Magnetically modulated Superconductor-Graphene-Superconductor (SGS) Josephson junctions and their tunability

Graphene-based Josephson junctions played an important role in various quantum devices from their inception. Magnetic tunnel junctions or vertical devices were also made out of graphene by exposing the graphene layer to localised pattern of strong magnetic field created by hard ferromagnetic material. By combining the essence of these different methods for constructing graphene based junctions, in this work we propose that the temperature-dependent Josephson current in such junctions can be tuned by exposing the graphene regions to a combination of highly localised non-uniform magnetic field, dubbed as magnetic barrier, and spatially modulated gate voltage. Within the framework of Dirac-Bogoliubov-de-Gennes (DBDG) theory, we show by explicit calculation that in such magnetically modulated Josephson Junctions, the band structure of graphene gets significantly altered, which results in the change of the Andreev reflections in such junctions. This leads to a significant modulation of the Josephson current. We numerically evaluated the Josephson current as a function of the strength of the magnetic barrier and the gate voltage and discussed the practical consequences of such controlling of Josephson currents.