  The orbital susceptibility for graphene is calculated exactly up to the first
order with respect to the overlap integrals between neighboring atomic
orbitals. The general and rigorous theory of orbital susceptibility developed
in the preceding paper is applied to a model for graphene as a typical two-band
model. It is found that there are contributions from interband, Fermi surface,
and occupied states in addition to the Landau--Peierls orbital susceptibility.
The relative phase between the atomic orbitals on the two sublattices related
to the chirality of Dirac cones plays an important role. It is shown that there
are some additional contributions to the orbital susceptibility that are not
included in the previous calculations using the Peierls phase in the
tight-binding model for graphene. The physical origin of this difference is
clarified in terms of the corrections to the Peierls phase.
