  Motivated by the recent experiments [Scientific reports 6, 23051 (2016),
Phys. Rev. Lett. 114, 096602 (2015)], we theoretically investigate Cooper pair
splitting current in a graphene based Cooper pair beam splitter geometry. By
considering the graphene based superconductor as an entangler device, instead
of normal (2D) BCS superconductor, we show that the Cooper pair splitting
current mediated by Crossed Andreev process is amplified compared to its normal
superconductor counterpart. This amplification is attributed to the strong
suppression of local normal Andreev reflection process (arising from the Cooper
pair splitting) from the graphene based superconductor to lead via the same
quantum dot, in comparison to the usual 2D superconductor. Due to the vanishing
density of states at the Dirac point of undoped graphene, a doped graphene
based superconductor is considered here and it is observed that Cooper pair
splitting current is very insensitive to the doping level in comparison to the
usual 2D superconductor. The transport process of non-local spin entangled
electrons also depends on the type of pairing i.e. whether the electron-hole
pairing is on-site, inter-sublattice or the combination of both. The
inter-sublattice pairing of graphene causes the maximum non-local Cooper pair
splitting current, whereas presence of both pairing reduces the Cooper pair
splitting current.
