  In a heterostructure of graphene and the ferromagnetic insulator EuO, the Eu
atoms induce proximity exchange and inter-valley interactions in the graphene
layer. Constrained by the lattice symmetries, and guided by ab initio
calculations, a model Hamiltonian is constructed that describes the low-energy
bands. Band parameters such as proximity induced exchange splitting, spin orbit
coupling, and inter-valley interaction are determined. Calculations of the
Chern number identify the conditions under which the hetero-structures exhibit
topologically non-trivial bands that give rise to the quantum anomalous Hall
effect with a Hall conductivity of $\sigma_{xy} = 2 e^2/h$.
