Light-modulated Andreev effects in graphene-based superconducting junctions

We investigate the transport properties, including Andreev reflection, $0\text{\ensuremath{-}}\ensuremath{\pi}$ transition, and crossed Andreev reflection, of graphene-based superconducting junctions modulated by an off-resonant circularly polarized light and a staggered sublattice potential. Using the Dirac-Bogoliubov--de Gennes equation and the Blonder-Tinkham-Klapwijk formula associated with numerical calculations, we can make the following findings. In a graphene-based normal conductor/superconductor (NS) junction, the differential conductance from Andreev reflection can be used to distinguish band structures. However, in a graphene-based superconductor/normal conductor/superconductor (SNS) junction, the valley polarization is induced and brings in a $0\text{\ensuremath{-}}\ensuremath{\pi}$ transition. Moreover, in a graphene-based normal conductor/superconductor/normal conductor (NSN) junction, the opposite valley polarization in two normal regions can lead to the pure and even perfect crossed Andreev reflections. The appreciable differential conductance of the pure crossed Andreev reflection is found for the 20--50 nm junction length, far less than the previous result in the graphene-based NSN junction, and it is helpful for the integration of superconducting quantum circuits. Our findings provide experimental possibilities to characterize the band structures, to realize the valley polarization-induced $0\text{\ensuremath{-}}\ensuremath{\pi}$ transition, and to design the valley-based highly efficient Cooper pair splitter in the light-modulated graphene-based superconducting junctions.