  We reveal a proximity effect between a topological band (Chern) insulator
described by a Haldane model and spin-polarized Dirac particles of a graphene
layer. Coupling weakly the two systems through a tunneling term in the bulk,
the topological Chern insulator induces a gap and an opposite Chern number on
the Dirac particles at half-filling resulting in a sign flip of the Berry
curvature at one Dirac point. We study different aspects of the bulk-edge
correspondence and present protocols to observe the evolution of the Berry
curvature as well as two counter-propagating (protected) edge modes with
different velocities. In the strong-coupling limit, the energy spectrum shows
flat bands. Therefore we build a perturbation theory and address further the
bulk-edge correspondence. We also show the occurrence of a topological
insulating phase with Chern number one when only the lowest band is filled. We
generalize the effect to Haldane bilayer systems with asymmetric Semenoff
masses. We propose an alternative definition of the topological invariant on
the Bloch sphere.
