▎ 摘　　要

Recent experiments demonstrating proximity induced ferromagnetism in graphene motivate this study of commensurate graphene/EuO heterostructures. Due to the commensurability of graphene with the (111)-EuO layer, graphene's Dirac points are mapped to the Gamma point of the commensurate Brillouin zone. The Eu atoms not only induce proximity exchange on the graphene layer, but they also introduce intervalley interactions resulting in a nonlinear dispersion at Gamma. We develop a model Hamiltonian, consistent with the lattice symmetries, that includes proximity induced exchange splitting, spin-orbit coupling, and intervalley interactions with parameters fitted to ab initio calculations. The intervalley interaction opens up a trivial gap preventing the system from crossing into a nontrivial state. The model Hamiltonian is analyzed to determine the conditions under which the heterostructures can exhibit topologically nontrivial bands.