Weak localization properties of graphene with intrinsic and Rashba spin-orbit couplings

We propose the notion of counting the number of activated spins to identify the weak localization properties of graphene under effects of inter-valley scattering, intrinsic and Rashba spin-orbit interactions (SOI). It is predicted that perpendicular electric field due to gate voltage of the substrate drives the system to anti-localization by enhancing the Rashba SOI.