing.

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