On the basis of self-consistent Born approximation, we present a theory of weak localization of Dirac fermions under finite-range scatters in graphene. With an explicit solution to the ground state of singlet pseudospin Cooperons, we solve the Bethe-Salpeter matrix equation for all the singlet and triplet pseudospin Cooperons at long-wave length states by perturbation treatment. The solution to the Cooperon in the presence of the external weak magnetic field is also obtained. We calculate the quantum interference correction to the conductivity and present the comparison with experiments. It is shown that the present calculation for the magnetoconductivity is in good agreement with some of the experimental measurements.
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