  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.
