Spin-orbit coupling assisted magnetoanisotropic Josephson effect in ferromagnetic graphene Josephson junctions

Abstract

The spin-flipping effect can be induced by the Rashba spin-orbit coupling (RSOC), leading to triplet equal-spin pairs in a superconducting hybrid structure. Herein, by combining the Dirac–Bogoliubov–de Gennes equation and the Furusaki-Tsukada formalism at a finite temperature, we theoretically investigate the Josephson effect in graphene-based superconductor-ferromagnet-R-superconductor junctions, where R refers to a region with the RSOC. It is demonstrated that as a result of the RSOC, one 0−π transition can be attained by tuning the orientation of the exchange field h⃗, which is determined by its magnitude h that could be periodically taken, and the periodical 0−π transitions are also caused by manipulating h during a considerable scope of the orientation. More interestingly, although varying the RSOC strength λ cannot give rise to the 0−π transition in itself, not only is it a necessary condition for the 0−π transition induced by modulating the orientation of h⃗ but also can produce the shift of the crossover point. Furthermore, two different kinds of anomalous Josephson current effect are exhibited by controlling the orientation of h⃗. Particularly, the out-of- and in-plane magnetoanisotropic Josephson currents always exist, varying monotonically with λ while nonmonotonically with h. The characteristics may provide more insights into the proximity-induced RSOC and pave the way to a new class of tunable superconducting spintronic devices based on large-scale graphene.

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